-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | A more progressive alternative to the "base" package
--   
--   This package is intended for those who are tired of keeping long lists
--   of dependencies to the same essential libraries in each package as
--   well as the endless imports of the same APIs all over again. It also
--   supports the modern tendencies in the language.
--   
--   To solve those problems this package does the following:
--   
--   <ul>
--   <li>Reexport the original APIs under the "Rebase" namespace.</li>
--   <li>Export all the possible non-conflicting symbols from the
--   "Rebase.Prelude" module.</li>
--   <li>Give priority to the modern practices in the conflicting
--   cases.</li>
--   </ul>
--   
--   The policy behind the package is only to reexport the non-ambiguous
--   and non-controversial APIs, which the community has obviously settled
--   on. The package is intended to rapidly evolve with the contribution
--   from the community, with the missing features being added with
--   pull-requests.
--   
--   If you don't need the "Rebase" namespace and want to import modules
--   from the reexported packages as they are check out the
--   "<a>rerebase</a>" package which simply reexports the original symbols
--   in the original namespace. Thus it simply lets you depend on all the
--   de-facto default packages, by yourself having to maintain only the
--   dependency on "rerebase". Also it comes packed with a prelude as rich
--   as here.
@package rebase
@version 1.17

module Rebase.Control.Applicative

module Rebase.Control.Applicative.Backwards

module Rebase.Control.Applicative.Lift

module Rebase.Control.Arrow

module Rebase.Control.Category

module Rebase.Control.Comonad

module Rebase.Control.Concurrent

module Rebase.Control.Concurrent.Chan

module Rebase.Control.Concurrent.MVar

module Rebase.Control.Concurrent.QSem

module Rebase.Control.Concurrent.QSemN

module Rebase.Control.Concurrent.STM

module Rebase.Control.Concurrent.STM.TArray

module Rebase.Control.Concurrent.STM.TBQueue

module Rebase.Control.Concurrent.STM.TChan

module Rebase.Control.Concurrent.STM.TMVar

module Rebase.Control.Concurrent.STM.TQueue

module Rebase.Control.Concurrent.STM.TSem

module Rebase.Control.Concurrent.STM.TVar

module Rebase.Control.DeepSeq

module Rebase.Control.Exception

module Rebase.Control.Exception.Base

module Rebase.Control.Monad

module Rebase.Control.Monad.Cont

module Rebase.Control.Monad.Cont.Class

module Rebase.Control.Monad.Error.Class

module Rebase.Control.Monad.Fail

module Rebase.Control.Monad.Fix

module Rebase.Control.Monad.IO.Class

module Rebase.Control.Monad.Identity

module Rebase.Control.Monad.RWS

module Rebase.Control.Monad.RWS.Class

module Rebase.Control.Monad.RWS.Lazy

module Rebase.Control.Monad.RWS.Strict

module Rebase.Control.Monad.Reader

module Rebase.Control.Monad.Reader.Class

module Rebase.Control.Monad.ST

module Rebase.Control.Monad.ST.Lazy

module Rebase.Control.Monad.ST.Lazy.Safe

module Rebase.Control.Monad.ST.Lazy.Unsafe

module Rebase.Control.Monad.ST.Safe

module Rebase.Control.Monad.ST.Strict

module Rebase.Control.Monad.ST.Unsafe

module Rebase.Control.Monad.STM

module Rebase.Control.Monad.Signatures

module Rebase.Control.Monad.State

module Rebase.Control.Monad.State.Class

module Rebase.Control.Monad.State.Lazy

module Rebase.Control.Monad.State.Strict

module Rebase.Control.Monad.Trans

module Rebase.Control.Monad.Trans.Class

module Rebase.Control.Monad.Trans.Cont

module Rebase.Control.Monad.Trans.Except

module Rebase.Control.Monad.Trans.Identity

module Rebase.Control.Monad.Trans.List

module Rebase.Control.Monad.Trans.Maybe

module Rebase.Control.Monad.Trans.RWS

module Rebase.Control.Monad.Trans.RWS.Lazy

module Rebase.Control.Monad.Trans.RWS.Strict

module Rebase.Control.Monad.Trans.Reader

module Rebase.Control.Monad.Trans.State

module Rebase.Control.Monad.Trans.State.Lazy

module Rebase.Control.Monad.Trans.State.Strict

module Rebase.Control.Monad.Trans.Writer

module Rebase.Control.Monad.Trans.Writer.Lazy

module Rebase.Control.Monad.Trans.Writer.Strict

module Rebase.Control.Monad.Writer

module Rebase.Control.Monad.Writer.Class

module Rebase.Control.Monad.Writer.Lazy

module Rebase.Control.Monad.Writer.Strict

module Rebase.Control.Monad.Zip

module Rebase.Control.Selective

module Rebase.Control.Selective.Free

module Rebase.Control.Selective.Multi

module Rebase.Control.Selective.Rigid.Free

module Rebase.Control.Selective.Rigid.Freer

module Rebase.Control.Selective.Trans.Except

module Rebase.Data.Biapplicative

module Rebase.Data.Bifoldable

module Rebase.Data.Bifunctor

-- | A more meaningful and conflict-free alias for <a>first</a>.
mapLeft :: Bifunctor p => (a -> b) -> p a c -> p b c

-- | A more meaningful and conflict-free alias for <a>second</a>.
mapRight :: Bifunctor p => (b -> c) -> p a b -> p a c

module Rebase.Data.Bifunctor.Apply

module Rebase.Data.Bifunctor.Biff

module Rebase.Data.Bifunctor.Clown

module Rebase.Data.Bifunctor.Flip

module Rebase.Data.Bifunctor.Join

module Rebase.Data.Bifunctor.Joker

module Rebase.Data.Bifunctor.Product

module Rebase.Data.Bifunctor.Tannen

module Rebase.Data.Bifunctor.Wrapped

module Rebase.Data.Bitraversable

module Rebase.Data.Bits

module Rebase.Data.Bool

module Rebase.Data.ByteString

module Rebase.Data.ByteString.Builder

module Rebase.Data.ByteString.Builder.Extra

module Rebase.Data.ByteString.Builder.Internal

module Rebase.Data.ByteString.Builder.Prim

module Rebase.Data.ByteString.Builder.Prim.Internal

module Rebase.Data.ByteString.Builder.Scientific

module Rebase.Data.ByteString.Char8

module Rebase.Data.ByteString.Internal

module Rebase.Data.ByteString.Lazy

module Rebase.Data.ByteString.Lazy.Char8

module Rebase.Data.ByteString.Lazy.Internal

module Rebase.Data.ByteString.Short

module Rebase.Data.ByteString.Short.Internal

module Rebase.Data.ByteString.Unsafe

module Rebase.Data.Char

module Rebase.Data.Coerce

module Rebase.Data.Complex

module Rebase.Data.DList

module Rebase.Data.Data

module Rebase.Data.Dynamic

module Rebase.Data.Either

module Rebase.Data.Either.Combinators

module Rebase.Data.Either.Validation

module Rebase.Data.Eq

module Rebase.Data.Fixed

module Rebase.Data.Foldable

module Rebase.Data.Function

module Rebase.Data.Functor

module Rebase.Data.Functor.Alt

module Rebase.Data.Functor.Apply

module Rebase.Data.Functor.Bind

module Rebase.Data.Functor.Bind.Class

module Rebase.Data.Functor.Bind.Trans

module Rebase.Data.Functor.Classes

module Rebase.Data.Functor.Compose

module Rebase.Data.Functor.Constant

module Rebase.Data.Functor.Contravariant

module Rebase.Data.Functor.Contravariant.Compose

module Rebase.Data.Functor.Contravariant.Divisible

module Rebase.Data.Functor.Extend

module Rebase.Data.Functor.Identity

module Rebase.Data.Functor.Invariant

module Rebase.Data.Functor.Invariant.TH

module Rebase.Data.Functor.Plus

module Rebase.Data.Functor.Product

module Rebase.Data.Functor.Reverse

module Rebase.Data.Functor.Sum

module Rebase.Data.Graph

module Rebase.Data.Group

module Rebase.Data.Groupoid

module Rebase.Data.HashMap.Lazy

module Rebase.Data.HashMap.Strict

module Rebase.Data.HashSet

module Rebase.Data.Hashable

module Rebase.Data.IORef

module Rebase.Data.Int

module Rebase.Data.IntMap

module Rebase.Data.IntMap.Lazy

module Rebase.Data.IntMap.Strict

module Rebase.Data.IntSet

module Rebase.Data.Isomorphism

module Rebase.Data.Ix

module Rebase.Data.Kind

module Rebase.Data.List

-- | If you're not a fan of magical or special cases, you probably have
--   already been looking for this alias.
type List = []

module Rebase.Data.List.NonEmpty


-- | This module simply provides a more meaningful name to
--   <a>Data.List.NonEmpty</a>.
module Rebase.Data.List1

-- | A more meaningful name for the non-empty list. Follows the convention
--   behind such names as <tt>foldr1</tt>.
type List1 = NonEmpty

module Rebase.Data.Map

module Rebase.Data.Map.Lazy

module Rebase.Data.Map.Strict

module Rebase.Data.Maybe

module Rebase.Data.Monoid

module Rebase.Data.Ord

module Rebase.Data.Profunctor

module Rebase.Data.Profunctor.Adjunction

module Rebase.Data.Profunctor.Cayley

module Rebase.Data.Profunctor.Choice

module Rebase.Data.Profunctor.Closed

module Rebase.Data.Profunctor.Composition

module Rebase.Data.Profunctor.Mapping

module Rebase.Data.Profunctor.Monad

module Rebase.Data.Profunctor.Ran

module Rebase.Data.Profunctor.Rep

module Rebase.Data.Profunctor.Sieve

module Rebase.Data.Profunctor.Strong

module Rebase.Data.Profunctor.Traversing

module Rebase.Data.Profunctor.Types

module Rebase.Data.Profunctor.Unsafe

module Rebase.Data.Profunctor.Yoneda

module Rebase.Data.Proxy

module Rebase.Data.Ratio

module Rebase.Data.STRef

module Rebase.Data.STRef.Lazy

module Rebase.Data.STRef.Strict

module Rebase.Data.Scientific

module Rebase.Data.Semigroup
sappend :: Semigroup a => a -> a -> a

module Rebase.Data.Semigroup.Bifoldable

module Rebase.Data.Semigroup.Bitraversable

module Rebase.Data.Semigroup.Foldable

module Rebase.Data.Semigroup.Foldable.Class

module Rebase.Data.Semigroup.Traversable

module Rebase.Data.Semigroup.Traversable.Class

module Rebase.Data.Semigroupoid

module Rebase.Data.Semigroupoid.Dual

module Rebase.Data.Semigroupoid.Ob

module Rebase.Data.Semigroupoid.Static

module Rebase.Data.Sequence

module Rebase.Data.Set

module Rebase.Data.String


-- | Unifies some modules, which are separated in the original API for
--   unknown reasons.
module Rebase.Data.Text

module Rebase.Data.Text.Array

module Rebase.Data.Text.Encoding

module Rebase.Data.Text.Encoding.Error

module Rebase.Data.Text.Foreign

module Rebase.Data.Text.IO

module Rebase.Data.Text.Internal


-- | Unifies some modules, which are separated in the original API for
--   unknown reasons.
module Rebase.Data.Text.Lazy

module Rebase.Data.Text.Lazy.Builder

module Rebase.Data.Text.Lazy.Builder.Int

module Rebase.Data.Text.Lazy.Builder.RealFloat

module Rebase.Data.Text.Lazy.Builder.Scientific

module Rebase.Data.Text.Lazy.Encoding

module Rebase.Data.Text.Lazy.IO

module Rebase.Data.Text.Lazy.Read

module Rebase.Data.Text.Read

module Rebase.Data.Text.Unsafe

module Rebase.Data.Time

module Rebase.Data.Time.Calendar

module Rebase.Data.Time.Calendar.Easter

module Rebase.Data.Time.Calendar.Julian

module Rebase.Data.Time.Calendar.MonthDay

module Rebase.Data.Time.Calendar.OrdinalDate

module Rebase.Data.Time.Calendar.WeekDate

module Rebase.Data.Time.Clock

module Rebase.Data.Time.Clock.POSIX

module Rebase.Data.Time.Clock.System

module Rebase.Data.Time.Clock.TAI

module Rebase.Data.Time.Compat

module Rebase.Data.Time.Format

module Rebase.Data.Time.Format.ISO8601

module Rebase.Data.Time.LocalTime

module Rebase.Data.Traversable

module Rebase.Data.Traversable.Instances

module Rebase.Data.Tree

module Rebase.Data.Tuple

module Rebase.Data.Type.Bool

module Rebase.Data.Type.Coercion

module Rebase.Data.Type.Equality

module Rebase.Data.Typeable

module Rebase.Data.UUID

module Rebase.Data.Unique

module Rebase.Data.Vector

module Rebase.Data.Vector.Fusion.Stream.Monadic

module Rebase.Data.Vector.Fusion.Util

module Rebase.Data.Vector.Generic

module Rebase.Data.Vector.Generic.Base

module Rebase.Data.Vector.Generic.Mutable

module Rebase.Data.Vector.Generic.New

module Rebase.Data.Vector.Instances

module Rebase.Data.Vector.Internal.Check

module Rebase.Data.Vector.Mutable

module Rebase.Data.Vector.Primitive

module Rebase.Data.Vector.Primitive.Mutable

module Rebase.Data.Vector.Storable

module Rebase.Data.Vector.Storable.Internal

module Rebase.Data.Vector.Storable.Mutable

module Rebase.Data.Vector.Unboxed

module Rebase.Data.Vector.Unboxed.Base

module Rebase.Data.Vector.Unboxed.Mutable

module Rebase.Data.Version

module Rebase.Data.Void

module Rebase.Data.Void.Unsafe

module Rebase.Data.Word

module Rebase.Debug.Trace

module Rebase.Foreign

module Rebase.Foreign.C

module Rebase.Foreign.C.Error

module Rebase.Foreign.C.String

module Rebase.Foreign.C.Types

module Rebase.Foreign.Concurrent

module Rebase.Foreign.ForeignPtr

module Rebase.Foreign.ForeignPtr.Safe

module Rebase.Foreign.ForeignPtr.Unsafe

module Rebase.Foreign.Marshal

module Rebase.Foreign.Marshal.Alloc

module Rebase.Foreign.Marshal.Array

module Rebase.Foreign.Marshal.Error

module Rebase.Foreign.Marshal.Pool

module Rebase.Foreign.Marshal.Safe

module Rebase.Foreign.Marshal.Unsafe

module Rebase.Foreign.Marshal.Utils

module Rebase.Foreign.Ptr

module Rebase.Foreign.Safe

module Rebase.Foreign.StablePtr

module Rebase.Foreign.Storable

module Rebase.GHC.Arr

module Rebase.GHC.Base

module Rebase.GHC.Char

module Rebase.GHC.Conc

module Rebase.GHC.Conc.IO

module Rebase.GHC.Conc.Signal

module Rebase.GHC.Conc.Sync

module Rebase.GHC.ConsoleHandler

module Rebase.GHC.Constants

module Rebase.GHC.Desugar

module Rebase.GHC.Enum

module Rebase.GHC.Environment

module Rebase.GHC.Err

module Rebase.GHC.Exception

module Rebase.GHC.Exts

module Rebase.GHC.Fingerprint

module Rebase.GHC.Fingerprint.Type

module Rebase.GHC.Float

module Rebase.GHC.Float.ConversionUtils

module Rebase.GHC.Float.RealFracMethods

module Rebase.GHC.Foreign

module Rebase.GHC.ForeignPtr

module Rebase.GHC.GHCi

module Rebase.GHC.Generics

module Rebase.GHC.IO

module Rebase.GHC.IO.Buffer

module Rebase.GHC.IO.BufferedIO

module Rebase.GHC.IO.Device

module Rebase.GHC.IO.Encoding

module Rebase.GHC.IO.Encoding.CodePage

module Rebase.GHC.IO.Encoding.Failure

module Rebase.GHC.IO.Encoding.Iconv

module Rebase.GHC.IO.Encoding.Latin1

module Rebase.GHC.IO.Encoding.Types

module Rebase.GHC.IO.Encoding.UTF16

module Rebase.GHC.IO.Encoding.UTF32

module Rebase.GHC.IO.Encoding.UTF8

module Rebase.GHC.IO.Exception

module Rebase.GHC.IO.FD

module Rebase.GHC.IO.Handle

module Rebase.GHC.IO.Handle.FD

module Rebase.GHC.IO.Handle.Internals

module Rebase.GHC.IO.Handle.Text

module Rebase.GHC.IO.Handle.Types

module Rebase.GHC.IO.IOMode

module Rebase.GHC.IOArray

module Rebase.GHC.IORef

module Rebase.GHC.Int

module Rebase.GHC.List

module Rebase.GHC.MVar

module Rebase.GHC.Num

module Rebase.GHC.OverloadedLabels

module Rebase.GHC.Pack

module Rebase.GHC.Profiling

module Rebase.GHC.Ptr

module Rebase.GHC.Read

module Rebase.GHC.Real

module Rebase.GHC.Records

module Rebase.GHC.ST

module Rebase.GHC.STRef

module Rebase.GHC.Show

module Rebase.GHC.Stable

module Rebase.GHC.Stack

module Rebase.GHC.Stats

module Rebase.GHC.Storable

module Rebase.GHC.TopHandler

module Rebase.GHC.TypeLits

module Rebase.GHC.TypeNats

module Rebase.GHC.Unicode

module Rebase.GHC.Weak

module Rebase.GHC.Word

module Rebase.Numeric

module Rebase.Numeric.Natural

module Rebase.System.CPUTime

module Rebase.System.Console.GetOpt

module Rebase.System.Environment

module Rebase.System.Exit

module Rebase.System.IO

module Rebase.System.IO.Error

module Rebase.System.IO.Unsafe

module Rebase.System.Info

module Rebase.System.Mem

module Rebase.System.Mem.StableName

module Rebase.System.Mem.Weak

module Rebase.System.Posix.Internals

module Rebase.System.Posix.Types

module Rebase.System.Timeout

module Rebase.Text.ParserCombinators.ReadP

module Rebase.Text.ParserCombinators.ReadPrec

module Rebase.Text.Printf

module Rebase.Text.Read

module Rebase.Text.Read.Lex

module Rebase.Text.Show

module Rebase.Text.Show.Functions

module Rebase.Unsafe.Coerce


-- | This module reexports the non-conflicting definitions from the modules
--   exported by this package, providing a much more featureful alternative
--   to the standard Prelude.
--   
--   For details check out the source.
module Rebase.Prelude

-- | Append two lists, i.e.,
--   
--   <pre>
--   [x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn]
--   [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]
--   </pre>
--   
--   If the first list is not finite, the result is the first list.
(++) :: [a] -> [a] -> [a]
infixr 5 ++

-- | The value of <tt>seq a b</tt> is bottom if <tt>a</tt> is bottom, and
--   otherwise equal to <tt>b</tt>. In other words, it evaluates the first
--   argument <tt>a</tt> to weak head normal form (WHNF). <tt>seq</tt> is
--   usually introduced to improve performance by avoiding unneeded
--   laziness.
--   
--   A note on evaluation order: the expression <tt>seq a b</tt> does
--   <i>not</i> guarantee that <tt>a</tt> will be evaluated before
--   <tt>b</tt>. The only guarantee given by <tt>seq</tt> is that the both
--   <tt>a</tt> and <tt>b</tt> will be evaluated before <tt>seq</tt>
--   returns a value. In particular, this means that <tt>b</tt> may be
--   evaluated before <tt>a</tt>. If you need to guarantee a specific order
--   of evaluation, you must use the function <tt>pseq</tt> from the
--   "parallel" package.
seq :: forall {r :: RuntimeRep} a (b :: TYPE r). a -> b -> b
infixr 0 `seq`

-- | &lt;math&gt;. <a>filter</a>, applied to a predicate and a list,
--   returns the list of those elements that satisfy the predicate; i.e.,
--   
--   <pre>
--   filter p xs = [ x | x &lt;- xs, p x]
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; filter odd [1, 2, 3]
--   [1,3]
--   </pre>
filter :: (a -> Bool) -> [a] -> [a]

-- | &lt;math&gt;. <a>zip</a> takes two lists and returns a list of
--   corresponding pairs.
--   
--   <pre>
--   &gt;&gt;&gt; zip [1, 2] ['a', 'b']
--   [(1,'a'),(2,'b')]
--   </pre>
--   
--   If one input list is shorter than the other, excess elements of the
--   longer list are discarded, even if one of the lists is infinite:
--   
--   <pre>
--   &gt;&gt;&gt; zip [1] ['a', 'b']
--   [(1,'a')]
--   
--   &gt;&gt;&gt; zip [1, 2] ['a']
--   [(1,'a')]
--   
--   &gt;&gt;&gt; zip [] [1..]
--   []
--   
--   &gt;&gt;&gt; zip [1..] []
--   []
--   </pre>
--   
--   <a>zip</a> is right-lazy:
--   
--   <pre>
--   &gt;&gt;&gt; zip [] undefined
--   []
--   
--   &gt;&gt;&gt; zip undefined []
--   *** Exception: Prelude.undefined
--   ...
--   </pre>
--   
--   <a>zip</a> is capable of list fusion, but it is restricted to its
--   first list argument and its resulting list.
zip :: [a] -> [b] -> [(a, b)]

-- | Create a stable pointer referring to the given Haskell value.
newStablePtr :: a -> IO (StablePtr a)

-- | The <a>print</a> function outputs a value of any printable type to the
--   standard output device. Printable types are those that are instances
--   of class <a>Show</a>; <a>print</a> converts values to strings for
--   output using the <a>show</a> operation and adds a newline.
--   
--   For example, a program to print the first 20 integers and their powers
--   of 2 could be written as:
--   
--   <pre>
--   main = print ([(n, 2^n) | n &lt;- [0..19]])
--   </pre>
print :: Show a => a -> IO ()

-- | Extract the first component of a pair.
fst :: (a, b) -> a

-- | Extract the second component of a pair.
snd :: (a, b) -> b

-- | <a>otherwise</a> is defined as the value <a>True</a>. It helps to make
--   guards more readable. eg.
--   
--   <pre>
--   f x | x &lt; 0     = ...
--       | otherwise = ...
--   </pre>
otherwise :: Bool

-- | If the first argument evaluates to <a>True</a>, then the result is the
--   second argument. Otherwise an <a>AssertionFailed</a> exception is
--   raised, containing a <a>String</a> with the source file and line
--   number of the call to <a>assert</a>.
--   
--   Assertions can normally be turned on or off with a compiler flag (for
--   GHC, assertions are normally on unless optimisation is turned on with
--   <tt>-O</tt> or the <tt>-fignore-asserts</tt> option is given). When
--   assertions are turned off, the first argument to <a>assert</a> is
--   ignored, and the second argument is returned as the result.
assert :: Bool -> a -> a

-- | The <a>lazy</a> function restrains strictness analysis a little. The
--   call <tt>lazy e</tt> means the same as <tt>e</tt>, but <a>lazy</a> has
--   a magical property so far as strictness analysis is concerned: it is
--   lazy in its first argument, even though its semantics is strict. After
--   strictness analysis has run, calls to <a>lazy</a> are inlined to be
--   the identity function.
--   
--   This behaviour is occasionally useful when controlling evaluation
--   order. Notably, <a>lazy</a> is used in the library definition of
--   <a>par</a>:
--   
--   <pre>
--   par :: a -&gt; b -&gt; b
--   par x y = case (par# x) of _ -&gt; lazy y
--   </pre>
--   
--   If <a>lazy</a> were not lazy, <a>par</a> would look strict in
--   <tt>y</tt> which would defeat the whole purpose of <a>par</a>.
lazy :: a -> a
assertError :: (?callStack :: CallStack) => Bool -> a -> a

-- | The <a>trace</a> function outputs the trace message given as its first
--   argument, before returning the second argument as its result.
--   
--   For example, this returns the value of <tt>f x</tt> and outputs the
--   message to stderr. Depending on your terminal (settings), they may or
--   may not be mixed.
--   
--   <pre>
--   &gt;&gt;&gt; let x = 123; f = show
--   
--   &gt;&gt;&gt; trace ("calling f with x = " ++ show x) (f x)
--   calling f with x = 123
--   "123"
--   </pre>
--   
--   The <a>trace</a> function should <i>only</i> be used for debugging, or
--   for monitoring execution. The function is not referentially
--   transparent: its type indicates that it is a pure function but it has
--   the side effect of outputting the trace message.
trace :: String -> a -> a

-- | The call <tt>inline f</tt> arranges that <tt>f</tt> is inlined,
--   regardless of its size. More precisely, the call <tt>inline f</tt>
--   rewrites to the right-hand side of <tt>f</tt>'s definition. This
--   allows the programmer to control inlining from a particular call site
--   rather than the definition site of the function (c.f. <tt>INLINE</tt>
--   pragmas).
--   
--   This inlining occurs regardless of the argument to the call or the
--   size of <tt>f</tt>'s definition; it is unconditional. The main caveat
--   is that <tt>f</tt>'s definition must be visible to the compiler; it is
--   therefore recommended to mark the function with an <tt>INLINABLE</tt>
--   pragma at its definition so that GHC guarantees to record its
--   unfolding regardless of size.
--   
--   If no inlining takes place, the <a>inline</a> function expands to the
--   identity function in Phase zero, so its use imposes no overhead.
inline :: a -> a

-- | &lt;math&gt;. <a>map</a> <tt>f xs</tt> is the list obtained by
--   applying <tt>f</tt> to each element of <tt>xs</tt>, i.e.,
--   
--   <pre>
--   map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
--   map f [x1, x2, ...] == [f x1, f x2, ...]
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; map (+1) [1, 2, 3]
--   [2,3,4]
--   </pre>
map :: (a -> b) -> [a] -> [b]

-- | The <a>groupWith</a> function uses the user supplied function which
--   projects an element out of every list element in order to first sort
--   the input list and then to form groups by equality on these projected
--   elements
groupWith :: Ord b => (a -> b) -> [a] -> [[a]]

-- | Application operator. This operator is redundant, since ordinary
--   application <tt>(f x)</tt> means the same as <tt>(f <a>$</a> x)</tt>.
--   However, <a>$</a> has low, right-associative binding precedence, so it
--   sometimes allows parentheses to be omitted; for example:
--   
--   <pre>
--   f $ g $ h x  =  f (g (h x))
--   </pre>
--   
--   It is also useful in higher-order situations, such as <tt><a>map</a>
--   (<a>$</a> 0) xs</tt>, or <tt><a>zipWith</a> (<a>$</a>) fs xs</tt>.
--   
--   Note that <tt>(<a>$</a>)</tt> is levity-polymorphic in its result
--   type, so that <tt>foo <a>$</a> True</tt> where <tt>foo :: Bool -&gt;
--   Int#</tt> is well-typed.
($) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
infixr 0 $

-- | The function <tt>coerce</tt> allows you to safely convert between
--   values of types that have the same representation with no run-time
--   overhead. In the simplest case you can use it instead of a newtype
--   constructor, to go from the newtype's concrete type to the abstract
--   type. But it also works in more complicated settings, e.g. converting
--   a list of newtypes to a list of concrete types.
--   
--   This function is runtime-representation polymorphic, but the
--   <tt>RuntimeRep</tt> type argument is marked as <tt>Inferred</tt>,
--   meaning that it is not available for visible type application. This
--   means the typechecker will accept <tt>coerce @Int @Age 42</tt>.
coerce :: forall {k :: RuntimeRep} (a :: TYPE k) (b :: TYPE k). Coercible a b => a -> b

-- | general coercion from integral types
fromIntegral :: (Integral a, Num b) => a -> b

-- | general coercion to fractional types
realToFrac :: (Real a, Fractional b) => a -> b

-- | Conditional failure of <a>Alternative</a> computations. Defined by
--   
--   <pre>
--   guard True  = <a>pure</a> ()
--   guard False = <a>empty</a>
--   </pre>
--   
--   <h4><b>Examples</b></h4>
--   
--   Common uses of <a>guard</a> include conditionally signaling an error
--   in an error monad and conditionally rejecting the current choice in an
--   <a>Alternative</a>-based parser.
--   
--   As an example of signaling an error in the error monad <a>Maybe</a>,
--   consider a safe division function <tt>safeDiv x y</tt> that returns
--   <a>Nothing</a> when the denominator <tt>y</tt> is zero and
--   <tt><a>Just</a> (x `div` y)</tt> otherwise. For example:
--   
--   <pre>
--   &gt;&gt;&gt; safeDiv 4 0
--   Nothing
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; safeDiv 4 2
--   Just 2
--   </pre>
--   
--   A definition of <tt>safeDiv</tt> using guards, but not <a>guard</a>:
--   
--   <pre>
--   safeDiv :: Int -&gt; Int -&gt; Maybe Int
--   safeDiv x y | y /= 0    = Just (x `div` y)
--               | otherwise = Nothing
--   </pre>
--   
--   A definition of <tt>safeDiv</tt> using <a>guard</a> and <a>Monad</a>
--   <tt>do</tt>-notation:
--   
--   <pre>
--   safeDiv :: Int -&gt; Int -&gt; Maybe Int
--   safeDiv x y = do
--     guard (y /= 0)
--     return (x `div` y)
--   </pre>
guard :: Alternative f => Bool -> f ()

-- | The <a>IsList</a> class and its methods are intended to be used in
--   conjunction with the OverloadedLists extension.
class IsList l where {
    
    -- | The <a>Item</a> type function returns the type of items of the
    --   structure <tt>l</tt>.
    type family Item l;
}

-- | The <a>fromList</a> function constructs the structure <tt>l</tt> from
--   the given list of <tt>Item l</tt>
fromList :: IsList l => [Item l] -> l

-- | The <a>fromListN</a> function takes the input list's length and
--   potentially uses it to construct the structure <tt>l</tt> more
--   efficiently compared to <a>fromList</a>. If the given number does not
--   equal to the input list's length the behaviour of <a>fromListN</a> is
--   not specified.
--   
--   <pre>
--   fromListN (length xs) xs == fromList xs
--   </pre>
fromListN :: IsList l => Int -> [Item l] -> l

-- | The <a>toList</a> function extracts a list of <tt>Item l</tt> from the
--   structure <tt>l</tt>. It should satisfy fromList . toList = id.
toList :: IsList l => l -> [Item l]

-- | Converts an arbitrary value into an object of type <a>Dynamic</a>.
--   
--   The type of the object must be an instance of <a>Typeable</a>, which
--   ensures that only monomorphically-typed objects may be converted to
--   <a>Dynamic</a>. To convert a polymorphic object into <a>Dynamic</a>,
--   give it a monomorphic type signature. For example:
--   
--   <pre>
--   toDyn (id :: Int -&gt; Int)
--   </pre>
toDyn :: Typeable a => a -> Dynamic
unsafeEqualityProof :: forall {k} (a :: k) (b :: k). UnsafeEquality a b

-- | Highly, terribly dangerous coercion from one representation type to
--   another. Misuse of this function can invite the garbage collector to
--   trounce upon your data and then laugh in your face. You don't want
--   this function. Really.
unsafeCoerce# :: forall (q :: RuntimeRep) (r :: RuntimeRep) (a :: TYPE q) (b :: TYPE r). a -> b

-- | The <a>join</a> function is the conventional monad join operator. It
--   is used to remove one level of monadic structure, projecting its bound
--   argument into the outer level.
--   
--   '<tt><a>join</a> bss</tt>' can be understood as the <tt>do</tt>
--   expression
--   
--   <pre>
--   do bs &lt;- bss
--      bs
--   </pre>
--   
--   <h4><b>Examples</b></h4>
--   
--   A common use of <a>join</a> is to run an <a>IO</a> computation
--   returned from an <a>STM</a> transaction, since <a>STM</a> transactions
--   can't perform <a>IO</a> directly. Recall that
--   
--   <pre>
--   <a>atomically</a> :: STM a -&gt; IO a
--   </pre>
--   
--   is used to run <a>STM</a> transactions atomically. So, by specializing
--   the types of <a>atomically</a> and <a>join</a> to
--   
--   <pre>
--   <a>atomically</a> :: STM (IO b) -&gt; IO (IO b)
--   <a>join</a>       :: IO (IO b)  -&gt; IO b
--   </pre>
--   
--   we can compose them as
--   
--   <pre>
--   <a>join</a> . <a>atomically</a> :: STM (IO b) -&gt; IO b
--   </pre>
--   
--   to run an <a>STM</a> transaction and the <a>IO</a> action it returns.
join :: Monad m => m (m a) -> m a

-- | The <a>Bounded</a> class is used to name the upper and lower limits of
--   a type. <a>Ord</a> is not a superclass of <a>Bounded</a> since types
--   that are not totally ordered may also have upper and lower bounds.
--   
--   The <a>Bounded</a> class may be derived for any enumeration type;
--   <a>minBound</a> is the first constructor listed in the <tt>data</tt>
--   declaration and <a>maxBound</a> is the last. <a>Bounded</a> may also
--   be derived for single-constructor datatypes whose constituent types
--   are in <a>Bounded</a>.
class Bounded a
minBound :: Bounded a => a
maxBound :: Bounded a => a

-- | Class <a>Enum</a> defines operations on sequentially ordered types.
--   
--   The <tt>enumFrom</tt>... methods are used in Haskell's translation of
--   arithmetic sequences.
--   
--   Instances of <a>Enum</a> may be derived for any enumeration type
--   (types whose constructors have no fields). The nullary constructors
--   are assumed to be numbered left-to-right by <a>fromEnum</a> from
--   <tt>0</tt> through <tt>n-1</tt>. See Chapter 10 of the <i>Haskell
--   Report</i> for more details.
--   
--   For any type that is an instance of class <a>Bounded</a> as well as
--   <a>Enum</a>, the following should hold:
--   
--   <ul>
--   <li>The calls <tt><a>succ</a> <a>maxBound</a></tt> and <tt><a>pred</a>
--   <a>minBound</a></tt> should result in a runtime error.</li>
--   <li><a>fromEnum</a> and <a>toEnum</a> should give a runtime error if
--   the result value is not representable in the result type. For example,
--   <tt><a>toEnum</a> 7 :: <a>Bool</a></tt> is an error.</li>
--   <li><a>enumFrom</a> and <a>enumFromThen</a> should be defined with an
--   implicit bound, thus:</li>
--   </ul>
--   
--   <pre>
--   enumFrom     x   = enumFromTo     x maxBound
--   enumFromThen x y = enumFromThenTo x y bound
--     where
--       bound | fromEnum y &gt;= fromEnum x = maxBound
--             | otherwise                = minBound
--   </pre>
class Enum a

-- | the successor of a value. For numeric types, <a>succ</a> adds 1.
succ :: Enum a => a -> a

-- | the predecessor of a value. For numeric types, <a>pred</a> subtracts
--   1.
pred :: Enum a => a -> a

-- | Convert from an <a>Int</a>.
toEnum :: Enum a => Int -> a

-- | Convert to an <a>Int</a>. It is implementation-dependent what
--   <a>fromEnum</a> returns when applied to a value that is too large to
--   fit in an <a>Int</a>.
fromEnum :: Enum a => a -> Int

-- | Used in Haskell's translation of <tt>[n..]</tt> with <tt>[n..] =
--   enumFrom n</tt>, a possible implementation being <tt>enumFrom n = n :
--   enumFrom (succ n)</tt>. For example:
--   
--   <ul>
--   <li><pre>enumFrom 4 :: [Integer] = [4,5,6,7,...]</pre></li>
--   <li><pre>enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound ::
--   Int]</pre></li>
--   </ul>
enumFrom :: Enum a => a -> [a]

-- | Used in Haskell's translation of <tt>[n,n'..]</tt> with <tt>[n,n'..] =
--   enumFromThen n n'</tt>, a possible implementation being
--   <tt>enumFromThen n n' = n : n' : worker (f x) (f x n')</tt>,
--   <tt>worker s v = v : worker s (s v)</tt>, <tt>x = fromEnum n' -
--   fromEnum n</tt> and <tt>f n y | n &gt; 0 = f (n - 1) (succ y) | n &lt;
--   0 = f (n + 1) (pred y) | otherwise = y</tt> For example:
--   
--   <ul>
--   <li><pre>enumFromThen 4 6 :: [Integer] = [4,6,8,10...]</pre></li>
--   <li><pre>enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound ::
--   Int]</pre></li>
--   </ul>
enumFromThen :: Enum a => a -> a -> [a]

-- | Used in Haskell's translation of <tt>[n..m]</tt> with <tt>[n..m] =
--   enumFromTo n m</tt>, a possible implementation being <tt>enumFromTo n
--   m | n &lt;= m = n : enumFromTo (succ n) m | otherwise = []</tt>. For
--   example:
--   
--   <ul>
--   <li><pre>enumFromTo 6 10 :: [Int] = [6,7,8,9,10]</pre></li>
--   <li><pre>enumFromTo 42 1 :: [Integer] = []</pre></li>
--   </ul>
enumFromTo :: Enum a => a -> a -> [a]

-- | Used in Haskell's translation of <tt>[n,n'..m]</tt> with <tt>[n,n'..m]
--   = enumFromThenTo n n' m</tt>, a possible implementation being
--   <tt>enumFromThenTo n n' m = worker (f x) (c x) n m</tt>, <tt>x =
--   fromEnum n' - fromEnum n</tt>, <tt>c x = bool (&gt;=) (<a>(x</a>
--   0)</tt> <tt>f n y | n &gt; 0 = f (n - 1) (succ y) | n &lt; 0 = f (n +
--   1) (pred y) | otherwise = y</tt> and <tt>worker s c v m | c v m = v :
--   worker s c (s v) m | otherwise = []</tt> For example:
--   
--   <ul>
--   <li><pre>enumFromThenTo 4 2 -6 :: [Integer] =
--   [4,2,0,-2,-4,-6]</pre></li>
--   <li><pre>enumFromThenTo 6 8 2 :: [Int] = []</pre></li>
--   </ul>
enumFromThenTo :: Enum a => a -> a -> a -> [a]

-- | The <a>Eq</a> class defines equality (<a>==</a>) and inequality
--   (<a>/=</a>). All the basic datatypes exported by the <a>Prelude</a>
--   are instances of <a>Eq</a>, and <a>Eq</a> may be derived for any
--   datatype whose constituents are also instances of <a>Eq</a>.
--   
--   The Haskell Report defines no laws for <a>Eq</a>. However, instances
--   are encouraged to follow these properties:
--   
--   <ul>
--   <li><i><b>Reflexivity</b></i> <tt>x == x</tt> = <a>True</a></li>
--   <li><i><b>Symmetry</b></i> <tt>x == y</tt> = <tt>y == x</tt></li>
--   <li><i><b>Transitivity</b></i> if <tt>x == y &amp;&amp; y == z</tt> =
--   <a>True</a>, then <tt>x == z</tt> = <a>True</a></li>
--   <li><i><b>Extensionality</b></i> if <tt>x == y</tt> = <a>True</a> and
--   <tt>f</tt> is a function whose return type is an instance of
--   <a>Eq</a>, then <tt>f x == f y</tt> = <a>True</a></li>
--   <li><i><b>Negation</b></i> <tt>x /= y</tt> = <tt>not (x ==
--   y)</tt></li>
--   </ul>
--   
--   Minimal complete definition: either <a>==</a> or <a>/=</a>.
class Eq a
(==) :: Eq a => a -> a -> Bool
(/=) :: Eq a => a -> a -> Bool
infix 4 ==
infix 4 /=

-- | Trigonometric and hyperbolic functions and related functions.
--   
--   The Haskell Report defines no laws for <a>Floating</a>. However,
--   <tt>(<a>+</a>)</tt>, <tt>(<a>*</a>)</tt> and <a>exp</a> are
--   customarily expected to define an exponential field and have the
--   following properties:
--   
--   <ul>
--   <li><tt>exp (a + b)</tt> = <tt>exp a * exp b</tt></li>
--   <li><tt>exp (fromInteger 0)</tt> = <tt>fromInteger 1</tt></li>
--   </ul>
class Fractional a => Floating a
pi :: Floating a => a
exp :: Floating a => a -> a
log :: Floating a => a -> a
sqrt :: Floating a => a -> a
(**) :: Floating a => a -> a -> a
logBase :: Floating a => a -> a -> a
sin :: Floating a => a -> a
cos :: Floating a => a -> a
tan :: Floating a => a -> a
asin :: Floating a => a -> a
acos :: Floating a => a -> a
atan :: Floating a => a -> a
sinh :: Floating a => a -> a
cosh :: Floating a => a -> a
tanh :: Floating a => a -> a
asinh :: Floating a => a -> a
acosh :: Floating a => a -> a
atanh :: Floating a => a -> a

-- | <tt><a>log1p</a> x</tt> computes <tt><a>log</a> (1 + x)</tt>, but
--   provides more precise results for small (absolute) values of
--   <tt>x</tt> if possible.
log1p :: Floating a => a -> a

-- | <tt><a>expm1</a> x</tt> computes <tt><a>exp</a> x - 1</tt>, but
--   provides more precise results for small (absolute) values of
--   <tt>x</tt> if possible.
expm1 :: Floating a => a -> a

-- | <tt><a>log1pexp</a> x</tt> computes <tt><a>log</a> (1 + <a>exp</a>
--   x)</tt>, but provides more precise results if possible.
--   
--   Examples:
--   
--   <ul>
--   <li>if <tt>x</tt> is a large negative number, <tt><a>log</a> (1 +
--   <a>exp</a> x)</tt> will be imprecise for the reasons given in
--   <a>log1p</a>.</li>
--   <li>if <tt><a>exp</a> x</tt> is close to <tt>-1</tt>, <tt><a>log</a>
--   (1 + <a>exp</a> x)</tt> will be imprecise for the reasons given in
--   <a>expm1</a>.</li>
--   </ul>
log1pexp :: Floating a => a -> a

-- | <tt><a>log1mexp</a> x</tt> computes <tt><a>log</a> (1 - <a>exp</a>
--   x)</tt>, but provides more precise results if possible.
--   
--   Examples:
--   
--   <ul>
--   <li>if <tt>x</tt> is a large negative number, <tt><a>log</a> (1 -
--   <a>exp</a> x)</tt> will be imprecise for the reasons given in
--   <a>log1p</a>.</li>
--   <li>if <tt><a>exp</a> x</tt> is close to <tt>1</tt>, <tt><a>log</a> (1
--   - <a>exp</a> x)</tt> will be imprecise for the reasons given in
--   <a>expm1</a>.</li>
--   </ul>
log1mexp :: Floating a => a -> a
infixr 8 **

-- | Fractional numbers, supporting real division.
--   
--   The Haskell Report defines no laws for <a>Fractional</a>. However,
--   <tt>(<a>+</a>)</tt> and <tt>(<a>*</a>)</tt> are customarily expected
--   to define a division ring and have the following properties:
--   
--   <ul>
--   <li><i><b><a>recip</a> gives the multiplicative inverse</b></i> <tt>x
--   * recip x</tt> = <tt>recip x * x</tt> = <tt>fromInteger 1</tt></li>
--   </ul>
--   
--   Note that it <i>isn't</i> customarily expected that a type instance of
--   <a>Fractional</a> implement a field. However, all instances in
--   <tt>base</tt> do.
class Num a => Fractional a

-- | Fractional division.
(/) :: Fractional a => a -> a -> a

-- | Reciprocal fraction.
recip :: Fractional a => a -> a

-- | Conversion from a <a>Rational</a> (that is <tt><a>Ratio</a>
--   <a>Integer</a></tt>). A floating literal stands for an application of
--   <a>fromRational</a> to a value of type <a>Rational</a>, so such
--   literals have type <tt>(<a>Fractional</a> a) =&gt; a</tt>.
fromRational :: Fractional a => Rational -> a
infixl 7 /

-- | Integral numbers, supporting integer division.
--   
--   The Haskell Report defines no laws for <a>Integral</a>. However,
--   <a>Integral</a> instances are customarily expected to define a
--   Euclidean domain and have the following properties for the
--   <a>div</a>/<a>mod</a> and <a>quot</a>/<a>rem</a> pairs, given suitable
--   Euclidean functions <tt>f</tt> and <tt>g</tt>:
--   
--   <ul>
--   <li><tt>x</tt> = <tt>y * quot x y + rem x y</tt> with <tt>rem x y</tt>
--   = <tt>fromInteger 0</tt> or <tt>g (rem x y)</tt> &lt; <tt>g
--   y</tt></li>
--   <li><tt>x</tt> = <tt>y * div x y + mod x y</tt> with <tt>mod x y</tt>
--   = <tt>fromInteger 0</tt> or <tt>f (mod x y)</tt> &lt; <tt>f
--   y</tt></li>
--   </ul>
--   
--   An example of a suitable Euclidean function, for <a>Integer</a>'s
--   instance, is <a>abs</a>.
class (Real a, Enum a) => Integral a

-- | integer division truncated toward zero
quot :: Integral a => a -> a -> a

-- | integer remainder, satisfying
--   
--   <pre>
--   (x `quot` y)*y + (x `rem` y) == x
--   </pre>
rem :: Integral a => a -> a -> a

-- | integer division truncated toward negative infinity
div :: Integral a => a -> a -> a

-- | integer modulus, satisfying
--   
--   <pre>
--   (x `div` y)*y + (x `mod` y) == x
--   </pre>
mod :: Integral a => a -> a -> a

-- | simultaneous <a>quot</a> and <a>rem</a>
quotRem :: Integral a => a -> a -> (a, a)

-- | simultaneous <a>div</a> and <a>mod</a>
divMod :: Integral a => a -> a -> (a, a)

-- | conversion to <a>Integer</a>
toInteger :: Integral a => a -> Integer
infixl 7 `rem`
infixl 7 `quot`
infixl 7 `mod`
infixl 7 `div`

-- | The <a>Monad</a> class defines the basic operations over a
--   <i>monad</i>, a concept from a branch of mathematics known as
--   <i>category theory</i>. From the perspective of a Haskell programmer,
--   however, it is best to think of a monad as an <i>abstract datatype</i>
--   of actions. Haskell's <tt>do</tt> expressions provide a convenient
--   syntax for writing monadic expressions.
--   
--   Instances of <a>Monad</a> should satisfy the following:
--   
--   <ul>
--   <li><i>Left identity</i> <tt><a>return</a> a <a>&gt;&gt;=</a> k = k
--   a</tt></li>
--   <li><i>Right identity</i> <tt>m <a>&gt;&gt;=</a> <a>return</a> =
--   m</tt></li>
--   <li><i>Associativity</i> <tt>m <a>&gt;&gt;=</a> (\x -&gt; k x
--   <a>&gt;&gt;=</a> h) = (m <a>&gt;&gt;=</a> k) <a>&gt;&gt;=</a>
--   h</tt></li>
--   </ul>
--   
--   Furthermore, the <a>Monad</a> and <a>Applicative</a> operations should
--   relate as follows:
--   
--   <ul>
--   <li><pre><a>pure</a> = <a>return</a></pre></li>
--   <li><pre>m1 <a>&lt;*&gt;</a> m2 = m1 <a>&gt;&gt;=</a> (x1 -&gt; m2
--   <a>&gt;&gt;=</a> (x2 -&gt; <a>return</a> (x1 x2)))</pre></li>
--   </ul>
--   
--   The above laws imply:
--   
--   <ul>
--   <li><pre><a>fmap</a> f xs = xs <a>&gt;&gt;=</a> <a>return</a> .
--   f</pre></li>
--   <li><pre>(<a>&gt;&gt;</a>) = (<a>*&gt;</a>)</pre></li>
--   </ul>
--   
--   and that <a>pure</a> and (<a>&lt;*&gt;</a>) satisfy the applicative
--   functor laws.
--   
--   The instances of <a>Monad</a> for lists, <a>Maybe</a> and <a>IO</a>
--   defined in the <a>Prelude</a> satisfy these laws.
class Applicative m => Monad (m :: Type -> Type)

-- | Sequentially compose two actions, passing any value produced by the
--   first as an argument to the second.
--   
--   '<tt>as <a>&gt;&gt;=</a> bs</tt>' can be understood as the <tt>do</tt>
--   expression
--   
--   <pre>
--   do a &lt;- as
--      bs a
--   </pre>
(>>=) :: Monad m => m a -> (a -> m b) -> m b

-- | Sequentially compose two actions, discarding any value produced by the
--   first, like sequencing operators (such as the semicolon) in imperative
--   languages.
--   
--   '<tt>as <a>&gt;&gt;</a> bs</tt>' can be understood as the <tt>do</tt>
--   expression
--   
--   <pre>
--   do as
--      bs
--   </pre>
(>>) :: Monad m => m a -> m b -> m b

-- | Inject a value into the monadic type.
return :: Monad m => a -> m a
infixl 1 >>=
infixl 1 >>

-- | The <a>Data</a> class comprehends a fundamental primitive
--   <a>gfoldl</a> for folding over constructor applications, say terms.
--   This primitive can be instantiated in several ways to map over the
--   immediate subterms of a term; see the <tt>gmap</tt> combinators later
--   in this class. Indeed, a generic programmer does not necessarily need
--   to use the ingenious gfoldl primitive but rather the intuitive
--   <tt>gmap</tt> combinators. The <a>gfoldl</a> primitive is completed by
--   means to query top-level constructors, to turn constructor
--   representations into proper terms, and to list all possible datatype
--   constructors. This completion allows us to serve generic programming
--   scenarios like read, show, equality, term generation.
--   
--   The combinators <a>gmapT</a>, <a>gmapQ</a>, <a>gmapM</a>, etc are all
--   provided with default definitions in terms of <a>gfoldl</a>, leaving
--   open the opportunity to provide datatype-specific definitions. (The
--   inclusion of the <tt>gmap</tt> combinators as members of class
--   <a>Data</a> allows the programmer or the compiler to derive
--   specialised, and maybe more efficient code per datatype. <i>Note</i>:
--   <a>gfoldl</a> is more higher-order than the <tt>gmap</tt> combinators.
--   This is subject to ongoing benchmarking experiments. It might turn out
--   that the <tt>gmap</tt> combinators will be moved out of the class
--   <a>Data</a>.)
--   
--   Conceptually, the definition of the <tt>gmap</tt> combinators in terms
--   of the primitive <a>gfoldl</a> requires the identification of the
--   <a>gfoldl</a> function arguments. Technically, we also need to
--   identify the type constructor <tt>c</tt> for the construction of the
--   result type from the folded term type.
--   
--   In the definition of <tt>gmapQ</tt><i>x</i> combinators, we use
--   phantom type constructors for the <tt>c</tt> in the type of
--   <a>gfoldl</a> because the result type of a query does not involve the
--   (polymorphic) type of the term argument. In the definition of
--   <a>gmapQl</a> we simply use the plain constant type constructor
--   because <a>gfoldl</a> is left-associative anyway and so it is readily
--   suited to fold a left-associative binary operation over the immediate
--   subterms. In the definition of gmapQr, extra effort is needed. We use
--   a higher-order accumulation trick to mediate between left-associative
--   constructor application vs. right-associative binary operation (e.g.,
--   <tt>(:)</tt>). When the query is meant to compute a value of type
--   <tt>r</tt>, then the result type within generic folding is <tt>r -&gt;
--   r</tt>. So the result of folding is a function to which we finally
--   pass the right unit.
--   
--   With the <tt>-XDeriveDataTypeable</tt> option, GHC can generate
--   instances of the <a>Data</a> class automatically. For example, given
--   the declaration
--   
--   <pre>
--   data T a b = C1 a b | C2 deriving (Typeable, Data)
--   </pre>
--   
--   GHC will generate an instance that is equivalent to
--   
--   <pre>
--   instance (Data a, Data b) =&gt; Data (T a b) where
--       gfoldl k z (C1 a b) = z C1 `k` a `k` b
--       gfoldl k z C2       = z C2
--   
--       gunfold k z c = case constrIndex c of
--                           1 -&gt; k (k (z C1))
--                           2 -&gt; z C2
--   
--       toConstr (C1 _ _) = con_C1
--       toConstr C2       = con_C2
--   
--       dataTypeOf _ = ty_T
--   
--   con_C1 = mkConstr ty_T "C1" [] Prefix
--   con_C2 = mkConstr ty_T "C2" [] Prefix
--   ty_T   = mkDataType "Module.T" [con_C1, con_C2]
--   </pre>
--   
--   This is suitable for datatypes that are exported transparently.
class Typeable a => Data a

-- | Left-associative fold operation for constructor applications.
--   
--   The type of <a>gfoldl</a> is a headache, but operationally it is a
--   simple generalisation of a list fold.
--   
--   The default definition for <a>gfoldl</a> is <tt><a>const</a>
--   <a>id</a></tt>, which is suitable for abstract datatypes with no
--   substructures.
gfoldl :: Data a => (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. () => g -> c g) -> a -> c a

-- | Unfolding constructor applications
gunfold :: Data a => (forall b r. Data b => c (b -> r) -> c r) -> (forall r. () => r -> c r) -> Constr -> c a

-- | Obtaining the constructor from a given datum. For proper terms, this
--   is meant to be the top-level constructor. Primitive datatypes are here
--   viewed as potentially infinite sets of values (i.e., constructors).
toConstr :: Data a => a -> Constr

-- | The outer type constructor of the type
dataTypeOf :: Data a => a -> DataType

-- | Mediate types and unary type constructors.
--   
--   In <a>Data</a> instances of the form
--   
--   <pre>
--   instance (Data a, ...) =&gt; Data (T a)
--   </pre>
--   
--   <a>dataCast1</a> should be defined as <a>gcast1</a>.
--   
--   The default definition is <tt><a>const</a> <a>Nothing</a></tt>, which
--   is appropriate for instances of other forms.
dataCast1 :: (Data a, Typeable t) => (forall d. Data d => c (t d)) -> Maybe (c a)

-- | Mediate types and binary type constructors.
--   
--   In <a>Data</a> instances of the form
--   
--   <pre>
--   instance (Data a, Data b, ...) =&gt; Data (T a b)
--   </pre>
--   
--   <a>dataCast2</a> should be defined as <a>gcast2</a>.
--   
--   The default definition is <tt><a>const</a> <a>Nothing</a></tt>, which
--   is appropriate for instances of other forms.
dataCast2 :: (Data a, Typeable t) => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a)

-- | A generic transformation that maps over the immediate subterms
--   
--   The default definition instantiates the type constructor <tt>c</tt> in
--   the type of <a>gfoldl</a> to an identity datatype constructor, using
--   the isomorphism pair as injection and projection.
gmapT :: Data a => (forall b. Data b => b -> b) -> a -> a

-- | A generic query with a left-associative binary operator
gmapQl :: Data a => (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r

-- | A generic query with a right-associative binary operator
gmapQr :: forall r r'. Data a => (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r

-- | A generic query that processes the immediate subterms and returns a
--   list of results. The list is given in the same order as originally
--   specified in the declaration of the data constructors.
gmapQ :: Data a => (forall d. Data d => d -> u) -> a -> [u]

-- | A generic query that processes one child by index (zero-based)
gmapQi :: Data a => Int -> (forall d. Data d => d -> u) -> a -> u

-- | A generic monadic transformation that maps over the immediate subterms
--   
--   The default definition instantiates the type constructor <tt>c</tt> in
--   the type of <a>gfoldl</a> to the monad datatype constructor, defining
--   injection and projection using <a>return</a> and <a>&gt;&gt;=</a>.
gmapM :: (Data a, Monad m) => (forall d. Data d => d -> m d) -> a -> m a

-- | Transformation of at least one immediate subterm does not fail
gmapMp :: (Data a, MonadPlus m) => (forall d. Data d => d -> m d) -> a -> m a

-- | Transformation of one immediate subterm with success
gmapMo :: (Data a, MonadPlus m) => (forall d. Data d => d -> m d) -> a -> m a

-- | A type <tt>f</tt> is a Functor if it provides a function <tt>fmap</tt>
--   which, given any types <tt>a</tt> and <tt>b</tt> lets you apply any
--   function from <tt>(a -&gt; b)</tt> to turn an <tt>f a</tt> into an
--   <tt>f b</tt>, preserving the structure of <tt>f</tt>. Furthermore
--   <tt>f</tt> needs to adhere to the following:
--   
--   <ul>
--   <li><i>Identity</i> <tt><a>fmap</a> <a>id</a> == <a>id</a></tt></li>
--   <li><i>Composition</i> <tt><a>fmap</a> (f . g) == <a>fmap</a> f .
--   <a>fmap</a> g</tt></li>
--   </ul>
--   
--   Note, that the second law follows from the free theorem of the type
--   <a>fmap</a> and the first law, so you need only check that the former
--   condition holds.
class Functor (f :: Type -> Type)

-- | <a>fmap</a> is used to apply a function of type <tt>(a -&gt; b)</tt>
--   to a value of type <tt>f a</tt>, where f is a functor, to produce a
--   value of type <tt>f b</tt>. Note that for any type constructor with
--   more than one parameter (e.g., <tt>Either</tt>), only the last type
--   parameter can be modified with <a>fmap</a> (e.g., <tt>b</tt> in
--   `Either a b`).
--   
--   Some type constructors with two parameters or more have a
--   <tt><a>Bifunctor</a></tt> instance that allows both the last and the
--   penultimate parameters to be mapped over.
--   
--   <h4><b>Examples</b></h4>
--   
--   Convert from a <tt><a>Maybe</a> Int</tt> to a <tt>Maybe String</tt>
--   using <a>show</a>:
--   
--   <pre>
--   &gt;&gt;&gt; fmap show Nothing
--   Nothing
--   
--   &gt;&gt;&gt; fmap show (Just 3)
--   Just "3"
--   </pre>
--   
--   Convert from an <tt><a>Either</a> Int Int</tt> to an <tt>Either Int
--   String</tt> using <a>show</a>:
--   
--   <pre>
--   &gt;&gt;&gt; fmap show (Left 17)
--   Left 17
--   
--   &gt;&gt;&gt; fmap show (Right 17)
--   Right "17"
--   </pre>
--   
--   Double each element of a list:
--   
--   <pre>
--   &gt;&gt;&gt; fmap (*2) [1,2,3]
--   [2,4,6]
--   </pre>
--   
--   Apply <a>even</a> to the second element of a pair:
--   
--   <pre>
--   &gt;&gt;&gt; fmap even (2,2)
--   (2,True)
--   </pre>
--   
--   It may seem surprising that the function is only applied to the last
--   element of the tuple compared to the list example above which applies
--   it to every element in the list. To understand, remember that tuples
--   are type constructors with multiple type parameters: a tuple of 3
--   elements <tt>(a,b,c)</tt> can also be written <tt>(,,) a b c</tt> and
--   its <tt>Functor</tt> instance is defined for <tt>Functor ((,,) a
--   b)</tt> (i.e., only the third parameter is free to be mapped over with
--   <tt>fmap</tt>).
--   
--   It explains why <tt>fmap</tt> can be used with tuples containing
--   values of different types as in the following example:
--   
--   <pre>
--   &gt;&gt;&gt; fmap even ("hello", 1.0, 4)
--   ("hello",1.0,True)
--   </pre>
fmap :: Functor f => (a -> b) -> f a -> f b

-- | Replace all locations in the input with the same value. The default
--   definition is <tt><a>fmap</a> . <a>const</a></tt>, but this may be
--   overridden with a more efficient version.
(<$) :: Functor f => a -> f b -> f a
infixl 4 <$

-- | Basic numeric class.
--   
--   The Haskell Report defines no laws for <a>Num</a>. However,
--   <tt>(<a>+</a>)</tt> and <tt>(<a>*</a>)</tt> are customarily expected
--   to define a ring and have the following properties:
--   
--   <ul>
--   <li><i><b>Associativity of <tt>(<a>+</a>)</tt></b></i> <tt>(x + y) +
--   z</tt> = <tt>x + (y + z)</tt></li>
--   <li><i><b>Commutativity of <tt>(<a>+</a>)</tt></b></i> <tt>x + y</tt>
--   = <tt>y + x</tt></li>
--   <li><i><b><tt><a>fromInteger</a> 0</tt> is the additive
--   identity</b></i> <tt>x + fromInteger 0</tt> = <tt>x</tt></li>
--   <li><i><b><a>negate</a> gives the additive inverse</b></i> <tt>x +
--   negate x</tt> = <tt>fromInteger 0</tt></li>
--   <li><i><b>Associativity of <tt>(<a>*</a>)</tt></b></i> <tt>(x * y) *
--   z</tt> = <tt>x * (y * z)</tt></li>
--   <li><i><b><tt><a>fromInteger</a> 1</tt> is the multiplicative
--   identity</b></i> <tt>x * fromInteger 1</tt> = <tt>x</tt> and
--   <tt>fromInteger 1 * x</tt> = <tt>x</tt></li>
--   <li><i><b>Distributivity of <tt>(<a>*</a>)</tt> with respect to
--   <tt>(<a>+</a>)</tt></b></i> <tt>a * (b + c)</tt> = <tt>(a * b) + (a *
--   c)</tt> and <tt>(b + c) * a</tt> = <tt>(b * a) + (c * a)</tt></li>
--   </ul>
--   
--   Note that it <i>isn't</i> customarily expected that a type instance of
--   both <a>Num</a> and <a>Ord</a> implement an ordered ring. Indeed, in
--   <tt>base</tt> only <a>Integer</a> and <a>Rational</a> do.
class Num a
(+) :: Num a => a -> a -> a
(-) :: Num a => a -> a -> a
(*) :: Num a => a -> a -> a

-- | Unary negation.
negate :: Num a => a -> a

-- | Absolute value.
abs :: Num a => a -> a

-- | Sign of a number. The functions <a>abs</a> and <a>signum</a> should
--   satisfy the law:
--   
--   <pre>
--   abs x * signum x == x
--   </pre>
--   
--   For real numbers, the <a>signum</a> is either <tt>-1</tt> (negative),
--   <tt>0</tt> (zero) or <tt>1</tt> (positive).
signum :: Num a => a -> a

-- | Conversion from an <a>Integer</a>. An integer literal represents the
--   application of the function <a>fromInteger</a> to the appropriate
--   value of type <a>Integer</a>, so such literals have type
--   <tt>(<a>Num</a> a) =&gt; a</tt>.
fromInteger :: Num a => Integer -> a
infixl 7 *
infixl 6 +
infixl 6 -

-- | The <a>Ord</a> class is used for totally ordered datatypes.
--   
--   Instances of <a>Ord</a> can be derived for any user-defined datatype
--   whose constituent types are in <a>Ord</a>. The declared order of the
--   constructors in the data declaration determines the ordering in
--   derived <a>Ord</a> instances. The <a>Ordering</a> datatype allows a
--   single comparison to determine the precise ordering of two objects.
--   
--   <a>Ord</a>, as defined by the Haskell report, implements a total order
--   and has the following properties:
--   
--   <ul>
--   <li><i><b>Comparability</b></i> <tt>x &lt;= y || y &lt;= x</tt> =
--   <a>True</a></li>
--   <li><i><b>Transitivity</b></i> if <tt>x &lt;= y &amp;&amp; y &lt;=
--   z</tt> = <a>True</a>, then <tt>x &lt;= z</tt> = <a>True</a></li>
--   <li><i><b>Reflexivity</b></i> <tt>x &lt;= x</tt> = <a>True</a></li>
--   <li><i><b>Antisymmetry</b></i> if <tt>x &lt;= y &amp;&amp; y &lt;=
--   x</tt> = <a>True</a>, then <tt>x == y</tt> = <a>True</a></li>
--   </ul>
--   
--   The following operator interactions are expected to hold:
--   
--   <ol>
--   <li><tt>x &gt;= y</tt> = <tt>y &lt;= x</tt></li>
--   <li><tt>x &lt; y</tt> = <tt>x &lt;= y &amp;&amp; x /= y</tt></li>
--   <li><tt>x &gt; y</tt> = <tt>y &lt; x</tt></li>
--   <li><tt>x &lt; y</tt> = <tt>compare x y == LT</tt></li>
--   <li><tt>x &gt; y</tt> = <tt>compare x y == GT</tt></li>
--   <li><tt>x == y</tt> = <tt>compare x y == EQ</tt></li>
--   <li><tt>min x y == if x &lt;= y then x else y</tt> = <a>True</a></li>
--   <li><tt>max x y == if x &gt;= y then x else y</tt> = <a>True</a></li>
--   </ol>
--   
--   Note that (7.) and (8.) do <i>not</i> require <a>min</a> and
--   <a>max</a> to return either of their arguments. The result is merely
--   required to <i>equal</i> one of the arguments in terms of <a>(==)</a>.
--   
--   Minimal complete definition: either <a>compare</a> or <a>&lt;=</a>.
--   Using <a>compare</a> can be more efficient for complex types.
class Eq a => Ord a
compare :: Ord a => a -> a -> Ordering
(<) :: Ord a => a -> a -> Bool
(<=) :: Ord a => a -> a -> Bool
(>) :: Ord a => a -> a -> Bool
(>=) :: Ord a => a -> a -> Bool
max :: Ord a => a -> a -> a
min :: Ord a => a -> a -> a
infix 4 <
infix 4 <=
infix 4 >
infix 4 >=

-- | Parsing of <a>String</a>s, producing values.
--   
--   Derived instances of <a>Read</a> make the following assumptions, which
--   derived instances of <a>Show</a> obey:
--   
--   <ul>
--   <li>If the constructor is defined to be an infix operator, then the
--   derived <a>Read</a> instance will parse only infix applications of the
--   constructor (not the prefix form).</li>
--   <li>Associativity is not used to reduce the occurrence of parentheses,
--   although precedence may be.</li>
--   <li>If the constructor is defined using record syntax, the derived
--   <a>Read</a> will parse only the record-syntax form, and furthermore,
--   the fields must be given in the same order as the original
--   declaration.</li>
--   <li>The derived <a>Read</a> instance allows arbitrary Haskell
--   whitespace between tokens of the input string. Extra parentheses are
--   also allowed.</li>
--   </ul>
--   
--   For example, given the declarations
--   
--   <pre>
--   infixr 5 :^:
--   data Tree a =  Leaf a  |  Tree a :^: Tree a
--   </pre>
--   
--   the derived instance of <a>Read</a> in Haskell 2010 is equivalent to
--   
--   <pre>
--   instance (Read a) =&gt; Read (Tree a) where
--   
--           readsPrec d r =  readParen (d &gt; app_prec)
--                            (\r -&gt; [(Leaf m,t) |
--                                    ("Leaf",s) &lt;- lex r,
--                                    (m,t) &lt;- readsPrec (app_prec+1) s]) r
--   
--                         ++ readParen (d &gt; up_prec)
--                            (\r -&gt; [(u:^:v,w) |
--                                    (u,s) &lt;- readsPrec (up_prec+1) r,
--                                    (":^:",t) &lt;- lex s,
--                                    (v,w) &lt;- readsPrec (up_prec+1) t]) r
--   
--             where app_prec = 10
--                   up_prec = 5
--   </pre>
--   
--   Note that right-associativity of <tt>:^:</tt> is unused.
--   
--   The derived instance in GHC is equivalent to
--   
--   <pre>
--   instance (Read a) =&gt; Read (Tree a) where
--   
--           readPrec = parens $ (prec app_prec $ do
--                                    Ident "Leaf" &lt;- lexP
--                                    m &lt;- step readPrec
--                                    return (Leaf m))
--   
--                        +++ (prec up_prec $ do
--                                    u &lt;- step readPrec
--                                    Symbol ":^:" &lt;- lexP
--                                    v &lt;- step readPrec
--                                    return (u :^: v))
--   
--             where app_prec = 10
--                   up_prec = 5
--   
--           readListPrec = readListPrecDefault
--   </pre>
--   
--   Why do both <a>readsPrec</a> and <a>readPrec</a> exist, and why does
--   GHC opt to implement <a>readPrec</a> in derived <a>Read</a> instances
--   instead of <a>readsPrec</a>? The reason is that <a>readsPrec</a> is
--   based on the <a>ReadS</a> type, and although <a>ReadS</a> is mentioned
--   in the Haskell 2010 Report, it is not a very efficient parser data
--   structure.
--   
--   <a>readPrec</a>, on the other hand, is based on a much more efficient
--   <a>ReadPrec</a> datatype (a.k.a "new-style parsers"), but its
--   definition relies on the use of the <tt>RankNTypes</tt> language
--   extension. Therefore, <a>readPrec</a> (and its cousin,
--   <a>readListPrec</a>) are marked as GHC-only. Nevertheless, it is
--   recommended to use <a>readPrec</a> instead of <a>readsPrec</a>
--   whenever possible for the efficiency improvements it brings.
--   
--   As mentioned above, derived <a>Read</a> instances in GHC will
--   implement <a>readPrec</a> instead of <a>readsPrec</a>. The default
--   implementations of <a>readsPrec</a> (and its cousin, <a>readList</a>)
--   will simply use <a>readPrec</a> under the hood. If you are writing a
--   <a>Read</a> instance by hand, it is recommended to write it like so:
--   
--   <pre>
--   instance <a>Read</a> T where
--     <a>readPrec</a>     = ...
--     <a>readListPrec</a> = <a>readListPrecDefault</a>
--   </pre>
class Read a

-- | attempts to parse a value from the front of the string, returning a
--   list of (parsed value, remaining string) pairs. If there is no
--   successful parse, the returned list is empty.
--   
--   Derived instances of <a>Read</a> and <a>Show</a> satisfy the
--   following:
--   
--   <ul>
--   <li><tt>(x,"")</tt> is an element of <tt>(<a>readsPrec</a> d
--   (<a>showsPrec</a> d x ""))</tt>.</li>
--   </ul>
--   
--   That is, <a>readsPrec</a> parses the string produced by
--   <a>showsPrec</a>, and delivers the value that <a>showsPrec</a> started
--   with.
readsPrec :: Read a => Int -> ReadS a

-- | The method <a>readList</a> is provided to allow the programmer to give
--   a specialised way of parsing lists of values. For example, this is
--   used by the predefined <a>Read</a> instance of the <a>Char</a> type,
--   where values of type <a>String</a> should be are expected to use
--   double quotes, rather than square brackets.
readList :: Read a => ReadS [a]

-- | Proposed replacement for <a>readsPrec</a> using new-style parsers (GHC
--   only).
readPrec :: Read a => ReadPrec a

-- | Proposed replacement for <a>readList</a> using new-style parsers (GHC
--   only). The default definition uses <a>readList</a>. Instances that
--   define <a>readPrec</a> should also define <a>readListPrec</a> as
--   <a>readListPrecDefault</a>.
readListPrec :: Read a => ReadPrec [a]
class (Num a, Ord a) => Real a

-- | the rational equivalent of its real argument with full precision
toRational :: Real a => a -> Rational

-- | Efficient, machine-independent access to the components of a
--   floating-point number.
class (RealFrac a, Floating a) => RealFloat a

-- | a constant function, returning the radix of the representation (often
--   <tt>2</tt>)
floatRadix :: RealFloat a => a -> Integer

-- | a constant function, returning the number of digits of
--   <a>floatRadix</a> in the significand
floatDigits :: RealFloat a => a -> Int

-- | a constant function, returning the lowest and highest values the
--   exponent may assume
floatRange :: RealFloat a => a -> (Int, Int)

-- | The function <a>decodeFloat</a> applied to a real floating-point
--   number returns the significand expressed as an <a>Integer</a> and an
--   appropriately scaled exponent (an <a>Int</a>). If
--   <tt><a>decodeFloat</a> x</tt> yields <tt>(m,n)</tt>, then <tt>x</tt>
--   is equal in value to <tt>m*b^^n</tt>, where <tt>b</tt> is the
--   floating-point radix, and furthermore, either <tt>m</tt> and
--   <tt>n</tt> are both zero or else <tt>b^(d-1) &lt;= <a>abs</a> m &lt;
--   b^d</tt>, where <tt>d</tt> is the value of <tt><a>floatDigits</a>
--   x</tt>. In particular, <tt><a>decodeFloat</a> 0 = (0,0)</tt>. If the
--   type contains a negative zero, also <tt><a>decodeFloat</a> (-0.0) =
--   (0,0)</tt>. <i>The result of</i> <tt><a>decodeFloat</a> x</tt> <i>is
--   unspecified if either of</i> <tt><a>isNaN</a> x</tt> <i>or</i>
--   <tt><a>isInfinite</a> x</tt> <i>is</i> <a>True</a>.
decodeFloat :: RealFloat a => a -> (Integer, Int)

-- | <a>encodeFloat</a> performs the inverse of <a>decodeFloat</a> in the
--   sense that for finite <tt>x</tt> with the exception of <tt>-0.0</tt>,
--   <tt><a>uncurry</a> <a>encodeFloat</a> (<a>decodeFloat</a> x) = x</tt>.
--   <tt><a>encodeFloat</a> m n</tt> is one of the two closest
--   representable floating-point numbers to <tt>m*b^^n</tt> (or
--   <tt>±Infinity</tt> if overflow occurs); usually the closer, but if
--   <tt>m</tt> contains too many bits, the result may be rounded in the
--   wrong direction.
encodeFloat :: RealFloat a => Integer -> Int -> a

-- | <a>exponent</a> corresponds to the second component of
--   <a>decodeFloat</a>. <tt><a>exponent</a> 0 = 0</tt> and for finite
--   nonzero <tt>x</tt>, <tt><a>exponent</a> x = snd (<a>decodeFloat</a> x)
--   + <a>floatDigits</a> x</tt>. If <tt>x</tt> is a finite floating-point
--   number, it is equal in value to <tt><a>significand</a> x * b ^^
--   <a>exponent</a> x</tt>, where <tt>b</tt> is the floating-point radix.
--   The behaviour is unspecified on infinite or <tt>NaN</tt> values.
exponent :: RealFloat a => a -> Int

-- | The first component of <a>decodeFloat</a>, scaled to lie in the open
--   interval (<tt>-1</tt>,<tt>1</tt>), either <tt>0.0</tt> or of absolute
--   value <tt>&gt;= 1/b</tt>, where <tt>b</tt> is the floating-point
--   radix. The behaviour is unspecified on infinite or <tt>NaN</tt>
--   values.
significand :: RealFloat a => a -> a

-- | multiplies a floating-point number by an integer power of the radix
scaleFloat :: RealFloat a => Int -> a -> a

-- | <a>True</a> if the argument is an IEEE "not-a-number" (NaN) value
isNaN :: RealFloat a => a -> Bool

-- | <a>True</a> if the argument is an IEEE infinity or negative infinity
isInfinite :: RealFloat a => a -> Bool

-- | <a>True</a> if the argument is too small to be represented in
--   normalized format
isDenormalized :: RealFloat a => a -> Bool

-- | <a>True</a> if the argument is an IEEE negative zero
isNegativeZero :: RealFloat a => a -> Bool

-- | <a>True</a> if the argument is an IEEE floating point number
isIEEE :: RealFloat a => a -> Bool

-- | a version of arctangent taking two real floating-point arguments. For
--   real floating <tt>x</tt> and <tt>y</tt>, <tt><a>atan2</a> y x</tt>
--   computes the angle (from the positive x-axis) of the vector from the
--   origin to the point <tt>(x,y)</tt>. <tt><a>atan2</a> y x</tt> returns
--   a value in the range [<tt>-pi</tt>, <tt>pi</tt>]. It follows the
--   Common Lisp semantics for the origin when signed zeroes are supported.
--   <tt><a>atan2</a> y 1</tt>, with <tt>y</tt> in a type that is
--   <a>RealFloat</a>, should return the same value as <tt><a>atan</a>
--   y</tt>. A default definition of <a>atan2</a> is provided, but
--   implementors can provide a more accurate implementation.
atan2 :: RealFloat a => a -> a -> a

-- | Extracting components of fractions.
class (Real a, Fractional a) => RealFrac a

-- | The function <a>properFraction</a> takes a real fractional number
--   <tt>x</tt> and returns a pair <tt>(n,f)</tt> such that <tt>x =
--   n+f</tt>, and:
--   
--   <ul>
--   <li><tt>n</tt> is an integral number with the same sign as <tt>x</tt>;
--   and</li>
--   <li><tt>f</tt> is a fraction with the same type and sign as
--   <tt>x</tt>, and with absolute value less than <tt>1</tt>.</li>
--   </ul>
--   
--   The default definitions of the <a>ceiling</a>, <a>floor</a>,
--   <a>truncate</a> and <a>round</a> functions are in terms of
--   <a>properFraction</a>.
properFraction :: (RealFrac a, Integral b) => a -> (b, a)

-- | <tt><a>truncate</a> x</tt> returns the integer nearest <tt>x</tt>
--   between zero and <tt>x</tt>
truncate :: (RealFrac a, Integral b) => a -> b

-- | <tt><a>round</a> x</tt> returns the nearest integer to <tt>x</tt>; the
--   even integer if <tt>x</tt> is equidistant between two integers
round :: (RealFrac a, Integral b) => a -> b

-- | <tt><a>ceiling</a> x</tt> returns the least integer not less than
--   <tt>x</tt>
ceiling :: (RealFrac a, Integral b) => a -> b

-- | <tt><a>floor</a> x</tt> returns the greatest integer not greater than
--   <tt>x</tt>
floor :: (RealFrac a, Integral b) => a -> b

-- | Conversion of values to readable <a>String</a>s.
--   
--   Derived instances of <a>Show</a> have the following properties, which
--   are compatible with derived instances of <a>Read</a>:
--   
--   <ul>
--   <li>The result of <a>show</a> is a syntactically correct Haskell
--   expression containing only constants, given the fixity declarations in
--   force at the point where the type is declared. It contains only the
--   constructor names defined in the data type, parentheses, and spaces.
--   When labelled constructor fields are used, braces, commas, field
--   names, and equal signs are also used.</li>
--   <li>If the constructor is defined to be an infix operator, then
--   <a>showsPrec</a> will produce infix applications of the
--   constructor.</li>
--   <li>the representation will be enclosed in parentheses if the
--   precedence of the top-level constructor in <tt>x</tt> is less than
--   <tt>d</tt> (associativity is ignored). Thus, if <tt>d</tt> is
--   <tt>0</tt> then the result is never surrounded in parentheses; if
--   <tt>d</tt> is <tt>11</tt> it is always surrounded in parentheses,
--   unless it is an atomic expression.</li>
--   <li>If the constructor is defined using record syntax, then
--   <a>show</a> will produce the record-syntax form, with the fields given
--   in the same order as the original declaration.</li>
--   </ul>
--   
--   For example, given the declarations
--   
--   <pre>
--   infixr 5 :^:
--   data Tree a =  Leaf a  |  Tree a :^: Tree a
--   </pre>
--   
--   the derived instance of <a>Show</a> is equivalent to
--   
--   <pre>
--   instance (Show a) =&gt; Show (Tree a) where
--   
--          showsPrec d (Leaf m) = showParen (d &gt; app_prec) $
--               showString "Leaf " . showsPrec (app_prec+1) m
--            where app_prec = 10
--   
--          showsPrec d (u :^: v) = showParen (d &gt; up_prec) $
--               showsPrec (up_prec+1) u .
--               showString " :^: "      .
--               showsPrec (up_prec+1) v
--            where up_prec = 5
--   </pre>
--   
--   Note that right-associativity of <tt>:^:</tt> is ignored. For example,
--   
--   <ul>
--   <li><tt><a>show</a> (Leaf 1 :^: Leaf 2 :^: Leaf 3)</tt> produces the
--   string <tt>"Leaf 1 :^: (Leaf 2 :^: Leaf 3)"</tt>.</li>
--   </ul>
class Show a

-- | Convert a value to a readable <a>String</a>.
--   
--   <a>showsPrec</a> should satisfy the law
--   
--   <pre>
--   showsPrec d x r ++ s  ==  showsPrec d x (r ++ s)
--   </pre>
--   
--   Derived instances of <a>Read</a> and <a>Show</a> satisfy the
--   following:
--   
--   <ul>
--   <li><tt>(x,"")</tt> is an element of <tt>(<a>readsPrec</a> d
--   (<a>showsPrec</a> d x ""))</tt>.</li>
--   </ul>
--   
--   That is, <a>readsPrec</a> parses the string produced by
--   <a>showsPrec</a>, and delivers the value that <a>showsPrec</a> started
--   with.
showsPrec :: Show a => Int -> a -> ShowS

-- | A specialised variant of <a>showsPrec</a>, using precedence context
--   zero, and returning an ordinary <a>String</a>.
show :: Show a => a -> String

-- | The method <a>showList</a> is provided to allow the programmer to give
--   a specialised way of showing lists of values. For example, this is
--   used by the predefined <a>Show</a> instance of the <a>Char</a> type,
--   where values of type <a>String</a> should be shown in double quotes,
--   rather than between square brackets.
showList :: Show a => [a] -> ShowS

-- | The <a>Ix</a> class is used to map a contiguous subrange of values in
--   a type onto integers. It is used primarily for array indexing (see the
--   array package).
--   
--   The first argument <tt>(l,u)</tt> of each of these operations is a
--   pair specifying the lower and upper bounds of a contiguous subrange of
--   values.
--   
--   An implementation is entitled to assume the following laws about these
--   operations:
--   
--   <ul>
--   <li><tt><a>inRange</a> (l,u) i == <tt>elem</tt> i (<a>range</a>
--   (l,u))</tt> <tt> </tt></li>
--   <li><tt><a>range</a> (l,u) <tt>!!</tt> <a>index</a> (l,u) i == i</tt>,
--   when <tt><a>inRange</a> (l,u) i</tt></li>
--   <li><tt><a>map</a> (<a>index</a> (l,u)) (<a>range</a> (l,u))) ==
--   [0..<a>rangeSize</a> (l,u)-1]</tt> <tt> </tt></li>
--   <li><tt><a>rangeSize</a> (l,u) == <tt>length</tt> (<a>range</a>
--   (l,u))</tt> <tt> </tt></li>
--   </ul>
class Ord a => Ix a

-- | The list of values in the subrange defined by a bounding pair.
range :: Ix a => (a, a) -> [a]

-- | The position of a subscript in the subrange.
index :: Ix a => (a, a) -> a -> Int

-- | Returns <a>True</a> the given subscript lies in the range defined the
--   bounding pair.
inRange :: Ix a => (a, a) -> a -> Bool

-- | The size of the subrange defined by a bounding pair.
rangeSize :: Ix a => (a, a) -> Int

-- | The class <a>Typeable</a> allows a concrete representation of a type
--   to be calculated.
class Typeable (a :: k)

-- | Monads having fixed points with a 'knot-tying' semantics. Instances of
--   <a>MonadFix</a> should satisfy the following laws:
--   
--   <ul>
--   <li><i>Purity</i> <tt><a>mfix</a> (<a>return</a> . h) = <a>return</a>
--   (<a>fix</a> h)</tt></li>
--   <li><i>Left shrinking (or Tightening)</i> <tt><a>mfix</a> (\x -&gt; a
--   &gt;&gt;= \y -&gt; f x y) = a &gt;&gt;= \y -&gt; <a>mfix</a> (\x -&gt;
--   f x y)</tt></li>
--   <li><i>Sliding</i> <tt><a>mfix</a> (<a>liftM</a> h . f) = <a>liftM</a>
--   h (<a>mfix</a> (f . h))</tt>, for strict <tt>h</tt>.</li>
--   <li><i>Nesting</i> <tt><a>mfix</a> (\x -&gt; <a>mfix</a> (\y -&gt; f x
--   y)) = <a>mfix</a> (\x -&gt; f x x)</tt></li>
--   </ul>
--   
--   This class is used in the translation of the recursive <tt>do</tt>
--   notation supported by GHC and Hugs.
class Monad m => MonadFix (m :: Type -> Type)

-- | The fixed point of a monadic computation. <tt><a>mfix</a> f</tt>
--   executes the action <tt>f</tt> only once, with the eventual output fed
--   back as the input. Hence <tt>f</tt> should not be strict, for then
--   <tt><a>mfix</a> f</tt> would diverge.
mfix :: MonadFix m => (a -> m a) -> m a

-- | When a value is bound in <tt>do</tt>-notation, the pattern on the left
--   hand side of <tt>&lt;-</tt> might not match. In this case, this class
--   provides a function to recover.
--   
--   A <a>Monad</a> without a <a>MonadFail</a> instance may only be used in
--   conjunction with pattern that always match, such as newtypes, tuples,
--   data types with only a single data constructor, and irrefutable
--   patterns (<tt>~pat</tt>).
--   
--   Instances of <a>MonadFail</a> should satisfy the following law:
--   <tt>fail s</tt> should be a left zero for <a>&gt;&gt;=</a>,
--   
--   <pre>
--   fail s &gt;&gt;= f  =  fail s
--   </pre>
--   
--   If your <a>Monad</a> is also <a>MonadPlus</a>, a popular definition is
--   
--   <pre>
--   fail _ = mzero
--   </pre>
class Monad m => MonadFail (m :: Type -> Type)
fail :: MonadFail m => String -> m a

-- | Class for string-like datastructures; used by the overloaded string
--   extension (-XOverloadedStrings in GHC).
class IsString a
fromString :: IsString a => String -> a

-- | A functor with application, providing operations to
--   
--   <ul>
--   <li>embed pure expressions (<a>pure</a>), and</li>
--   <li>sequence computations and combine their results (<a>&lt;*&gt;</a>
--   and <a>liftA2</a>).</li>
--   </ul>
--   
--   A minimal complete definition must include implementations of
--   <a>pure</a> and of either <a>&lt;*&gt;</a> or <a>liftA2</a>. If it
--   defines both, then they must behave the same as their default
--   definitions:
--   
--   <pre>
--   (<a>&lt;*&gt;</a>) = <a>liftA2</a> <a>id</a>
--   </pre>
--   
--   <pre>
--   <a>liftA2</a> f x y = f <a>&lt;$&gt;</a> x <a>&lt;*&gt;</a> y
--   </pre>
--   
--   Further, any definition must satisfy the following:
--   
--   <ul>
--   <li><i>Identity</i> <pre><a>pure</a> <a>id</a> <a>&lt;*&gt;</a> v =
--   v</pre></li>
--   <li><i>Composition</i> <pre><a>pure</a> (.) <a>&lt;*&gt;</a> u
--   <a>&lt;*&gt;</a> v <a>&lt;*&gt;</a> w = u <a>&lt;*&gt;</a> (v
--   <a>&lt;*&gt;</a> w)</pre></li>
--   <li><i>Homomorphism</i> <pre><a>pure</a> f <a>&lt;*&gt;</a>
--   <a>pure</a> x = <a>pure</a> (f x)</pre></li>
--   <li><i>Interchange</i> <pre>u <a>&lt;*&gt;</a> <a>pure</a> y =
--   <a>pure</a> (<a>$</a> y) <a>&lt;*&gt;</a> u</pre></li>
--   </ul>
--   
--   The other methods have the following default definitions, which may be
--   overridden with equivalent specialized implementations:
--   
--   <ul>
--   <li><pre>u <a>*&gt;</a> v = (<a>id</a> <a>&lt;$</a> u)
--   <a>&lt;*&gt;</a> v</pre></li>
--   <li><pre>u <a>&lt;*</a> v = <a>liftA2</a> <a>const</a> u v</pre></li>
--   </ul>
--   
--   As a consequence of these laws, the <a>Functor</a> instance for
--   <tt>f</tt> will satisfy
--   
--   <ul>
--   <li><pre><a>fmap</a> f x = <a>pure</a> f <a>&lt;*&gt;</a> x</pre></li>
--   </ul>
--   
--   It may be useful to note that supposing
--   
--   <pre>
--   forall x y. p (q x y) = f x . g y
--   </pre>
--   
--   it follows from the above that
--   
--   <pre>
--   <a>liftA2</a> p (<a>liftA2</a> q u v) = <a>liftA2</a> f u . <a>liftA2</a> g v
--   </pre>
--   
--   If <tt>f</tt> is also a <a>Monad</a>, it should satisfy
--   
--   <ul>
--   <li><pre><a>pure</a> = <a>return</a></pre></li>
--   <li><pre>m1 <a>&lt;*&gt;</a> m2 = m1 <a>&gt;&gt;=</a> (x1 -&gt; m2
--   <a>&gt;&gt;=</a> (x2 -&gt; <a>return</a> (x1 x2)))</pre></li>
--   <li><pre>(<a>*&gt;</a>) = (<a>&gt;&gt;</a>)</pre></li>
--   </ul>
--   
--   (which implies that <a>pure</a> and <a>&lt;*&gt;</a> satisfy the
--   applicative functor laws).
class Functor f => Applicative (f :: Type -> Type)

-- | Lift a value.
pure :: Applicative f => a -> f a

-- | Sequential application.
--   
--   A few functors support an implementation of <a>&lt;*&gt;</a> that is
--   more efficient than the default one.
--   
--   <h4><b>Example</b></h4>
--   
--   Used in combination with <tt>(<tt>&lt;$&gt;</tt>)</tt>,
--   <tt>(<a>&lt;*&gt;</a>)</tt> can be used to build a record.
--   
--   <pre>
--   &gt;&gt;&gt; data MyState = MyState {arg1 :: Foo, arg2 :: Bar, arg3 :: Baz}
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; produceFoo :: Applicative f =&gt; f Foo
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; produceBar :: Applicative f =&gt; f Bar
--   
--   &gt;&gt;&gt; produceBaz :: Applicative f =&gt; f Baz
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; mkState :: Applicative f =&gt; f MyState
--   
--   &gt;&gt;&gt; mkState = MyState &lt;$&gt; produceFoo &lt;*&gt; produceBar &lt;*&gt; produceBaz
--   </pre>
(<*>) :: Applicative f => f (a -> b) -> f a -> f b

-- | Lift a binary function to actions.
--   
--   Some functors support an implementation of <a>liftA2</a> that is more
--   efficient than the default one. In particular, if <a>fmap</a> is an
--   expensive operation, it is likely better to use <a>liftA2</a> than to
--   <a>fmap</a> over the structure and then use <a>&lt;*&gt;</a>.
--   
--   This became a typeclass method in 4.10.0.0. Prior to that, it was a
--   function defined in terms of <a>&lt;*&gt;</a> and <a>fmap</a>.
--   
--   <h4><b>Example</b></h4>
--   
--   <pre>
--   &gt;&gt;&gt; liftA2 (,) (Just 3) (Just 5)
--   Just (3,5)
--   </pre>
liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c

-- | Sequence actions, discarding the value of the first argument.
--   
--   <h4><b>Examples</b></h4>
--   
--   If used in conjunction with the Applicative instance for <a>Maybe</a>,
--   you can chain Maybe computations, with a possible "early return" in
--   case of <a>Nothing</a>.
--   
--   <pre>
--   &gt;&gt;&gt; Just 2 *&gt; Just 3
--   Just 3
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; Nothing *&gt; Just 3
--   Nothing
--   </pre>
--   
--   Of course a more interesting use case would be to have effectful
--   computations instead of just returning pure values.
--   
--   <pre>
--   &gt;&gt;&gt; import Data.Char
--   
--   &gt;&gt;&gt; import Text.ParserCombinators.ReadP
--   
--   &gt;&gt;&gt; let p = string "my name is " *&gt; munch1 isAlpha &lt;* eof
--   
--   &gt;&gt;&gt; readP_to_S p "my name is Simon"
--   [("Simon","")]
--   </pre>
(*>) :: Applicative f => f a -> f b -> f b

-- | Sequence actions, discarding the value of the second argument.
(<*) :: Applicative f => f a -> f b -> f a
infixl 4 <*
infixl 4 *>
infixl 4 <*>

-- | The Foldable class represents data structures that can be reduced to a
--   summary value one element at a time. Strict left-associative folds are
--   a good fit for space-efficient reduction, while lazy right-associative
--   folds are a good fit for corecursive iteration, or for folds that
--   short-circuit after processing an initial subsequence of the
--   structure's elements.
--   
--   Instances can be derived automatically by enabling the
--   <tt>DeriveFoldable</tt> extension. For example, a derived instance for
--   a binary tree might be:
--   
--   <pre>
--   {-# LANGUAGE DeriveFoldable #-}
--   data Tree a = Empty
--               | Leaf a
--               | Node (Tree a) a (Tree a)
--       deriving Foldable
--   </pre>
--   
--   A more detailed description can be found in the <b>Overview</b>
--   section of <a>Data.Foldable#overview</a>.
--   
--   For the class laws see the <b>Laws</b> section of
--   <a>Data.Foldable#laws</a>.
class Foldable (t :: TYPE LiftedRep -> Type)

-- | Given a structure with elements whose type is a <a>Monoid</a>, combine
--   them via the monoid's <tt>(<a>&lt;&gt;</a>)</tt> operator. This fold
--   is right-associative and lazy in the accumulator. When you need a
--   strict left-associative fold, use <a>foldMap'</a> instead, with
--   <a>id</a> as the map.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; fold [[1, 2, 3], [4, 5], [6], []]
--   [1,2,3,4,5,6]
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; fold $ Node (Leaf (Sum 1)) (Sum 3) (Leaf (Sum 5))
--   Sum {getSum = 9}
--   </pre>
--   
--   Folds of unbounded structures do not terminate when the monoid's
--   <tt>(<a>&lt;&gt;</a>)</tt> operator is strict:
--   
--   <pre>
--   &gt;&gt;&gt; fold (repeat Nothing)
--   * Hangs forever *
--   </pre>
--   
--   Lazy corecursive folds of unbounded structures are fine:
--   
--   <pre>
--   &gt;&gt;&gt; take 12 $ fold $ map (\i -&gt; [i..i+2]) [0..]
--   [0,1,2,1,2,3,2,3,4,3,4,5]
--   
--   &gt;&gt;&gt; sum $ take 4000000 $ fold $ map (\i -&gt; [i..i+2]) [0..]
--   2666668666666
--   </pre>
fold :: (Foldable t, Monoid m) => t m -> m

-- | Map each element of the structure into a monoid, and combine the
--   results with <tt>(<a>&lt;&gt;</a>)</tt>. This fold is
--   right-associative and lazy in the accumulator. For strict
--   left-associative folds consider <a>foldMap'</a> instead.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; foldMap Sum [1, 3, 5]
--   Sum {getSum = 9}
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; foldMap Product [1, 3, 5]
--   Product {getProduct = 15}
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; foldMap (replicate 3) [1, 2, 3]
--   [1,1,1,2,2,2,3,3,3]
--   </pre>
--   
--   When a Monoid's <tt>(<a>&lt;&gt;</a>)</tt> is lazy in its second
--   argument, <a>foldMap</a> can return a result even from an unbounded
--   structure. For example, lazy accumulation enables
--   <a>Data.ByteString.Builder</a> to efficiently serialise large data
--   structures and produce the output incrementally:
--   
--   <pre>
--   &gt;&gt;&gt; import qualified Data.ByteString.Lazy as L
--   
--   &gt;&gt;&gt; import qualified Data.ByteString.Builder as B
--   
--   &gt;&gt;&gt; let bld :: Int -&gt; B.Builder; bld i = B.intDec i &lt;&gt; B.word8 0x20
--   
--   &gt;&gt;&gt; let lbs = B.toLazyByteString $ foldMap bld [0..]
--   
--   &gt;&gt;&gt; L.take 64 lbs
--   "0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24"
--   </pre>
foldMap :: (Foldable t, Monoid m) => (a -> m) -> t a -> m

-- | A left-associative variant of <a>foldMap</a> that is strict in the
--   accumulator. Use this method for strict reduction when partial results
--   are merged via <tt>(<a>&lt;&gt;</a>)</tt>.
--   
--   <h4><b>Examples</b></h4>
--   
--   Define a <a>Monoid</a> over finite bit strings under <tt>xor</tt>. Use
--   it to strictly compute the <tt>xor</tt> of a list of <a>Int</a>
--   values.
--   
--   <pre>
--   &gt;&gt;&gt; :set -XGeneralizedNewtypeDeriving
--   
--   &gt;&gt;&gt; import Data.Bits (Bits, FiniteBits, xor, zeroBits)
--   
--   &gt;&gt;&gt; import Data.Foldable (foldMap')
--   
--   &gt;&gt;&gt; import Numeric (showHex)
--   
--   &gt;&gt;&gt; 
--   
--   &gt;&gt;&gt; newtype X a = X a deriving (Eq, Bounded, Enum, Bits, FiniteBits)
--   
--   &gt;&gt;&gt; instance Bits a =&gt; Semigroup (X a) where X a &lt;&gt; X b = X (a `xor` b)
--   
--   &gt;&gt;&gt; instance Bits a =&gt; Monoid    (X a) where mempty     = X zeroBits
--   
--   &gt;&gt;&gt; 
--   
--   &gt;&gt;&gt; let bits :: [Int]; bits = [0xcafe, 0xfeed, 0xdeaf, 0xbeef, 0x5411]
--   
--   &gt;&gt;&gt; (\ (X a) -&gt; showString "0x" . showHex a $ "") $ foldMap' X bits
--   "0x42"
--   </pre>
foldMap' :: (Foldable t, Monoid m) => (a -> m) -> t a -> m

-- | Right-associative fold of a structure, lazy in the accumulator.
--   
--   In the case of lists, <a>foldr</a>, when applied to a binary operator,
--   a starting value (typically the right-identity of the operator), and a
--   list, reduces the list using the binary operator, from right to left:
--   
--   <pre>
--   foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
--   </pre>
--   
--   Note that since the head of the resulting expression is produced by an
--   application of the operator to the first element of the list, given an
--   operator lazy in its right argument, <a>foldr</a> can produce a
--   terminating expression from an unbounded list.
--   
--   For a general <a>Foldable</a> structure this should be semantically
--   identical to,
--   
--   <pre>
--   foldr f z = <a>foldr</a> f z . <a>toList</a>
--   </pre>
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; foldr (||) False [False, True, False]
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; foldr (||) False []
--   False
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; foldr (\c acc -&gt; acc ++ [c]) "foo" ['a', 'b', 'c', 'd']
--   "foodcba"
--   </pre>
--   
--   <h5>Infinite structures</h5>
--   
--   ⚠️ Applying <a>foldr</a> to infinite structures usually doesn't
--   terminate.
--   
--   It may still terminate under one of the following conditions:
--   
--   <ul>
--   <li>the folding function is short-circuiting</li>
--   <li>the folding function is lazy on its second argument</li>
--   </ul>
--   
--   <h6>Short-circuiting</h6>
--   
--   <tt>(<a>||</a>)</tt> short-circuits on <a>True</a> values, so the
--   following terminates because there is a <a>True</a> value finitely far
--   from the left side:
--   
--   <pre>
--   &gt;&gt;&gt; foldr (||) False (True : repeat False)
--   True
--   </pre>
--   
--   But the following doesn't terminate:
--   
--   <pre>
--   &gt;&gt;&gt; foldr (||) False (repeat False ++ [True])
--   * Hangs forever *
--   </pre>
--   
--   <h6>Laziness in the second argument</h6>
--   
--   Applying <a>foldr</a> to infinite structures terminates when the
--   operator is lazy in its second argument (the initial accumulator is
--   never used in this case, and so could be left <a>undefined</a>, but
--   <tt>[]</tt> is more clear):
--   
--   <pre>
--   &gt;&gt;&gt; take 5 $ foldr (\i acc -&gt; i : fmap (+3) acc) [] (repeat 1)
--   [1,4,7,10,13]
--   </pre>
foldr :: Foldable t => (a -> b -> b) -> b -> t a -> b

-- | Right-associative fold of a structure, strict in the accumulator. This
--   is rarely what you want.
foldr' :: Foldable t => (a -> b -> b) -> b -> t a -> b

-- | Left-associative fold of a structure, lazy in the accumulator. This is
--   rarely what you want, but can work well for structures with efficient
--   right-to-left sequencing and an operator that is lazy in its left
--   argument.
--   
--   In the case of lists, <a>foldl</a>, when applied to a binary operator,
--   a starting value (typically the left-identity of the operator), and a
--   list, reduces the list using the binary operator, from left to right:
--   
--   <pre>
--   foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn
--   </pre>
--   
--   Note that to produce the outermost application of the operator the
--   entire input list must be traversed. Like all left-associative folds,
--   <a>foldl</a> will diverge if given an infinite list.
--   
--   If you want an efficient strict left-fold, you probably want to use
--   <a>foldl'</a> instead of <a>foldl</a>. The reason for this is that the
--   latter does not force the <i>inner</i> results (e.g. <tt>z `f` x1</tt>
--   in the above example) before applying them to the operator (e.g. to
--   <tt>(`f` x2)</tt>). This results in a thunk chain &lt;math&gt;
--   elements long, which then must be evaluated from the outside-in.
--   
--   For a general <a>Foldable</a> structure this should be semantically
--   identical to:
--   
--   <pre>
--   foldl f z = <a>foldl</a> f z . <a>toList</a>
--   </pre>
--   
--   <h4><b>Examples</b></h4>
--   
--   The first example is a strict fold, which in practice is best
--   performed with <a>foldl'</a>.
--   
--   <pre>
--   &gt;&gt;&gt; foldl (+) 42 [1,2,3,4]
--   52
--   </pre>
--   
--   Though the result below is lazy, the input is reversed before
--   prepending it to the initial accumulator, so corecursion begins only
--   after traversing the entire input string.
--   
--   <pre>
--   &gt;&gt;&gt; foldl (\acc c -&gt; c : acc) "abcd" "efgh"
--   "hgfeabcd"
--   </pre>
--   
--   A left fold of a structure that is infinite on the right cannot
--   terminate, even when for any finite input the fold just returns the
--   initial accumulator:
--   
--   <pre>
--   &gt;&gt;&gt; foldl (\a _ -&gt; a) 0 $ repeat 1
--   * Hangs forever *
--   </pre>
--   
--   WARNING: When it comes to lists, you always want to use either
--   <a>foldl'</a> or <a>foldr</a> instead.
foldl :: Foldable t => (b -> a -> b) -> b -> t a -> b

-- | Left-associative fold of a structure but with strict application of
--   the operator.
--   
--   This ensures that each step of the fold is forced to Weak Head Normal
--   Form before being applied, avoiding the collection of thunks that
--   would otherwise occur. This is often what you want to strictly reduce
--   a finite structure to a single strict result (e.g. <a>sum</a>).
--   
--   For a general <a>Foldable</a> structure this should be semantically
--   identical to,
--   
--   <pre>
--   foldl' f z = <a>foldl'</a> f z . <a>toList</a>
--   </pre>
foldl' :: Foldable t => (b -> a -> b) -> b -> t a -> b

-- | A variant of <a>foldr</a> that has no base case, and thus may only be
--   applied to non-empty structures.
--   
--   This function is non-total and will raise a runtime exception if the
--   structure happens to be empty.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; foldr1 (+) [1..4]
--   10
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; foldr1 (+) []
--   Exception: Prelude.foldr1: empty list
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; foldr1 (+) Nothing
--   *** Exception: foldr1: empty structure
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; foldr1 (-) [1..4]
--   -2
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; foldr1 (&amp;&amp;) [True, False, True, True]
--   False
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; foldr1 (||) [False, False, True, True]
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; foldr1 (+) [1..]
--   * Hangs forever *
--   </pre>
foldr1 :: Foldable t => (a -> a -> a) -> t a -> a

-- | A variant of <a>foldl</a> that has no base case, and thus may only be
--   applied to non-empty structures.
--   
--   This function is non-total and will raise a runtime exception if the
--   structure happens to be empty.
--   
--   <pre>
--   <a>foldl1</a> f = <a>foldl1</a> f . <a>toList</a>
--   </pre>
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; foldl1 (+) [1..4]
--   10
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; foldl1 (+) []
--   *** Exception: Prelude.foldl1: empty list
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; foldl1 (+) Nothing
--   *** Exception: foldl1: empty structure
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; foldl1 (-) [1..4]
--   -8
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; foldl1 (&amp;&amp;) [True, False, True, True]
--   False
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; foldl1 (||) [False, False, True, True]
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; foldl1 (+) [1..]
--   * Hangs forever *
--   </pre>
foldl1 :: Foldable t => (a -> a -> a) -> t a -> a

-- | Test whether the structure is empty. The default implementation is
--   Left-associative and lazy in both the initial element and the
--   accumulator. Thus optimised for structures where the first element can
--   be accessed in constant time. Structures where this is not the case
--   should have a non-default implementation.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; null []
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; null [1]
--   False
--   </pre>
--   
--   <a>null</a> is expected to terminate even for infinite structures. The
--   default implementation terminates provided the structure is bounded on
--   the left (there is a leftmost element).
--   
--   <pre>
--   &gt;&gt;&gt; null [1..]
--   False
--   </pre>
null :: Foldable t => t a -> Bool

-- | Returns the size/length of a finite structure as an <a>Int</a>. The
--   default implementation just counts elements starting with the
--   leftmost. Instances for structures that can compute the element count
--   faster than via element-by-element counting, should provide a
--   specialised implementation.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; length []
--   0
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; length ['a', 'b', 'c']
--   3
--   
--   &gt;&gt;&gt; length [1..]
--   * Hangs forever *
--   </pre>
length :: Foldable t => t a -> Int

-- | Does the element occur in the structure?
--   
--   Note: <a>elem</a> is often used in infix form.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; 3 `elem` []
--   False
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; 3 `elem` [1,2]
--   False
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; 3 `elem` [1,2,3,4,5]
--   True
--   </pre>
--   
--   For infinite structures, the default implementation of <a>elem</a>
--   terminates if the sought-after value exists at a finite distance from
--   the left side of the structure:
--   
--   <pre>
--   &gt;&gt;&gt; 3 `elem` [1..]
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; 3 `elem` ([4..] ++ [3])
--   * Hangs forever *
--   </pre>
elem :: (Foldable t, Eq a) => a -> t a -> Bool

-- | The largest element of a non-empty structure.
--   
--   This function is non-total and will raise a runtime exception if the
--   structure happens to be empty. A structure that supports random access
--   and maintains its elements in order should provide a specialised
--   implementation to return the maximum in faster than linear time.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; maximum [1..10]
--   10
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; maximum []
--   *** Exception: Prelude.maximum: empty list
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; maximum Nothing
--   *** Exception: maximum: empty structure
--   </pre>
--   
--   WARNING: This function is partial for possibly-empty structures like
--   lists.
maximum :: (Foldable t, Ord a) => t a -> a

-- | The least element of a non-empty structure.
--   
--   This function is non-total and will raise a runtime exception if the
--   structure happens to be empty. A structure that supports random access
--   and maintains its elements in order should provide a specialised
--   implementation to return the minimum in faster than linear time.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; minimum [1..10]
--   1
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; minimum []
--   *** Exception: Prelude.minimum: empty list
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; minimum Nothing
--   *** Exception: minimum: empty structure
--   </pre>
--   
--   WARNING: This function is partial for possibly-empty structures like
--   lists.
minimum :: (Foldable t, Ord a) => t a -> a

-- | The <a>sum</a> function computes the sum of the numbers of a
--   structure.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; sum []
--   0
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; sum [42]
--   42
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; sum [1..10]
--   55
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; sum [4.1, 2.0, 1.7]
--   7.8
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; sum [1..]
--   * Hangs forever *
--   </pre>
sum :: (Foldable t, Num a) => t a -> a

-- | The <a>product</a> function computes the product of the numbers of a
--   structure.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; product []
--   1
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; product [42]
--   42
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; product [1..10]
--   3628800
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; product [4.1, 2.0, 1.7]
--   13.939999999999998
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; product [1..]
--   * Hangs forever *
--   </pre>
product :: (Foldable t, Num a) => t a -> a
infix 4 `elem`

-- | Functors representing data structures that can be transformed to
--   structures of the <i>same shape</i> by performing an
--   <a>Applicative</a> (or, therefore, <a>Monad</a>) action on each
--   element from left to right.
--   
--   A more detailed description of what <i>same shape</i> means, the
--   various methods, how traversals are constructed, and example advanced
--   use-cases can be found in the <b>Overview</b> section of
--   <a>Data.Traversable#overview</a>.
--   
--   For the class laws see the <b>Laws</b> section of
--   <a>Data.Traversable#laws</a>.
class (Functor t, Foldable t) => Traversable (t :: Type -> Type)

-- | Map each element of a structure to an action, evaluate these actions
--   from left to right, and collect the results. For a version that
--   ignores the results see <a>traverse_</a>.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   In the first two examples we show each evaluated action mapping to the
--   output structure.
--   
--   <pre>
--   &gt;&gt;&gt; traverse Just [1,2,3,4]
--   Just [1,2,3,4]
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; traverse id [Right 1, Right 2, Right 3, Right 4]
--   Right [1,2,3,4]
--   </pre>
--   
--   In the next examples, we show that <a>Nothing</a> and <a>Left</a>
--   values short circuit the created structure.
--   
--   <pre>
--   &gt;&gt;&gt; traverse (const Nothing) [1,2,3,4]
--   Nothing
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; traverse (\x -&gt; if odd x then Just x else Nothing)  [1,2,3,4]
--   Nothing
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; traverse id [Right 1, Right 2, Right 3, Right 4, Left 0]
--   Left 0
--   </pre>
traverse :: (Traversable t, Applicative f) => (a -> f b) -> t a -> f (t b)

-- | Evaluate each action in the structure from left to right, and collect
--   the results. For a version that ignores the results see
--   <a>sequenceA_</a>.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   For the first two examples we show sequenceA fully evaluating a a
--   structure and collecting the results.
--   
--   <pre>
--   &gt;&gt;&gt; sequenceA [Just 1, Just 2, Just 3]
--   Just [1,2,3]
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; sequenceA [Right 1, Right 2, Right 3]
--   Right [1,2,3]
--   </pre>
--   
--   The next two example show <a>Nothing</a> and <a>Just</a> will short
--   circuit the resulting structure if present in the input. For more
--   context, check the <a>Traversable</a> instances for <a>Either</a> and
--   <a>Maybe</a>.
--   
--   <pre>
--   &gt;&gt;&gt; sequenceA [Just 1, Just 2, Just 3, Nothing]
--   Nothing
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; sequenceA [Right 1, Right 2, Right 3, Left 4]
--   Left 4
--   </pre>
sequenceA :: (Traversable t, Applicative f) => t (f a) -> f (t a)

-- | Map each element of a structure to a monadic action, evaluate these
--   actions from left to right, and collect the results. For a version
--   that ignores the results see <a>mapM_</a>.
--   
--   <h4><b>Examples</b></h4>
--   
--   <a>mapM</a> is literally a <a>traverse</a> with a type signature
--   restricted to <a>Monad</a>. Its implementation may be more efficient
--   due to additional power of <a>Monad</a>.
mapM :: (Traversable t, Monad m) => (a -> m b) -> t a -> m (t b)

-- | Evaluate each monadic action in the structure from left to right, and
--   collect the results. For a version that ignores the results see
--   <a>sequence_</a>.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   The first two examples are instances where the input and and output of
--   <a>sequence</a> are isomorphic.
--   
--   <pre>
--   &gt;&gt;&gt; sequence $ Right [1,2,3,4]
--   [Right 1,Right 2,Right 3,Right 4]
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; sequence $ [Right 1,Right 2,Right 3,Right 4]
--   Right [1,2,3,4]
--   </pre>
--   
--   The following examples demonstrate short circuit behavior for
--   <a>sequence</a>.
--   
--   <pre>
--   &gt;&gt;&gt; sequence $ Left [1,2,3,4]
--   Left [1,2,3,4]
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; sequence $ [Left 0, Right 1,Right 2,Right 3,Right 4]
--   Left 0
--   </pre>
sequence :: (Traversable t, Monad m) => t (m a) -> m (t a)

-- | Representable types of kind <tt>*</tt>. This class is derivable in GHC
--   with the <tt>DeriveGeneric</tt> flag on.
--   
--   A <a>Generic</a> instance must satisfy the following laws:
--   
--   <pre>
--   <a>from</a> . <a>to</a> ≡ <a>id</a>
--   <a>to</a> . <a>from</a> ≡ <a>id</a>
--   </pre>
class Generic a

-- | The class of semigroups (types with an associative binary operation).
--   
--   Instances should satisfy the following:
--   
--   <ul>
--   <li><i>Associativity</i> <tt>x <a>&lt;&gt;</a> (y <a>&lt;&gt;</a> z) =
--   (x <a>&lt;&gt;</a> y) <a>&lt;&gt;</a> z</tt></li>
--   </ul>
class Semigroup a

-- | An associative operation.
--   
--   <pre>
--   &gt;&gt;&gt; [1,2,3] &lt;&gt; [4,5,6]
--   [1,2,3,4,5,6]
--   </pre>
(<>) :: Semigroup a => a -> a -> a

-- | Reduce a non-empty list with <a>&lt;&gt;</a>
--   
--   The default definition should be sufficient, but this can be
--   overridden for efficiency.
--   
--   <pre>
--   &gt;&gt;&gt; import Data.List.NonEmpty (NonEmpty (..))
--   
--   &gt;&gt;&gt; sconcat $ "Hello" :| [" ", "Haskell", "!"]
--   "Hello Haskell!"
--   </pre>
sconcat :: Semigroup a => NonEmpty a -> a

-- | Repeat a value <tt>n</tt> times.
--   
--   Given that this works on a <a>Semigroup</a> it is allowed to fail if
--   you request 0 or fewer repetitions, and the default definition will do
--   so.
--   
--   By making this a member of the class, idempotent semigroups and
--   monoids can upgrade this to execute in &lt;math&gt; by picking
--   <tt>stimes = <a>stimesIdempotent</a></tt> or <tt>stimes =
--   <a>stimesIdempotentMonoid</a></tt> respectively.
--   
--   <pre>
--   &gt;&gt;&gt; stimes 4 [1]
--   [1,1,1,1]
--   </pre>
stimes :: (Semigroup a, Integral b) => b -> a -> a
infixr 6 <>

-- | The class of monoids (types with an associative binary operation that
--   has an identity). Instances should satisfy the following:
--   
--   <ul>
--   <li><i>Right identity</i> <tt>x <a>&lt;&gt;</a> <a>mempty</a> =
--   x</tt></li>
--   <li><i>Left identity</i> <tt><a>mempty</a> <a>&lt;&gt;</a> x =
--   x</tt></li>
--   <li><i>Associativity</i> <tt>x <a>&lt;&gt;</a> (y <a>&lt;&gt;</a> z) =
--   (x <a>&lt;&gt;</a> y) <a>&lt;&gt;</a> z</tt> (<a>Semigroup</a>
--   law)</li>
--   <li><i>Concatenation</i> <tt><a>mconcat</a> = <a>foldr</a>
--   (<a>&lt;&gt;</a>) <a>mempty</a></tt></li>
--   </ul>
--   
--   The method names refer to the monoid of lists under concatenation, but
--   there are many other instances.
--   
--   Some types can be viewed as a monoid in more than one way, e.g. both
--   addition and multiplication on numbers. In such cases we often define
--   <tt>newtype</tt>s and make those instances of <a>Monoid</a>, e.g.
--   <a>Sum</a> and <a>Product</a>.
--   
--   <b>NOTE</b>: <a>Semigroup</a> is a superclass of <a>Monoid</a> since
--   <i>base-4.11.0.0</i>.
class Semigroup a => Monoid a

-- | Identity of <a>mappend</a>
--   
--   <pre>
--   &gt;&gt;&gt; "Hello world" &lt;&gt; mempty
--   "Hello world"
--   </pre>
mempty :: Monoid a => a

-- | An associative operation
--   
--   <b>NOTE</b>: This method is redundant and has the default
--   implementation <tt><a>mappend</a> = (<a>&lt;&gt;</a>)</tt> since
--   <i>base-4.11.0.0</i>. Should it be implemented manually, since
--   <a>mappend</a> is a synonym for (<a>&lt;&gt;</a>), it is expected that
--   the two functions are defined the same way. In a future GHC release
--   <a>mappend</a> will be removed from <a>Monoid</a>.
mappend :: Monoid a => a -> a -> a

-- | Fold a list using the monoid.
--   
--   For most types, the default definition for <a>mconcat</a> will be
--   used, but the function is included in the class definition so that an
--   optimized version can be provided for specific types.
--   
--   <pre>
--   &gt;&gt;&gt; mconcat ["Hello", " ", "Haskell", "!"]
--   "Hello Haskell!"
--   </pre>
mconcat :: Monoid a => [a] -> a

-- | Constraint representing the fact that the field <tt>x</tt> belongs to
--   the record type <tt>r</tt> and has field type <tt>a</tt>. This will be
--   solved automatically, but manual instances may be provided as well.
class HasField (x :: k) r a | x r -> a

-- | Selector function to extract the field from the record.
getField :: HasField x r a => r -> a
data Bool
False :: Bool
True :: Bool

-- | A <a>String</a> is a list of characters. String constants in Haskell
--   are values of type <a>String</a>.
--   
--   See <a>Data.List</a> for operations on lists.
type String = [Char]

-- | The character type <a>Char</a> is an enumeration whose values
--   represent Unicode (or equivalently ISO/IEC 10646) code points (i.e.
--   characters, see <a>http://www.unicode.org/</a> for details). This set
--   extends the ISO 8859-1 (Latin-1) character set (the first 256
--   characters), which is itself an extension of the ASCII character set
--   (the first 128 characters). A character literal in Haskell has type
--   <a>Char</a>.
--   
--   To convert a <a>Char</a> to or from the corresponding <a>Int</a> value
--   defined by Unicode, use <a>toEnum</a> and <a>fromEnum</a> from the
--   <a>Enum</a> class respectively (or equivalently <a>ord</a> and
--   <a>chr</a>).
data Char

-- | Double-precision floating point numbers. It is desirable that this
--   type be at least equal in range and precision to the IEEE
--   double-precision type.
data Double

-- | Single-precision floating point numbers. It is desirable that this
--   type be at least equal in range and precision to the IEEE
--   single-precision type.
data Float

-- | A fixed-precision integer type with at least the range <tt>[-2^29 ..
--   2^29-1]</tt>. The exact range for a given implementation can be
--   determined by using <a>minBound</a> and <a>maxBound</a> from the
--   <a>Bounded</a> class.
data Int

-- | 8-bit signed integer type
data Int8

-- | 16-bit signed integer type
data Int16

-- | 32-bit signed integer type
data Int32

-- | 64-bit signed integer type
data Int64

-- | Arbitrary precision integers. In contrast with fixed-size integral
--   types such as <a>Int</a>, the <a>Integer</a> type represents the
--   entire infinite range of integers.
--   
--   Integers are stored in a kind of sign-magnitude form, hence do not
--   expect two's complement form when using bit operations.
--   
--   If the value is small (fit into an <a>Int</a>), <a>IS</a> constructor
--   is used. Otherwise <a>Integer</a> and <a>IN</a> constructors are used
--   to store a <a>BigNat</a> representing respectively the positive or the
--   negative value magnitude.
--   
--   Invariant: <a>Integer</a> and <a>IN</a> are used iff value doesn't fit
--   in <a>IS</a>
data Integer

-- | Natural number
--   
--   Invariant: numbers &lt;= 0xffffffffffffffff use the <a>NS</a>
--   constructor
data Natural

-- | The <a>Maybe</a> type encapsulates an optional value. A value of type
--   <tt><a>Maybe</a> a</tt> either contains a value of type <tt>a</tt>
--   (represented as <tt><a>Just</a> a</tt>), or it is empty (represented
--   as <a>Nothing</a>). Using <a>Maybe</a> is a good way to deal with
--   errors or exceptional cases without resorting to drastic measures such
--   as <a>error</a>.
--   
--   The <a>Maybe</a> type is also a monad. It is a simple kind of error
--   monad, where all errors are represented by <a>Nothing</a>. A richer
--   error monad can be built using the <a>Either</a> type.
data Maybe a
Nothing :: Maybe a
Just :: a -> Maybe a
data Ordering
LT :: Ordering
EQ :: Ordering
GT :: Ordering

-- | Rational numbers, with numerator and denominator of some
--   <a>Integral</a> type.
--   
--   Note that <a>Ratio</a>'s instances inherit the deficiencies from the
--   type parameter's. For example, <tt>Ratio Natural</tt>'s <a>Num</a>
--   instance has similar problems to <a>Natural</a>'s.
data Ratio a

-- | Arbitrary-precision rational numbers, represented as a ratio of two
--   <a>Integer</a> values. A rational number may be constructed using the
--   <a>%</a> operator.
type Rational = Ratio Integer

-- | <tt>RealWorld</tt> is deeply magical. It is <i>primitive</i>, but it
--   is not <i>unlifted</i> (hence <tt>ptrArg</tt>). We never manipulate
--   values of type <tt>RealWorld</tt>; it's only used in the type system,
--   to parameterise <tt>State#</tt>.
data RealWorld

-- | A <i>stable pointer</i> is a reference to a Haskell expression that is
--   guaranteed not to be affected by garbage collection, i.e., it will
--   neither be deallocated nor will the value of the stable pointer itself
--   change during garbage collection (ordinary references may be relocated
--   during garbage collection). Consequently, stable pointers can be
--   passed to foreign code, which can treat it as an opaque reference to a
--   Haskell value.
--   
--   A value of type <tt>StablePtr a</tt> is a stable pointer to a Haskell
--   expression of type <tt>a</tt>.
data StablePtr a

-- | A value of type <tt><a>IO</a> a</tt> is a computation which, when
--   performed, does some I/O before returning a value of type <tt>a</tt>.
--   
--   There is really only one way to "perform" an I/O action: bind it to
--   <tt>Main.main</tt> in your program. When your program is run, the I/O
--   will be performed. It isn't possible to perform I/O from an arbitrary
--   function, unless that function is itself in the <a>IO</a> monad and
--   called at some point, directly or indirectly, from <tt>Main.main</tt>.
--   
--   <a>IO</a> is a monad, so <a>IO</a> actions can be combined using
--   either the do-notation or the <a>&gt;&gt;</a> and <a>&gt;&gt;=</a>
--   operations from the <a>Monad</a> class.
data IO a

-- | A <a>Word</a> is an unsigned integral type, with the same size as
--   <a>Int</a>.
data Word

-- | 8-bit unsigned integer type
data Word8

-- | 16-bit unsigned integer type
data Word16

-- | 32-bit unsigned integer type
data Word32

-- | 64-bit unsigned integer type
data Word64

-- | A value of type <tt><a>Ptr</a> a</tt> represents a pointer to an
--   object, or an array of objects, which may be marshalled to or from
--   Haskell values of type <tt>a</tt>.
--   
--   The type <tt>a</tt> will often be an instance of class <a>Storable</a>
--   which provides the marshalling operations. However this is not
--   essential, and you can provide your own operations to access the
--   pointer. For example you might write small foreign functions to get or
--   set the fields of a C <tt>struct</tt>.
data Ptr a

-- | A value of type <tt><a>FunPtr</a> a</tt> is a pointer to a function
--   callable from foreign code. The type <tt>a</tt> will normally be a
--   <i>foreign type</i>, a function type with zero or more arguments where
--   
--   <ul>
--   <li>the argument types are <i>marshallable foreign types</i>, i.e.
--   <a>Char</a>, <a>Int</a>, <a>Double</a>, <a>Float</a>, <a>Bool</a>,
--   <a>Int8</a>, <a>Int16</a>, <a>Int32</a>, <a>Int64</a>, <a>Word8</a>,
--   <a>Word16</a>, <a>Word32</a>, <a>Word64</a>, <tt><a>Ptr</a> a</tt>,
--   <tt><a>FunPtr</a> a</tt>, <tt><a>StablePtr</a> a</tt> or a renaming of
--   any of these using <tt>newtype</tt>.</li>
--   <li>the return type is either a marshallable foreign type or has the
--   form <tt><a>IO</a> t</tt> where <tt>t</tt> is a marshallable foreign
--   type or <tt>()</tt>.</li>
--   </ul>
--   
--   A value of type <tt><a>FunPtr</a> a</tt> may be a pointer to a foreign
--   function, either returned by another foreign function or imported with
--   a a static address import like
--   
--   <pre>
--   foreign import ccall "stdlib.h &amp;free"
--     p_free :: FunPtr (Ptr a -&gt; IO ())
--   </pre>
--   
--   or a pointer to a Haskell function created using a <i>wrapper</i> stub
--   declared to produce a <a>FunPtr</a> of the correct type. For example:
--   
--   <pre>
--   type Compare = Int -&gt; Int -&gt; Bool
--   foreign import ccall "wrapper"
--     mkCompare :: Compare -&gt; IO (FunPtr Compare)
--   </pre>
--   
--   Calls to wrapper stubs like <tt>mkCompare</tt> allocate storage, which
--   should be released with <a>freeHaskellFunPtr</a> when no longer
--   required.
--   
--   To convert <a>FunPtr</a> values to corresponding Haskell functions,
--   one can define a <i>dynamic</i> stub for the specific foreign type,
--   e.g.
--   
--   <pre>
--   type IntFunction = CInt -&gt; IO ()
--   foreign import ccall "dynamic"
--     mkFun :: FunPtr IntFunction -&gt; IntFunction
--   </pre>
data FunPtr a

-- | The <a>Either</a> type represents values with two possibilities: a
--   value of type <tt><a>Either</a> a b</tt> is either <tt><a>Left</a>
--   a</tt> or <tt><a>Right</a> b</tt>.
--   
--   The <a>Either</a> type is sometimes used to represent a value which is
--   either correct or an error; by convention, the <a>Left</a> constructor
--   is used to hold an error value and the <a>Right</a> constructor is
--   used to hold a correct value (mnemonic: "right" also means "correct").
--   
--   <h4><b>Examples</b></h4>
--   
--   The type <tt><a>Either</a> <a>String</a> <a>Int</a></tt> is the type
--   of values which can be either a <a>String</a> or an <a>Int</a>. The
--   <a>Left</a> constructor can be used only on <a>String</a>s, and the
--   <a>Right</a> constructor can be used only on <a>Int</a>s:
--   
--   <pre>
--   &gt;&gt;&gt; let s = Left "foo" :: Either String Int
--   
--   &gt;&gt;&gt; s
--   Left "foo"
--   
--   &gt;&gt;&gt; let n = Right 3 :: Either String Int
--   
--   &gt;&gt;&gt; n
--   Right 3
--   
--   &gt;&gt;&gt; :type s
--   s :: Either String Int
--   
--   &gt;&gt;&gt; :type n
--   n :: Either String Int
--   </pre>
--   
--   The <a>fmap</a> from our <a>Functor</a> instance will ignore
--   <a>Left</a> values, but will apply the supplied function to values
--   contained in a <a>Right</a>:
--   
--   <pre>
--   &gt;&gt;&gt; let s = Left "foo" :: Either String Int
--   
--   &gt;&gt;&gt; let n = Right 3 :: Either String Int
--   
--   &gt;&gt;&gt; fmap (*2) s
--   Left "foo"
--   
--   &gt;&gt;&gt; fmap (*2) n
--   Right 6
--   </pre>
--   
--   The <a>Monad</a> instance for <a>Either</a> allows us to chain
--   together multiple actions which may fail, and fail overall if any of
--   the individual steps failed. First we'll write a function that can
--   either parse an <a>Int</a> from a <a>Char</a>, or fail.
--   
--   <pre>
--   &gt;&gt;&gt; import Data.Char ( digitToInt, isDigit )
--   
--   &gt;&gt;&gt; :{
--       let parseEither :: Char -&gt; Either String Int
--           parseEither c
--             | isDigit c = Right (digitToInt c)
--             | otherwise = Left "parse error"
--   
--   &gt;&gt;&gt; :}
--   </pre>
--   
--   The following should work, since both <tt>'1'</tt> and <tt>'2'</tt>
--   can be parsed as <a>Int</a>s.
--   
--   <pre>
--   &gt;&gt;&gt; :{
--       let parseMultiple :: Either String Int
--           parseMultiple = do
--             x &lt;- parseEither '1'
--             y &lt;- parseEither '2'
--             return (x + y)
--   
--   &gt;&gt;&gt; :}
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; parseMultiple
--   Right 3
--   </pre>
--   
--   But the following should fail overall, since the first operation where
--   we attempt to parse <tt>'m'</tt> as an <a>Int</a> will fail:
--   
--   <pre>
--   &gt;&gt;&gt; :{
--       let parseMultiple :: Either String Int
--           parseMultiple = do
--             x &lt;- parseEither 'm'
--             y &lt;- parseEither '2'
--             return (x + y)
--   
--   &gt;&gt;&gt; :}
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; parseMultiple
--   Left "parse error"
--   </pre>
data Either a b
Left :: a -> Either a b
Right :: b -> Either a b

-- | Non-empty (and non-strict) list type.
data NonEmpty a
(:|) :: a -> [a] -> NonEmpty a
infixr 5 :|

-- | <tt>Coercible</tt> is a two-parameter class that has instances for
--   types <tt>a</tt> and <tt>b</tt> if the compiler can infer that they
--   have the same representation. This class does not have regular
--   instances; instead they are created on-the-fly during type-checking.
--   Trying to manually declare an instance of <tt>Coercible</tt> is an
--   error.
--   
--   Nevertheless one can pretend that the following three kinds of
--   instances exist. First, as a trivial base-case:
--   
--   <pre>
--   instance Coercible a a
--   </pre>
--   
--   Furthermore, for every type constructor there is an instance that
--   allows to coerce under the type constructor. For example, let
--   <tt>D</tt> be a prototypical type constructor (<tt>data</tt> or
--   <tt>newtype</tt>) with three type arguments, which have roles
--   <tt>nominal</tt>, <tt>representational</tt> resp. <tt>phantom</tt>.
--   Then there is an instance of the form
--   
--   <pre>
--   instance Coercible b b' =&gt; Coercible (D a b c) (D a b' c')
--   </pre>
--   
--   Note that the <tt>nominal</tt> type arguments are equal, the
--   <tt>representational</tt> type arguments can differ, but need to have
--   a <tt>Coercible</tt> instance themself, and the <tt>phantom</tt> type
--   arguments can be changed arbitrarily.
--   
--   The third kind of instance exists for every <tt>newtype NT = MkNT
--   T</tt> and comes in two variants, namely
--   
--   <pre>
--   instance Coercible a T =&gt; Coercible a NT
--   </pre>
--   
--   <pre>
--   instance Coercible T b =&gt; Coercible NT b
--   </pre>
--   
--   This instance is only usable if the constructor <tt>MkNT</tt> is in
--   scope.
--   
--   If, as a library author of a type constructor like <tt>Set a</tt>, you
--   want to prevent a user of your module to write <tt>coerce :: Set T
--   -&gt; Set NT</tt>, you need to set the role of <tt>Set</tt>'s type
--   parameter to <tt>nominal</tt>, by writing
--   
--   <pre>
--   type role Set nominal
--   </pre>
--   
--   For more details about this feature, please refer to <a>Safe
--   Coercions</a> by Joachim Breitner, Richard A. Eisenberg, Simon Peyton
--   Jones and Stephanie Weirich.
class a ~R# b => Coercible (a :: k) (b :: k)

-- | This type is treated magically within GHC. Any pattern match of the
--   form <tt>case unsafeEqualityProof of UnsafeRefl -&gt; body</tt> gets
--   transformed just into <tt>body</tt>. This is ill-typed, but the
--   transformation takes place after type-checking is complete. It is used
--   to implement <a>unsafeCoerce</a>. You probably don't want to use
--   <a>UnsafeRefl</a> in an expression, but you might conceivably want to
--   pattern-match on it. Use <a>unsafeEqualityProof</a> to create one of
--   these.
data UnsafeEquality (a :: k) (b :: k)
[UnsafeRefl] :: forall {k} (a :: k). UnsafeEquality a a
data TyCon

-- | Promote a function to a monad.
liftM :: Monad m => (a1 -> r) -> m a1 -> m r

-- | Dual function arrows.
newtype Op a b
Op :: (b -> a) -> Op a b
[getOp] :: Op a b -> b -> a

-- | Case analysis for the <a>Either</a> type. If the value is
--   <tt><a>Left</a> a</tt>, apply the first function to <tt>a</tt>; if it
--   is <tt><a>Right</a> b</tt>, apply the second function to <tt>b</tt>.
--   
--   <h4><b>Examples</b></h4>
--   
--   We create two values of type <tt><a>Either</a> <a>String</a>
--   <a>Int</a></tt>, one using the <a>Left</a> constructor and another
--   using the <a>Right</a> constructor. Then we apply "either" the
--   <a>length</a> function (if we have a <a>String</a>) or the "times-two"
--   function (if we have an <a>Int</a>):
--   
--   <pre>
--   &gt;&gt;&gt; let s = Left "foo" :: Either String Int
--   
--   &gt;&gt;&gt; let n = Right 3 :: Either String Int
--   
--   &gt;&gt;&gt; either length (*2) s
--   3
--   
--   &gt;&gt;&gt; either length (*2) n
--   6
--   </pre>
either :: (a -> c) -> (b -> c) -> Either a b -> c

-- | The class of contravariant functors.
--   
--   Whereas in Haskell, one can think of a <a>Functor</a> as containing or
--   producing values, a contravariant functor is a functor that can be
--   thought of as <i>consuming</i> values.
--   
--   As an example, consider the type of predicate functions <tt>a -&gt;
--   Bool</tt>. One such predicate might be <tt>negative x = x &lt; 0</tt>,
--   which classifies integers as to whether they are negative. However,
--   given this predicate, we can re-use it in other situations, providing
--   we have a way to map values <i>to</i> integers. For instance, we can
--   use the <tt>negative</tt> predicate on a person's bank balance to work
--   out if they are currently overdrawn:
--   
--   <pre>
--   newtype Predicate a = Predicate { getPredicate :: a -&gt; Bool }
--   
--   instance Contravariant Predicate where
--     contramap :: (a' -&gt; a) -&gt; (Predicate a -&gt; Predicate a')
--     contramap f (Predicate p) = Predicate (p . f)
--                                            |   `- First, map the input...
--                                            `----- then apply the predicate.
--   
--   overdrawn :: Predicate Person
--   overdrawn = contramap personBankBalance negative
--   </pre>
--   
--   Any instance should be subject to the following laws:
--   
--   <ul>
--   <li><i>Identity</i> <tt><a>contramap</a> <a>id</a> =
--   <a>id</a></tt></li>
--   <li><i>Composition</i> <tt><a>contramap</a> (g . f) = <a>contramap</a>
--   f . <a>contramap</a> g</tt></li>
--   </ul>
--   
--   Note, that the second law follows from the free theorem of the type of
--   <a>contramap</a> and the first law, so you need only check that the
--   former condition holds.
class Contravariant (f :: Type -> Type)
contramap :: Contravariant f => (a' -> a) -> f a -> f a'

-- | Replace all locations in the output with the same value. The default
--   definition is <tt><a>contramap</a> . <a>const</a></tt>, but this may
--   be overridden with a more efficient version.
(>$) :: Contravariant f => b -> f b -> f a
infixl 4 >$

-- | See examples in <a>Control.Monad.Reader</a>. Note, the partially
--   applied function type <tt>(-&gt;) r</tt> is a simple reader monad. See
--   the <tt>instance</tt> declaration below.
class Monad m => MonadReader r (m :: Type -> Type) | m -> r

-- | Retrieves the monad environment.
ask :: MonadReader r m => m r

-- | Executes a computation in a modified environment.
local :: MonadReader r m => (r -> r) -> m a -> m a

-- | Retrieves a function of the current environment.
reader :: MonadReader r m => (r -> a) -> m a

-- | Minimal definition is either both of <tt>get</tt> and <tt>put</tt> or
--   just <tt>state</tt>
class Monad m => MonadState s (m :: Type -> Type) | m -> s

-- | Return the state from the internals of the monad.
get :: MonadState s m => m s

-- | Replace the state inside the monad.
put :: MonadState s m => s -> m ()

-- | Embed a simple state action into the monad.
state :: MonadState s m => (s -> (a, s)) -> m a

-- | The type <a>ForeignPtr</a> represents references to objects that are
--   maintained in a foreign language, i.e., that are not part of the data
--   structures usually managed by the Haskell storage manager. The
--   essential difference between <a>ForeignPtr</a>s and vanilla memory
--   references of type <tt>Ptr a</tt> is that the former may be associated
--   with <i>finalizers</i>. A finalizer is a routine that is invoked when
--   the Haskell storage manager detects that - within the Haskell heap and
--   stack - there are no more references left that are pointing to the
--   <a>ForeignPtr</a>. Typically, the finalizer will, then, invoke
--   routines in the foreign language that free the resources bound by the
--   foreign object.
--   
--   The <a>ForeignPtr</a> is parameterised in the same way as <a>Ptr</a>.
--   The type argument of <a>ForeignPtr</a> should normally be an instance
--   of class <a>Storable</a>.
data ForeignPtr a

-- | Haskell defines operations to read and write characters from and to
--   files, represented by values of type <tt>Handle</tt>. Each value of
--   this type is a <i>handle</i>: a record used by the Haskell run-time
--   system to <i>manage</i> I/O with file system objects. A handle has at
--   least the following properties:
--   
--   <ul>
--   <li>whether it manages input or output or both;</li>
--   <li>whether it is <i>open</i>, <i>closed</i> or
--   <i>semi-closed</i>;</li>
--   <li>whether the object is seekable;</li>
--   <li>whether buffering is disabled, or enabled on a line or block
--   basis;</li>
--   <li>a buffer (whose length may be zero).</li>
--   </ul>
--   
--   Most handles will also have a current I/O position indicating where
--   the next input or output operation will occur. A handle is
--   <i>readable</i> if it manages only input or both input and output;
--   likewise, it is <i>writable</i> if it manages only output or both
--   input and output. A handle is <i>open</i> when first allocated. Once
--   it is closed it can no longer be used for either input or output,
--   though an implementation cannot re-use its storage while references
--   remain to it. Handles are in the <a>Show</a> and <a>Eq</a> classes.
--   The string produced by showing a handle is system dependent; it should
--   include enough information to identify the handle for debugging. A
--   handle is equal according to <a>==</a> only to itself; no attempt is
--   made to compare the internal state of different handles for equality.
data Handle

-- | The strict <a>ST</a> monad. The <a>ST</a> monad allows for destructive
--   updates, but is escapable (unlike IO). A computation of type
--   <tt><a>ST</a> s a</tt> returns a value of type <tt>a</tt>, and execute
--   in "thread" <tt>s</tt>. The <tt>s</tt> parameter is either
--   
--   <ul>
--   <li>an uninstantiated type variable (inside invocations of
--   <a>runST</a>), or</li>
--   <li><a>RealWorld</a> (inside invocations of <a>stToIO</a>).</li>
--   </ul>
--   
--   It serves to keep the internal states of different invocations of
--   <a>runST</a> separate from each other and from invocations of
--   <a>stToIO</a>.
--   
--   The <a>&gt;&gt;=</a> and <a>&gt;&gt;</a> operations are strict in the
--   state (though not in values stored in the state). For example,
--   
--   <pre>
--   <a>runST</a> (writeSTRef _|_ v &gt;&gt;= f) = _|_
--   </pre>
data ST s a
newtype Predicate a
Predicate :: (a -> Bool) -> Predicate a
[getPredicate] :: Predicate a -> a -> Bool

-- | This data type represents an equivalence relation.
--   
--   Equivalence relations are expected to satisfy three laws:
--   
--   <ul>
--   <li><i>Reflexivity</i> <tt><a>getEquivalence</a> f a a =
--   True</tt></li>
--   <li><i>Symmetry</i> <tt><a>getEquivalence</a> f a b =
--   <a>getEquivalence</a> f b a</tt></li>
--   <li><i>Transitivity</i> If <tt><a>getEquivalence</a> f a b</tt> and
--   <tt><a>getEquivalence</a> f b c</tt> are both <a>True</a> then so is
--   <tt><a>getEquivalence</a> f a c</tt>.</li>
--   </ul>
--   
--   The types alone do not enforce these laws, so you'll have to check
--   them yourself.
newtype Equivalence a
Equivalence :: (a -> a -> Bool) -> Equivalence a
[getEquivalence] :: Equivalence a -> a -> a -> Bool

-- | Defines a total ordering on a type as per <a>compare</a>.
--   
--   This condition is not checked by the types. You must ensure that the
--   supplied values are valid total orderings yourself.
newtype Comparison a
Comparison :: (a -> a -> Ordering) -> Comparison a
[getComparison] :: Comparison a -> a -> a -> Ordering

-- | If <tt>f</tt> is both <a>Functor</a> and <a>Contravariant</a> then by
--   the time you factor in the laws of each of those classes, it can't
--   actually use its argument in any meaningful capacity.
--   
--   This method is surprisingly useful. Where both instances exist and are
--   lawful we have the following laws:
--   
--   <pre>
--   <a>fmap</a>      f ≡ <a>phantom</a>
--   <a>contramap</a> f ≡ <a>phantom</a>
--   </pre>
phantom :: (Functor f, Contravariant f) => f a -> f b

-- | Check for equivalence with <a>==</a>.
--   
--   Note: The instances for <a>Double</a> and <a>Float</a> violate
--   reflexivity for <tt>NaN</tt>.
defaultEquivalence :: Eq a => Equivalence a

-- | Compare using <a>compare</a>.
defaultComparison :: Ord a => Comparison a
comparisonEquivalence :: Comparison a -> Equivalence a

-- | This is an infix alias for <a>contramap</a>.
(>$<) :: Contravariant f => (a -> b) -> f b -> f a
infixl 4 >$<

-- | This is an infix version of <a>contramap</a> with the arguments
--   flipped.
(>$$<) :: Contravariant f => f b -> (a -> b) -> f a
infixl 4 >$$<

-- | This is <a>&gt;$</a> with its arguments flipped.
($<) :: Contravariant f => f b -> b -> f a
infixl 4 $<

-- | Right-to-left composition of functors. The composition of applicative
--   functors is always applicative, but the composition of monads is not
--   always a monad.
newtype Compose (f :: k -> Type) (g :: k1 -> k) (a :: k1)
Compose :: f (g a) -> Compose (f :: k -> Type) (g :: k1 -> k) (a :: k1)
[getCompose] :: Compose (f :: k -> Type) (g :: k1 -> k) (a :: k1) -> f (g a)
infixr 9 `Compose`
infixr 9 `Compose`

-- | Lifting of the <a>Show</a> class to binary type constructors.
class Show2 (f :: TYPE LiftedRep -> TYPE LiftedRep -> TYPE LiftedRep)

-- | <a>showsPrec</a> function for an application of the type constructor
--   based on <a>showsPrec</a> and <a>showList</a> functions for the
--   argument types.
liftShowsPrec2 :: Show2 f => (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> f a b -> ShowS

-- | <a>showList</a> function for an application of the type constructor
--   based on <a>showsPrec</a> and <a>showList</a> functions for the
--   argument types. The default implementation using standard list syntax
--   is correct for most types.
liftShowList2 :: Show2 f => (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [f a b] -> ShowS

-- | Lifting of the <a>Show</a> class to unary type constructors.
class Show1 (f :: TYPE LiftedRep -> TYPE LiftedRep)

-- | <a>showsPrec</a> function for an application of the type constructor
--   based on <a>showsPrec</a> and <a>showList</a> functions for the
--   argument type.
liftShowsPrec :: Show1 f => (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> f a -> ShowS

-- | <a>showList</a> function for an application of the type constructor
--   based on <a>showsPrec</a> and <a>showList</a> functions for the
--   argument type. The default implementation using standard list syntax
--   is correct for most types.
liftShowList :: Show1 f => (Int -> a -> ShowS) -> ([a] -> ShowS) -> [f a] -> ShowS

-- | Lifting of the <a>Read</a> class to binary type constructors.
--   
--   Both <a>liftReadsPrec2</a> and <a>liftReadPrec2</a> exist to match the
--   interface provided in the <a>Read</a> type class, but it is
--   recommended to implement <a>Read2</a> instances using
--   <a>liftReadPrec2</a> as opposed to <a>liftReadsPrec2</a>, since the
--   former is more efficient than the latter. For example:
--   
--   <pre>
--   instance <a>Read2</a> T where
--     <a>liftReadPrec2</a>     = ...
--     <a>liftReadListPrec2</a> = <a>liftReadListPrec2Default</a>
--   </pre>
--   
--   For more information, refer to the documentation for the <a>Read</a>
--   class.
class Read2 (f :: Type -> Type -> Type)

-- | <a>readsPrec</a> function for an application of the type constructor
--   based on <a>readsPrec</a> and <a>readList</a> functions for the
--   argument types.
liftReadsPrec2 :: Read2 f => (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (f a b)

-- | <a>readList</a> function for an application of the type constructor
--   based on <a>readsPrec</a> and <a>readList</a> functions for the
--   argument types. The default implementation using standard list syntax
--   is correct for most types.
liftReadList2 :: Read2 f => (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [f a b]

-- | <a>readPrec</a> function for an application of the type constructor
--   based on <a>readPrec</a> and <a>readListPrec</a> functions for the
--   argument types.
liftReadPrec2 :: Read2 f => ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (f a b)

-- | <a>readListPrec</a> function for an application of the type
--   constructor based on <a>readPrec</a> and <a>readListPrec</a> functions
--   for the argument types.
--   
--   The default definition uses <a>liftReadList2</a>. Instances that
--   define <a>liftReadPrec2</a> should also define
--   <a>liftReadListPrec2</a> as <a>liftReadListPrec2Default</a>.
liftReadListPrec2 :: Read2 f => ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [f a b]

-- | Lifting of the <a>Read</a> class to unary type constructors.
--   
--   Both <a>liftReadsPrec</a> and <a>liftReadPrec</a> exist to match the
--   interface provided in the <a>Read</a> type class, but it is
--   recommended to implement <a>Read1</a> instances using
--   <a>liftReadPrec</a> as opposed to <a>liftReadsPrec</a>, since the
--   former is more efficient than the latter. For example:
--   
--   <pre>
--   instance <a>Read1</a> T where
--     <a>liftReadPrec</a>     = ...
--     <a>liftReadListPrec</a> = <a>liftReadListPrecDefault</a>
--   </pre>
--   
--   For more information, refer to the documentation for the <a>Read</a>
--   class.
class Read1 (f :: Type -> Type)

-- | <a>readsPrec</a> function for an application of the type constructor
--   based on <a>readsPrec</a> and <a>readList</a> functions for the
--   argument type.
liftReadsPrec :: Read1 f => (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (f a)

-- | <a>readList</a> function for an application of the type constructor
--   based on <a>readsPrec</a> and <a>readList</a> functions for the
--   argument type. The default implementation using standard list syntax
--   is correct for most types.
liftReadList :: Read1 f => (Int -> ReadS a) -> ReadS [a] -> ReadS [f a]

-- | <a>readPrec</a> function for an application of the type constructor
--   based on <a>readPrec</a> and <a>readListPrec</a> functions for the
--   argument type.
liftReadPrec :: Read1 f => ReadPrec a -> ReadPrec [a] -> ReadPrec (f a)

-- | <a>readListPrec</a> function for an application of the type
--   constructor based on <a>readPrec</a> and <a>readListPrec</a> functions
--   for the argument type.
--   
--   The default definition uses <a>liftReadList</a>. Instances that define
--   <a>liftReadPrec</a> should also define <a>liftReadListPrec</a> as
--   <a>liftReadListPrecDefault</a>.
liftReadListPrec :: Read1 f => ReadPrec a -> ReadPrec [a] -> ReadPrec [f a]

-- | Lifting of the <a>Ord</a> class to binary type constructors.
class Eq2 f => Ord2 (f :: Type -> Type -> Type)

-- | Lift <a>compare</a> functions through the type constructor.
--   
--   The function will usually be applied to comparison functions, but the
--   more general type ensures that the implementation uses them to compare
--   elements of the first container with elements of the second.
liftCompare2 :: Ord2 f => (a -> b -> Ordering) -> (c -> d -> Ordering) -> f a c -> f b d -> Ordering

-- | Lifting of the <a>Ord</a> class to unary type constructors.
class Eq1 f => Ord1 (f :: Type -> Type)

-- | Lift a <a>compare</a> function through the type constructor.
--   
--   The function will usually be applied to a comparison function, but the
--   more general type ensures that the implementation uses it to compare
--   elements of the first container with elements of the second.
liftCompare :: Ord1 f => (a -> b -> Ordering) -> f a -> f b -> Ordering

-- | Lifting of the <a>Eq</a> class to binary type constructors.
class Eq2 (f :: Type -> Type -> Type)

-- | Lift equality tests through the type constructor.
--   
--   The function will usually be applied to equality functions, but the
--   more general type ensures that the implementation uses them to compare
--   elements of the first container with elements of the second.
liftEq2 :: Eq2 f => (a -> b -> Bool) -> (c -> d -> Bool) -> f a c -> f b d -> Bool

-- | Lifting of the <a>Eq</a> class to unary type constructors.
class Eq1 (f :: Type -> Type)

-- | Lift an equality test through the type constructor.
--   
--   The function will usually be applied to an equality function, but the
--   more general type ensures that the implementation uses it to compare
--   elements of the first container with elements of the second.
liftEq :: Eq1 f => (a -> b -> Bool) -> f a -> f b -> Bool

-- | <tt><a>showsUnaryWith</a> sp n d x</tt> produces the string
--   representation of a unary data constructor with name <tt>n</tt> and
--   argument <tt>x</tt>, in precedence context <tt>d</tt>.
showsUnaryWith :: (Int -> a -> ShowS) -> String -> Int -> a -> ShowS

-- | <tt><a>showsUnary1</a> n d x</tt> produces the string representation
--   of a unary data constructor with name <tt>n</tt> and argument
--   <tt>x</tt>, in precedence context <tt>d</tt>.
showsUnary1 :: (Show1 f, Show a) => String -> Int -> f a -> ShowS

-- | <tt><a>showsUnary</a> n d x</tt> produces the string representation of
--   a unary data constructor with name <tt>n</tt> and argument <tt>x</tt>,
--   in precedence context <tt>d</tt>.
showsUnary :: Show a => String -> Int -> a -> ShowS

-- | Lift the standard <a>showsPrec</a> function through the type
--   constructor.
showsPrec2 :: (Show2 f, Show a, Show b) => Int -> f a b -> ShowS

-- | Lift the standard <a>showsPrec</a> and <a>showList</a> functions
--   through the type constructor.
showsPrec1 :: (Show1 f, Show a) => Int -> f a -> ShowS

-- | <tt><a>showsBinaryWith</a> sp1 sp2 n d x y</tt> produces the string
--   representation of a binary data constructor with name <tt>n</tt> and
--   arguments <tt>x</tt> and <tt>y</tt>, in precedence context <tt>d</tt>.
showsBinaryWith :: (Int -> a -> ShowS) -> (Int -> b -> ShowS) -> String -> Int -> a -> b -> ShowS

-- | <tt><a>showsBinary1</a> n d x y</tt> produces the string
--   representation of a binary data constructor with name <tt>n</tt> and
--   arguments <tt>x</tt> and <tt>y</tt>, in precedence context <tt>d</tt>.
showsBinary1 :: (Show1 f, Show1 g, Show a) => String -> Int -> f a -> g a -> ShowS

-- | <tt><a>readsUnaryWith</a> rp n c n'</tt> matches the name of a unary
--   data constructor and then parses its argument using <tt>rp</tt>.
readsUnaryWith :: (Int -> ReadS a) -> String -> (a -> t) -> String -> ReadS t

-- | <tt><a>readsUnary1</a> n c n'</tt> matches the name of a unary data
--   constructor and then parses its argument using <a>readsPrec1</a>.
readsUnary1 :: (Read1 f, Read a) => String -> (f a -> t) -> String -> ReadS t

-- | <tt><a>readsUnary</a> n c n'</tt> matches the name of a unary data
--   constructor and then parses its argument using <a>readsPrec</a>.
readsUnary :: Read a => String -> (a -> t) -> String -> ReadS t

-- | Lift the standard <a>readsPrec</a> function through the type
--   constructor.
readsPrec2 :: (Read2 f, Read a, Read b) => Int -> ReadS (f a b)

-- | Lift the standard <a>readsPrec</a> and <a>readList</a> functions
--   through the type constructor.
readsPrec1 :: (Read1 f, Read a) => Int -> ReadS (f a)

-- | <tt><a>readsData</a> p d</tt> is a parser for datatypes where each
--   alternative begins with a data constructor. It parses the constructor
--   and passes it to <tt>p</tt>. Parsers for various constructors can be
--   constructed with <a>readsUnary</a>, <a>readsUnary1</a> and
--   <a>readsBinary1</a>, and combined with <tt>mappend</tt> from the
--   <tt>Monoid</tt> class.
readsData :: (String -> ReadS a) -> Int -> ReadS a

-- | <tt><a>readsBinaryWith</a> rp1 rp2 n c n'</tt> matches the name of a
--   binary data constructor and then parses its arguments using
--   <tt>rp1</tt> and <tt>rp2</tt> respectively.
readsBinaryWith :: (Int -> ReadS a) -> (Int -> ReadS b) -> String -> (a -> b -> t) -> String -> ReadS t

-- | <tt><a>readsBinary1</a> n c n'</tt> matches the name of a binary data
--   constructor and then parses its arguments using <a>readsPrec1</a>.
readsBinary1 :: (Read1 f, Read1 g, Read a) => String -> (f a -> g a -> t) -> String -> ReadS t

-- | <tt><a>readUnaryWith</a> rp n c'</tt> matches the name of a unary data
--   constructor and then parses its argument using <tt>rp</tt>.
readUnaryWith :: ReadPrec a -> String -> (a -> t) -> ReadPrec t

-- | Lift the standard <a>readPrec</a> function through the type
--   constructor.
readPrec2 :: (Read2 f, Read a, Read b) => ReadPrec (f a b)

-- | Lift the standard <a>readPrec</a> and <a>readListPrec</a> functions
--   through the type constructor.
readPrec1 :: (Read1 f, Read a) => ReadPrec (f a)

-- | <tt><a>readData</a> p</tt> is a parser for datatypes where each
--   alternative begins with a data constructor. It parses the constructor
--   and passes it to <tt>p</tt>. Parsers for various constructors can be
--   constructed with <a>readUnaryWith</a> and <a>readBinaryWith</a>, and
--   combined with <a>(&lt;|&gt;)</a> from the <a>Alternative</a> class.
readData :: ReadPrec a -> ReadPrec a

-- | <tt><a>readBinaryWith</a> rp1 rp2 n c'</tt> matches the name of a
--   binary data constructor and then parses its arguments using
--   <tt>rp1</tt> and <tt>rp2</tt> respectively.
readBinaryWith :: ReadPrec a -> ReadPrec b -> String -> (a -> b -> t) -> ReadPrec t

-- | A possible replacement definition for the <a>liftReadListPrec</a>
--   method, defined using <a>liftReadPrec</a>.
liftReadListPrecDefault :: Read1 f => ReadPrec a -> ReadPrec [a] -> ReadPrec [f a]

-- | A possible replacement definition for the <a>liftReadListPrec2</a>
--   method, defined using <a>liftReadPrec2</a>.
liftReadListPrec2Default :: Read2 f => ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [f a b]

-- | A possible replacement definition for the <a>liftReadList</a> method.
--   This is only needed for <a>Read1</a> instances where
--   <a>liftReadListPrec</a> isn't defined as
--   <a>liftReadListPrecDefault</a>.
liftReadListDefault :: Read1 f => (Int -> ReadS a) -> ReadS [a] -> ReadS [f a]

-- | A possible replacement definition for the <a>liftReadList2</a> method.
--   This is only needed for <a>Read2</a> instances where
--   <a>liftReadListPrec2</a> isn't defined as
--   <a>liftReadListPrec2Default</a>.
liftReadList2Default :: Read2 f => (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [f a b]

-- | Lift the standard <tt>(<a>==</a>)</tt> function through the type
--   constructor.
eq2 :: (Eq2 f, Eq a, Eq b) => f a b -> f a b -> Bool

-- | Lift the standard <tt>(<a>==</a>)</tt> function through the type
--   constructor.
eq1 :: (Eq1 f, Eq a) => f a -> f a -> Bool

-- | Lift the standard <a>compare</a> function through the type
--   constructor.
compare2 :: (Ord2 f, Ord a, Ord b) => f a b -> f a b -> Ordering

-- | Lift the standard <a>compare</a> function through the type
--   constructor.
compare1 :: (Ord1 f, Ord a) => f a -> f a -> Ordering

-- | Complex numbers are an algebraic type.
--   
--   For a complex number <tt>z</tt>, <tt><a>abs</a> z</tt> is a number
--   with the magnitude of <tt>z</tt>, but oriented in the positive real
--   direction, whereas <tt><a>signum</a> z</tt> has the phase of
--   <tt>z</tt>, but unit magnitude.
--   
--   The <a>Foldable</a> and <a>Traversable</a> instances traverse the real
--   part first.
--   
--   Note that <a>Complex</a>'s instances inherit the deficiencies from the
--   type parameter's. For example, <tt>Complex Float</tt>'s <a>Ord</a>
--   instance has similar problems to <a>Float</a>'s.
data Complex a

-- | forms a complex number from its real and imaginary rectangular
--   components.
(:+) :: !a -> !a -> Complex a
infix 6 :+

-- | Extracts the real part of a complex number.
realPart :: Complex a -> a

-- | The function <a>polar</a> takes a complex number and returns a
--   (magnitude, phase) pair in canonical form: the magnitude is
--   nonnegative, and the phase in the range <tt>(-<a>pi</a>,
--   <a>pi</a>]</tt>; if the magnitude is zero, then so is the phase.
polar :: RealFloat a => Complex a -> (a, a)

-- | The phase of a complex number, in the range <tt>(-<a>pi</a>,
--   <a>pi</a>]</tt>. If the magnitude is zero, then so is the phase.
phase :: RealFloat a => Complex a -> a

-- | Form a complex number from polar components of magnitude and phase.
mkPolar :: Floating a => a -> a -> Complex a

-- | The nonnegative magnitude of a complex number.
magnitude :: RealFloat a => Complex a -> a

-- | Extracts the imaginary part of a complex number.
imagPart :: Complex a -> a

-- | The conjugate of a complex number.
conjugate :: Num a => Complex a -> Complex a

-- | <tt><a>cis</a> t</tt> is a complex value with magnitude <tt>1</tt> and
--   phase <tt>t</tt> (modulo <tt>2*<a>pi</a></tt>).
cis :: Floating a => a -> Complex a

-- | resolution of 1, this works the same as Integer
type Uni = Fixed E0

-- | resolution of 10^-12 = .000000000001
type Pico = Fixed E12

-- | resolution of 10^-9 = .000000001
type Nano = Fixed E9

-- | resolution of 10^-3 = .001
type Milli = Fixed E3

-- | resolution of 10^-6 = .000001
type Micro = Fixed E6
class HasResolution (a :: k)
resolution :: HasResolution a => p a -> Integer

-- | The type parameter should be an instance of <a>HasResolution</a>.
newtype Fixed (a :: k)
MkFixed :: Integer -> Fixed (a :: k)
data E9
data E6
data E3
data E2
data E12
data E1
data E0

-- | resolution of 10^-1 = .1
type Deci = Fixed E1

-- | resolution of 10^-2 = .01, useful for many monetary currencies
type Centi = Fixed E2

-- | First arg is whether to chop off trailing zeros
showFixed :: forall {k} (a :: k). HasResolution a => Bool -> Fixed a -> String

-- | Generalisation of <a>mod</a> to any instance of <a>Real</a>
mod' :: Real a => a -> a -> a

-- | Generalisation of <a>divMod</a> to any instance of <a>Real</a>
divMod' :: (Real a, Integral b) => a -> a -> (b, a)

-- | Generalisation of <a>div</a> to any instance of <a>Real</a>
div' :: (Real a, Integral b) => a -> a -> b

-- | Uninhabited data type
data Void

-- | If <a>Void</a> is uninhabited then any <a>Functor</a> that holds only
--   values of type <a>Void</a> is holding no values. It is implemented in
--   terms of <tt>fmap absurd</tt>.
vacuous :: Functor f => f Void -> f a

-- | Since <a>Void</a> values logically don't exist, this witnesses the
--   logical reasoning tool of "ex falso quodlibet".
--   
--   <pre>
--   &gt;&gt;&gt; let x :: Either Void Int; x = Right 5
--   
--   &gt;&gt;&gt; :{
--   case x of
--       Right r -&gt; r
--       Left l  -&gt; absurd l
--   :}
--   5
--   </pre>
absurd :: Void -> a

-- | Provide a Semigroup for an arbitrary Monoid.
--   
--   <b>NOTE</b>: This is not needed anymore since <a>Semigroup</a> became
--   a superclass of <a>Monoid</a> in <i>base-4.11</i> and this newtype be
--   deprecated at some point in the future.
newtype WrappedMonoid m
WrapMonoid :: m -> WrappedMonoid m
[unwrapMonoid] :: WrappedMonoid m -> m
newtype Min a
Min :: a -> Min a
[getMin] :: Min a -> a
newtype Max a
Max :: a -> Max a
[getMax] :: Max a -> a
newtype Last a
Last :: a -> Last a
[getLast] :: Last a -> a
newtype First a
First :: a -> First a
[getFirst] :: First a -> a

-- | <pre>
--   &gt;&gt;&gt; Min (Arg 0 ()) &lt;&gt; Min (Arg 1 ())
--   Min {getMin = Arg 0 ()}
--   </pre>
type ArgMin a b = Min Arg a b

-- | <pre>
--   &gt;&gt;&gt; Max (Arg 0 ()) &lt;&gt; Max (Arg 1 ())
--   Max {getMax = Arg 1 ()}
--   </pre>
type ArgMax a b = Max Arg a b

-- | <a>Arg</a> isn't itself a <a>Semigroup</a> in its own right, but it
--   can be placed inside <a>Min</a> and <a>Max</a> to compute an arg min
--   or arg max.
--   
--   <pre>
--   &gt;&gt;&gt; minimum [ Arg (x * x) x | x &lt;- [-10 .. 10] ]
--   Arg 0 0
--   </pre>
data Arg a b
Arg :: a -> b -> Arg a b

-- | Repeat a value <tt>n</tt> times.
--   
--   <pre>
--   mtimesDefault n a = a &lt;&gt; a &lt;&gt; ... &lt;&gt; a  -- using &lt;&gt; (n-1) times
--   </pre>
--   
--   Implemented using <a>stimes</a> and <a>mempty</a>.
--   
--   This is a suitable definition for an <tt>mtimes</tt> member of
--   <a>Monoid</a>.
mtimesDefault :: (Integral b, Monoid a) => b -> a -> a

-- | This lets you use a difference list of a <a>Semigroup</a> as a
--   <a>Monoid</a>.
--   
--   <h3><b>Example:</b></h3>
--   
--   <pre>
--   &gt;&gt;&gt; let hello = diff "Hello, "
--   
--   &gt;&gt;&gt; appEndo hello "World!"
--   "Hello, World!"
--   
--   &gt;&gt;&gt; appEndo (hello &lt;&gt; mempty) "World!"
--   "Hello, World!"
--   
--   &gt;&gt;&gt; appEndo (mempty &lt;&gt; hello) "World!"
--   "Hello, World!"
--   
--   &gt;&gt;&gt; let world = diff "World"
--   
--   &gt;&gt;&gt; let excl = diff "!"
--   
--   &gt;&gt;&gt; appEndo (hello &lt;&gt; (world &lt;&gt; excl)) mempty
--   "Hello, World!"
--   
--   &gt;&gt;&gt; appEndo ((hello &lt;&gt; world) &lt;&gt; excl) mempty
--   "Hello, World!"
--   </pre>
diff :: Semigroup m => m -> Endo m

-- | A generalization of <a>cycle</a> to an arbitrary <a>Semigroup</a>. May
--   fail to terminate for some values in some semigroups.
cycle1 :: Semigroup m => m -> m

-- | The <a>Item</a> type function returns the type of items of the
--   structure <tt>l</tt>.
type family Item l

-- | The <a>sortWith</a> function sorts a list of elements using the user
--   supplied function to project something out of each element
sortWith :: Ord b => (a -> b) -> [a] -> [a]

-- | Fixity of constructors
data Fixity
Prefix :: Fixity
Infix :: Fixity

-- | Representation of datatypes. A package of constructor representations
--   with names of type and module.
data DataType

-- | Public representation of datatypes
data DataRep
AlgRep :: [Constr] -> DataRep
IntRep :: DataRep
FloatRep :: DataRep
CharRep :: DataRep
NoRep :: DataRep

-- | Public representation of constructors
data ConstrRep
AlgConstr :: ConIndex -> ConstrRep
IntConstr :: Integer -> ConstrRep
FloatConstr :: Rational -> ConstrRep
CharConstr :: Char -> ConstrRep

-- | Representation of constructors. Note that equality on constructors
--   with different types may not work -- i.e. the constructors for
--   <a>False</a> and <a>Nothing</a> may compare equal.
data Constr

-- | Unique index for datatype constructors, counting from 1 in the order
--   they are given in the program text.
type ConIndex = Int

-- | Gets the unqualified type constructor: drop *.*.*... before name
tyconUQname :: String -> String

-- | Gets the module of a type constructor: take *.*.*... before name
tyconModule :: String -> String

-- | Gets the string for a constructor
showConstr :: Constr -> String

-- | Look up a constructor by its representation
repConstr :: DataType -> ConstrRep -> Constr

-- | Lookup a constructor via a string
readConstr :: DataType -> String -> Maybe Constr
mkRealConstr :: (Real a, Show a) => DataType -> a -> Constr

-- | Constructs a non-representation for a non-representable type
mkNoRepType :: String -> DataType
mkIntegralConstr :: (Integral a, Show a) => DataType -> a -> Constr

-- | Constructs the <a>Int</a> type
mkIntType :: String -> DataType

-- | Constructs the <a>Float</a> type
mkFloatType :: String -> DataType

-- | Constructs an algebraic datatype
mkDataType :: String -> [Constr] -> DataType

-- | Constructs a constructor
mkConstrTag :: DataType -> String -> Int -> [String] -> Fixity -> Constr

-- | Constructs a constructor
mkConstr :: DataType -> String -> [String] -> Fixity -> Constr

-- | Constructs the <a>Char</a> type
mkCharType :: String -> DataType

-- | Makes a constructor for <a>Char</a>.
mkCharConstr :: DataType -> Char -> Constr

-- | Gets the maximum constructor index of an algebraic datatype
maxConstrIndex :: DataType -> ConIndex

-- | Test for a non-representable type
isNorepType :: DataType -> Bool

-- | Test for an algebraic type
isAlgType :: DataType -> Bool

-- | Gets the constructor for an index (algebraic datatypes only)
indexConstr :: DataType -> ConIndex -> Constr

-- | Monadic variation on <a>fromConstrB</a>
fromConstrM :: (Monad m, Data a) => (forall d. Data d => m d) -> Constr -> m a

-- | Build a term and use a generic function for subterms
fromConstrB :: Data a => (forall d. Data d => d) -> Constr -> a

-- | Build a term skeleton
fromConstr :: Data a => Constr -> a

-- | Gets the public presentation of a datatype
dataTypeRep :: DataType -> DataRep

-- | Gets the type constructor including the module
dataTypeName :: DataType -> String

-- | Gets the constructors of an algebraic datatype
dataTypeConstrs :: DataType -> [Constr]

-- | Gets the datatype of a constructor
constrType :: Constr -> DataType

-- | Gets the public presentation of constructors
constrRep :: Constr -> ConstrRep

-- | Gets the index of a constructor (algebraic datatypes only)
constrIndex :: Constr -> ConIndex

-- | Gets the fixity of a constructor
constrFixity :: Constr -> Fixity

-- | Gets the field labels of a constructor. The list of labels is returned
--   in the same order as they were given in the original constructor
--   declaration.
constrFields :: Constr -> [String]

-- | An exception thrown to a thread by <a>timeout</a> to interrupt a
--   timed-out computation.
data Timeout

-- | Wrap an <a>IO</a> computation to time out and return <tt>Nothing</tt>
--   in case no result is available within <tt>n</tt> microseconds
--   (<tt>1/10^6</tt> seconds). In case a result is available before the
--   timeout expires, <tt>Just a</tt> is returned. A negative timeout
--   interval means "wait indefinitely". When specifying long timeouts, be
--   careful not to exceed <tt>maxBound :: Int</tt>.
--   
--   <pre>
--   &gt;&gt;&gt; timeout 1000000 (threadDelay 1000 *&gt; pure "finished on time")
--   Just "finished on time"
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; timeout 10000 (threadDelay 100000 *&gt; pure "finished on time")
--   Nothing
--   </pre>
--   
--   The design of this combinator was guided by the objective that
--   <tt>timeout n f</tt> should behave exactly the same as <tt>f</tt> as
--   long as <tt>f</tt> doesn't time out. This means that <tt>f</tt> has
--   the same <a>myThreadId</a> it would have without the timeout wrapper.
--   Any exceptions <tt>f</tt> might throw cancel the timeout and propagate
--   further up. It also possible for <tt>f</tt> to receive exceptions
--   thrown to it by another thread.
--   
--   A tricky implementation detail is the question of how to abort an
--   <tt>IO</tt> computation. This combinator relies on asynchronous
--   exceptions internally (namely throwing the computation the
--   <a>Timeout</a> exception). The technique works very well for
--   computations executing inside of the Haskell runtime system, but it
--   doesn't work at all for non-Haskell code. Foreign function calls, for
--   example, cannot be timed out with this combinator simply because an
--   arbitrary C function cannot receive asynchronous exceptions. When
--   <tt>timeout</tt> is used to wrap an FFI call that blocks, no timeout
--   event can be delivered until the FFI call returns, which pretty much
--   negates the purpose of the combinator. In practice, however, this
--   limitation is less severe than it may sound. Standard I/O functions
--   like <a>hGetBuf</a>, <a>hPutBuf</a>, Network.Socket.accept, or
--   <a>hWaitForInput</a> appear to be blocking, but they really don't
--   because the runtime system uses scheduling mechanisms like
--   <tt>select(2)</tt> to perform asynchronous I/O, so it is possible to
--   interrupt standard socket I/O or file I/O using this combinator.
timeout :: Int -> IO a -> IO (Maybe a)

-- | Returns an STM action that can be used to wait until data can be
--   written to a file descriptor. The second returned value is an IO
--   action that can be used to deregister interest in the file descriptor.
threadWaitWriteSTM :: Fd -> IO (STM (), IO ())

-- | Block the current thread until data can be written to the given file
--   descriptor (GHC only).
--   
--   This will throw an <a>IOError</a> if the file descriptor was closed
--   while this thread was blocked. To safely close a file descriptor that
--   has been used with <a>threadWaitWrite</a>, use <a>closeFdWith</a>.
threadWaitWrite :: Fd -> IO ()

-- | Returns an STM action that can be used to wait for data to read from a
--   file descriptor. The second returned value is an IO action that can be
--   used to deregister interest in the file descriptor.
threadWaitReadSTM :: Fd -> IO (STM (), IO ())

-- | Block the current thread until data is available to read on the given
--   file descriptor (GHC only).
--   
--   This will throw an <a>IOError</a> if the file descriptor was closed
--   while this thread was blocked. To safely close a file descriptor that
--   has been used with <a>threadWaitRead</a>, use <a>closeFdWith</a>.
threadWaitRead :: Fd -> IO ()

-- | Run the <a>IO</a> computation passed as the first argument. If the
--   calling thread is <i>bound</i>, an unbound thread is created
--   temporarily using <a>forkIO</a>. <tt>runInBoundThread</tt> doesn't
--   finish until the <a>IO</a> computation finishes.
--   
--   Use this function <i>only</i> in the rare case that you have actually
--   observed a performance loss due to the use of bound threads. A program
--   that doesn't need its main thread to be bound and makes <i>heavy</i>
--   use of concurrency (e.g. a web server), might want to wrap its
--   <tt>main</tt> action in <tt>runInUnboundThread</tt>.
--   
--   Note that exceptions which are thrown to the current thread are thrown
--   in turn to the thread that is executing the given computation. This
--   ensures there's always a way of killing the forked thread.
runInUnboundThread :: IO a -> IO a

-- | Run the <a>IO</a> computation passed as the first argument. If the
--   calling thread is not <i>bound</i>, a bound thread is created
--   temporarily. <tt>runInBoundThread</tt> doesn't finish until the
--   <a>IO</a> computation finishes.
--   
--   You can wrap a series of foreign function calls that rely on
--   thread-local state with <tt>runInBoundThread</tt> so that you can use
--   them without knowing whether the current thread is <i>bound</i>.
runInBoundThread :: IO a -> IO a

-- | <a>True</a> if bound threads are supported. If
--   <tt>rtsSupportsBoundThreads</tt> is <a>False</a>,
--   <a>isCurrentThreadBound</a> will always return <a>False</a> and both
--   <a>forkOS</a> and <a>runInBoundThread</a> will fail.
rtsSupportsBoundThreads :: Bool

-- | Returns <a>True</a> if the calling thread is <i>bound</i>, that is, if
--   it is safe to use foreign libraries that rely on thread-local state
--   from the calling thread.
isCurrentThreadBound :: IO Bool

-- | Like <a>forkIOWithUnmask</a>, but the child thread is a bound thread,
--   as with <a>forkOS</a>.
forkOSWithUnmask :: ((forall a. () => IO a -> IO a) -> IO ()) -> IO ThreadId

-- | Like <a>forkIO</a>, this sparks off a new thread to run the <a>IO</a>
--   computation passed as the first argument, and returns the
--   <a>ThreadId</a> of the newly created thread.
--   
--   However, <a>forkOS</a> creates a <i>bound</i> thread, which is
--   necessary if you need to call foreign (non-Haskell) libraries that
--   make use of thread-local state, such as OpenGL (see
--   <a>Control.Concurrent#boundthreads</a>).
--   
--   Using <a>forkOS</a> instead of <a>forkIO</a> makes no difference at
--   all to the scheduling behaviour of the Haskell runtime system. It is a
--   common misconception that you need to use <a>forkOS</a> instead of
--   <a>forkIO</a> to avoid blocking all the Haskell threads when making a
--   foreign call; this isn't the case. To allow foreign calls to be made
--   without blocking all the Haskell threads (with GHC), it is only
--   necessary to use the <tt>-threaded</tt> option when linking your
--   program, and to make sure the foreign import is not marked
--   <tt>unsafe</tt>.
forkOS :: IO () -> IO ThreadId

-- | Fork a thread and call the supplied function when the thread is about
--   to terminate, with an exception or a returned value. The function is
--   called with asynchronous exceptions masked.
--   
--   <pre>
--   forkFinally action and_then =
--     mask $ \restore -&gt;
--       forkIO $ try (restore action) &gt;&gt;= and_then
--   </pre>
--   
--   This function is useful for informing the parent when a child
--   terminates, for example.
forkFinally :: IO a -> (Either SomeException a -> IO ()) -> IO ThreadId

-- | <a>Chan</a> is an abstract type representing an unbounded FIFO
--   channel.
data Chan a

-- | Write an entire list of items to a <a>Chan</a>.
writeList2Chan :: Chan a -> [a] -> IO ()

-- | Write a value to a <a>Chan</a>.
writeChan :: Chan a -> a -> IO ()

-- | Read the next value from the <a>Chan</a>. Blocks when the channel is
--   empty. Since the read end of a channel is an <a>MVar</a>, this
--   operation inherits fairness guarantees of <a>MVar</a>s (e.g. threads
--   blocked in this operation are woken up in FIFO order).
--   
--   Throws <a>BlockedIndefinitelyOnMVar</a> when the channel is empty and
--   no other thread holds a reference to the channel.
readChan :: Chan a -> IO a

-- | Build and returns a new instance of <a>Chan</a>.
newChan :: IO (Chan a)

-- | Return a lazy list representing the contents of the supplied
--   <a>Chan</a>, much like <a>hGetContents</a>.
getChanContents :: Chan a -> IO [a]

-- | Duplicate a <a>Chan</a>: the duplicate channel begins empty, but data
--   written to either channel from then on will be available from both.
--   Hence this creates a kind of broadcast channel, where data written by
--   anyone is seen by everyone else.
--   
--   (Note that a duplicated channel is not equal to its original. So:
--   <tt>fmap (c /=) $ dupChan c</tt> returns <tt>True</tt> for all
--   <tt>c</tt>.)
dupChan :: Chan a -> IO (Chan a)

-- | <a>QSem</a> is a quantity semaphore in which the resource is acquired
--   and released in units of one. It provides guaranteed FIFO ordering for
--   satisfying blocked <a>waitQSem</a> calls.
--   
--   The pattern
--   
--   <pre>
--   bracket_ waitQSem signalQSem (...)
--   </pre>
--   
--   is safe; it never loses a unit of the resource.
data QSem

-- | Wait for a unit to become available
waitQSem :: QSem -> IO ()

-- | Signal that a unit of the <a>QSem</a> is available
signalQSem :: QSem -> IO ()

-- | Build a new <a>QSem</a> with a supplied initial quantity. The initial
--   quantity must be at least 0.
newQSem :: Int -> IO QSem

-- | <a>QSemN</a> is a quantity semaphore in which the resource is acquired
--   and released in units of one. It provides guaranteed FIFO ordering for
--   satisfying blocked <a>waitQSemN</a> calls.
--   
--   The pattern
--   
--   <pre>
--   bracket_ (waitQSemN n) (signalQSemN n) (...)
--   </pre>
--   
--   is safe; it never loses any of the resource.
data QSemN

-- | Wait for the specified quantity to become available
waitQSemN :: QSemN -> Int -> IO ()

-- | Signal that a given quantity is now available from the <a>QSemN</a>.
signalQSemN :: QSemN -> Int -> IO ()

-- | Build a new <a>QSemN</a> with a supplied initial quantity. The initial
--   quantity must be at least 0.
newQSemN :: Int -> IO QSemN

-- | A bifunctor is a type constructor that takes two type arguments and is
--   a functor in <i>both</i> arguments. That is, unlike with
--   <a>Functor</a>, a type constructor such as <a>Either</a> does not need
--   to be partially applied for a <a>Bifunctor</a> instance, and the
--   methods in this class permit mapping functions over the <a>Left</a>
--   value or the <a>Right</a> value, or both at the same time.
--   
--   Formally, the class <a>Bifunctor</a> represents a bifunctor from
--   <tt>Hask</tt> -&gt; <tt>Hask</tt>.
--   
--   Intuitively it is a bifunctor where both the first and second
--   arguments are covariant.
--   
--   You can define a <a>Bifunctor</a> by either defining <a>bimap</a> or
--   by defining both <a>first</a> and <a>second</a>.
--   
--   If you supply <a>bimap</a>, you should ensure that:
--   
--   <pre>
--   <a>bimap</a> <a>id</a> <a>id</a> ≡ <a>id</a>
--   </pre>
--   
--   If you supply <a>first</a> and <a>second</a>, ensure:
--   
--   <pre>
--   <a>first</a> <a>id</a> ≡ <a>id</a>
--   <a>second</a> <a>id</a> ≡ <a>id</a>
--   </pre>
--   
--   If you supply both, you should also ensure:
--   
--   <pre>
--   <a>bimap</a> f g ≡ <a>first</a> f <a>.</a> <a>second</a> g
--   </pre>
--   
--   These ensure by parametricity:
--   
--   <pre>
--   <a>bimap</a>  (f <a>.</a> g) (h <a>.</a> i) ≡ <a>bimap</a> f h <a>.</a> <a>bimap</a> g i
--   <a>first</a>  (f <a>.</a> g) ≡ <a>first</a>  f <a>.</a> <a>first</a>  g
--   <a>second</a> (f <a>.</a> g) ≡ <a>second</a> f <a>.</a> <a>second</a> g
--   </pre>
class Bifunctor (p :: Type -> Type -> Type)

-- | Map over both arguments at the same time.
--   
--   <pre>
--   <a>bimap</a> f g ≡ <a>first</a> f <a>.</a> <a>second</a> g
--   </pre>
--   
--   <h4><b>Examples</b></h4>
--   
--   <pre>
--   &gt;&gt;&gt; bimap toUpper (+1) ('j', 3)
--   ('J',4)
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; bimap toUpper (+1) (Left 'j')
--   Left 'J'
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; bimap toUpper (+1) (Right 3)
--   Right 4
--   </pre>
bimap :: Bifunctor p => (a -> b) -> (c -> d) -> p a c -> p b d

-- | Map covariantly over the first argument.
--   
--   <pre>
--   <a>first</a> f ≡ <a>bimap</a> f <a>id</a>
--   </pre>
--   
--   <h4><b>Examples</b></h4>
--   
--   <pre>
--   &gt;&gt;&gt; first toUpper ('j', 3)
--   ('J',3)
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; first toUpper (Left 'j')
--   Left 'J'
--   </pre>
first :: Bifunctor p => (a -> b) -> p a c -> p b c

-- | Map covariantly over the second argument.
--   
--   <pre>
--   <a>second</a> ≡ <a>bimap</a> <a>id</a>
--   </pre>
--   
--   <h4><b>Examples</b></h4>
--   
--   <pre>
--   &gt;&gt;&gt; second (+1) ('j', 3)
--   ('j',4)
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; second (+1) (Right 3)
--   Right 4
--   </pre>
second :: Bifunctor p => (b -> c) -> p a b -> p a c

-- | Monads in which <a>IO</a> computations may be embedded. Any monad
--   built by applying a sequence of monad transformers to the <a>IO</a>
--   monad will be an instance of this class.
--   
--   Instances should satisfy the following laws, which state that
--   <a>liftIO</a> is a transformer of monads:
--   
--   <ul>
--   <li><pre><a>liftIO</a> . <a>return</a> = <a>return</a></pre></li>
--   <li><pre><a>liftIO</a> (m &gt;&gt;= f) = <a>liftIO</a> m &gt;&gt;=
--   (<a>liftIO</a> . f)</pre></li>
--   </ul>
class Monad m => MonadIO (m :: Type -> Type)

-- | Lift a computation from the <a>IO</a> monad. This allows us to run IO
--   computations in any monadic stack, so long as it supports these kinds
--   of operations (i.e. <a>IO</a> is the base monad for the stack).
--   
--   <h3><b>Example</b></h3>
--   
--   <pre>
--   import Control.Monad.Trans.State -- from the "transformers" library
--   
--   printState :: Show s =&gt; StateT s IO ()
--   printState = do
--     state &lt;- get
--     liftIO $ print state
--   </pre>
--   
--   Had we omitted <tt><a>liftIO</a></tt>, we would have ended up with
--   this error:
--   
--   <pre>
--   • Couldn't match type ‘IO’ with ‘StateT s IO’
--    Expected type: StateT s IO ()
--      Actual type: IO ()
--   </pre>
--   
--   The important part here is the mismatch between <tt>StateT s IO
--   ()</tt> and <tt><a>IO</a> ()</tt>.
--   
--   Luckily, we know of a function that takes an <tt><a>IO</a> a</tt> and
--   returns an <tt>(m a)</tt>: <tt><a>liftIO</a></tt>, enabling us to run
--   the program and see the expected results:
--   
--   <pre>
--   &gt; evalStateT printState "hello"
--   "hello"
--   
--   &gt; evalStateT printState 3
--   3
--   </pre>
liftIO :: MonadIO m => IO a -> m a

-- | <a>approxRational</a>, applied to two real fractional numbers
--   <tt>x</tt> and <tt>epsilon</tt>, returns the simplest rational number
--   within <tt>epsilon</tt> of <tt>x</tt>. A rational number <tt>y</tt> is
--   said to be <i>simpler</i> than another <tt>y'</tt> if
--   
--   <ul>
--   <li><tt><a>abs</a> (<a>numerator</a> y) &lt;= <a>abs</a>
--   (<a>numerator</a> y')</tt>, and</li>
--   <li><tt><a>denominator</a> y &lt;= <a>denominator</a> y'</tt>.</li>
--   </ul>
--   
--   Any real interval contains a unique simplest rational; in particular,
--   note that <tt>0/1</tt> is the simplest rational of all.
approxRational :: RealFrac a => a -> a -> Rational

-- | Strict version of <a>modifySTRef</a>
modifySTRef' :: STRef s a -> (a -> a) -> ST s ()

-- | Mutate the contents of an <a>STRef</a>.
--   
--   <pre>
--   &gt;&gt;&gt; :{
--   runST (do
--       ref &lt;- newSTRef ""
--       modifySTRef ref (const "world")
--       modifySTRef ref (++ "!")
--       modifySTRef ref ("Hello, " ++)
--       readSTRef ref )
--   :}
--   "Hello, world!"
--   </pre>
--   
--   Be warned that <a>modifySTRef</a> does not apply the function
--   strictly. This means if the program calls <a>modifySTRef</a> many
--   times, but seldom uses the value, thunks will pile up in memory
--   resulting in a space leak. This is a common mistake made when using an
--   <a>STRef</a> as a counter. For example, the following will leak memory
--   and may produce a stack overflow:
--   
--   <pre>
--   &gt;&gt;&gt; import Control.Monad (replicateM_)
--   
--   &gt;&gt;&gt; :{
--   print (runST (do
--       ref &lt;- newSTRef 0
--       replicateM_ 1000 $ modifySTRef ref (+1)
--       readSTRef ref ))
--   :}
--   1000
--   </pre>
--   
--   To avoid this problem, use <a>modifySTRef'</a> instead.
modifySTRef :: STRef s a -> (a -> a) -> ST s ()

-- | An abstract unique object. Objects of type <a>Unique</a> may be
--   compared for equality and ordering and hashed into <a>Int</a>.
--   
--   <pre>
--   &gt;&gt;&gt; :{
--   do x &lt;- newUnique
--      print (x == x)
--      y &lt;- newUnique
--      print (x == y)
--   :}
--   True
--   False
--   </pre>
data Unique

-- | Creates a new object of type <a>Unique</a>. The value returned will
--   not compare equal to any other value of type <a>Unique</a> returned by
--   previous calls to <a>newUnique</a>. There is no limit on the number of
--   times <a>newUnique</a> may be called.
newUnique :: IO Unique

-- | Hashes a <a>Unique</a> into an <a>Int</a>. Two <a>Unique</a>s may hash
--   to the same value, although in practice this is unlikely. The
--   <a>Int</a> returned makes a good hash key.
hashUnique :: Unique -> Int
class IsLabel (x :: Symbol) a
fromLabel :: IsLabel x a => a

-- | An abstract name for an object, that supports equality and hashing.
--   
--   Stable names have the following property:
--   
--   <ul>
--   <li>If <tt>sn1 :: StableName</tt> and <tt>sn2 :: StableName</tt> and
--   <tt>sn1 == sn2</tt> then <tt>sn1</tt> and <tt>sn2</tt> were created by
--   calls to <tt>makeStableName</tt> on the same object.</li>
--   </ul>
--   
--   The reverse is not necessarily true: if two stable names are not
--   equal, then the objects they name may still be equal. Note in
--   particular that <a>makeStableName</a> may return a different
--   <a>StableName</a> after an object is evaluated.
--   
--   Stable Names are similar to Stable Pointers
--   (<a>Foreign.StablePtr</a>), but differ in the following ways:
--   
--   <ul>
--   <li>There is no <tt>freeStableName</tt> operation, unlike
--   <a>Foreign.StablePtr</a>s. Stable names are reclaimed by the runtime
--   system when they are no longer needed.</li>
--   <li>There is no <tt>deRefStableName</tt> operation. You can't get back
--   from a stable name to the original Haskell object. The reason for this
--   is that the existence of a stable name for an object does not
--   guarantee the existence of the object itself; it can still be garbage
--   collected.</li>
--   </ul>
data StableName a

-- | Makes a <a>StableName</a> for an arbitrary object. The object passed
--   as the first argument is not evaluated by <a>makeStableName</a>.
makeStableName :: a -> IO (StableName a)

-- | Convert a <a>StableName</a> to an <a>Int</a>. The <a>Int</a> returned
--   is not necessarily unique; several <a>StableName</a>s may map to the
--   same <a>Int</a> (in practice however, the chances of this are small,
--   so the result of <a>hashStableName</a> makes a good hash key).
hashStableName :: StableName a -> Int

-- | Equality on <a>StableName</a> that does not require that the types of
--   the arguments match.
eqStableName :: StableName a -> StableName b -> Bool

-- | <a>withProgName</a> <tt>name act</tt> - while executing action
--   <tt>act</tt>, have <a>getProgName</a> return <tt>name</tt>.
withProgName :: String -> IO a -> IO a

-- | <a>withArgs</a> <tt>args act</tt> - while executing action
--   <tt>act</tt>, have <a>getArgs</a> return <tt>args</tt>.
withArgs :: [String] -> IO a -> IO a

-- | <tt>unsetEnv name</tt> removes the specified environment variable from
--   the environment of the current process.
--   
--   Throws <a>IOException</a> if <tt>name</tt> is the empty string or
--   contains an equals sign.
unsetEnv :: String -> IO ()

-- | <tt>setEnv name value</tt> sets the specified environment variable to
--   <tt>value</tt>.
--   
--   Early versions of this function operated under the mistaken belief
--   that setting an environment variable to the <i>empty string</i> on
--   Windows removes that environment variable from the environment. For
--   the sake of compatibility, it adopted that behavior on POSIX. In
--   particular
--   
--   <pre>
--   setEnv name ""
--   </pre>
--   
--   has the same effect as
--   
--   <pre>
--   <a>unsetEnv</a> name
--   </pre>
--   
--   If you'd like to be able to set environment variables to blank
--   strings, use <a>setEnv</a>.
--   
--   Throws <a>IOException</a> if <tt>name</tt> is the empty string or
--   contains an equals sign.
setEnv :: String -> String -> IO ()

-- | Return the value of the environment variable <tt>var</tt>, or
--   <tt>Nothing</tt> if there is no such value.
--   
--   For POSIX users, this is equivalent to <a>getEnv</a>.
lookupEnv :: String -> IO (Maybe String)

-- | Computation <a>getProgName</a> returns the name of the program as it
--   was invoked.
--   
--   However, this is hard-to-impossible to implement on some non-Unix
--   OSes, so instead, for maximum portability, we just return the leafname
--   of the program as invoked. Even then there are some differences
--   between platforms: on Windows, for example, a program invoked as foo
--   is probably really <tt>FOO.EXE</tt>, and that is what
--   <a>getProgName</a> will return.
getProgName :: IO String

-- | <a>getEnvironment</a> retrieves the entire environment as a list of
--   <tt>(key,value)</tt> pairs.
--   
--   If an environment entry does not contain an <tt>'='</tt> character,
--   the <tt>key</tt> is the whole entry and the <tt>value</tt> is the
--   empty string.
getEnvironment :: IO [(String, String)]

-- | Computation <a>getEnv</a> <tt>var</tt> returns the value of the
--   environment variable <tt>var</tt>. For the inverse, the <a>setEnv</a>
--   function can be used.
--   
--   This computation may fail with:
--   
--   <ul>
--   <li><a>isDoesNotExistError</a> if the environment variable does not
--   exist.</li>
--   </ul>
getEnv :: String -> IO String

-- | Computation <a>getArgs</a> returns a list of the program's command
--   line arguments (not including the program name).
getArgs :: IO [String]

-- | Returns the absolute pathname of the current executable.
--   
--   Note that for scripts and interactive sessions, this is the path to
--   the interpreter (e.g. ghci.)
--   
--   Since base 4.11.0.0, <a>getExecutablePath</a> resolves symlinks on
--   Windows. If an executable is launched through a symlink,
--   <a>getExecutablePath</a> returns the absolute path of the original
--   executable.
getExecutablePath :: IO FilePath

-- | Computation <a>exitWith</a> <tt>code</tt> throws <a>ExitCode</a>
--   <tt>code</tt>. Normally this terminates the program, returning
--   <tt>code</tt> to the program's caller.
--   
--   On program termination, the standard <a>Handle</a>s <a>stdout</a> and
--   <a>stderr</a> are flushed automatically; any other buffered
--   <a>Handle</a>s need to be flushed manually, otherwise the buffered
--   data will be discarded.
--   
--   A program that fails in any other way is treated as if it had called
--   <a>exitFailure</a>. A program that terminates successfully without
--   calling <a>exitWith</a> explicitly is treated as if it had called
--   <a>exitWith</a> <a>ExitSuccess</a>.
--   
--   As an <a>ExitCode</a> is not an <a>IOException</a>, <a>exitWith</a>
--   bypasses the error handling in the <a>IO</a> monad and cannot be
--   intercepted by <a>catch</a> from the <a>Prelude</a>. However it is a
--   <a>SomeException</a>, and can be caught using the functions of
--   <a>Control.Exception</a>. This means that cleanup computations added
--   with <a>bracket</a> (from <a>Control.Exception</a>) are also executed
--   properly on <a>exitWith</a>.
--   
--   Note: in GHC, <a>exitWith</a> should be called from the main program
--   thread in order to exit the process. When called from another thread,
--   <a>exitWith</a> will throw an <tt>ExitException</tt> as normal, but
--   the exception will not cause the process itself to exit.
exitWith :: ExitCode -> IO a

-- | The computation <a>exitSuccess</a> is equivalent to <a>exitWith</a>
--   <a>ExitSuccess</a>, It terminates the program successfully.
exitSuccess :: IO a

-- | The computation <a>exitFailure</a> is equivalent to <a>exitWith</a>
--   <tt>(</tt><a>ExitFailure</a> <i>exitfail</i><tt>)</tt>, where
--   <i>exitfail</i> is implementation-dependent.
exitFailure :: IO a

-- | Write given error message to <a>stderr</a> and terminate with
--   <a>exitFailure</a>.
die :: String -> IO a

-- | Triggers an immediate minor garbage collection.
performMinorGC :: IO ()

-- | Triggers an immediate major garbage collection.
performMajorGC :: IO ()

-- | Triggers an immediate major garbage collection.
performGC :: IO ()

-- | Format a variable number of arguments with the C-style formatting
--   string.
--   
--   <pre>
--   &gt;&gt;&gt; printf "%s, %d, %.4f" "hello" 123 pi
--   hello, 123, 3.1416
--   </pre>
--   
--   The return value is either <a>String</a> or <tt>(<a>IO</a> a)</tt>
--   (which should be <tt>(<a>IO</a> ())</tt>, but Haskell's type system
--   makes this hard).
--   
--   The format string consists of ordinary characters and <i>conversion
--   specifications</i>, which specify how to format one of the arguments
--   to <a>printf</a> in the output string. A format specification is
--   introduced by the <tt>%</tt> character; this character can be
--   self-escaped into the format string using <tt>%%</tt>. A format
--   specification ends with a <i>format character</i> that provides the
--   primary information about how to format the value. The rest of the
--   conversion specification is optional. In order, one may have flag
--   characters, a width specifier, a precision specifier, and
--   type-specific modifier characters.
--   
--   Unlike C <tt>printf(3)</tt>, the formatting of this <a>printf</a> is
--   driven by the argument type; formatting is type specific. The types
--   formatted by <a>printf</a> "out of the box" are:
--   
--   <ul>
--   <li><a>Integral</a> types, including <a>Char</a></li>
--   <li><a>String</a></li>
--   <li><a>RealFloat</a> types</li>
--   </ul>
--   
--   <a>printf</a> is also extensible to support other types: see below.
--   
--   A conversion specification begins with the character <tt>%</tt>,
--   followed by zero or more of the following flags:
--   
--   <pre>
--   -      left adjust (default is right adjust)
--   +      always use a sign (+ or -) for signed conversions
--   space  leading space for positive numbers in signed conversions
--   0      pad with zeros rather than spaces
--   #      use an \"alternate form\": see below
--   </pre>
--   
--   When both flags are given, <tt>-</tt> overrides <tt>0</tt> and
--   <tt>+</tt> overrides space. A negative width specifier in a <tt>*</tt>
--   conversion is treated as positive but implies the left adjust flag.
--   
--   The "alternate form" for unsigned radix conversions is as in C
--   <tt>printf(3)</tt>:
--   
--   <pre>
--   %o           prefix with a leading 0 if needed
--   %x           prefix with a leading 0x if nonzero
--   %X           prefix with a leading 0X if nonzero
--   %b           prefix with a leading 0b if nonzero
--   %[eEfFgG]    ensure that the number contains a decimal point
--   </pre>
--   
--   Any flags are followed optionally by a field width:
--   
--   <pre>
--   num    field width
--   *      as num, but taken from argument list
--   </pre>
--   
--   The field width is a minimum, not a maximum: it will be expanded as
--   needed to avoid mutilating a value.
--   
--   Any field width is followed optionally by a precision:
--   
--   <pre>
--   .num   precision
--   .      same as .0
--   .*     as num, but taken from argument list
--   </pre>
--   
--   Negative precision is taken as 0. The meaning of the precision depends
--   on the conversion type.
--   
--   <pre>
--   Integral    minimum number of digits to show
--   RealFloat   number of digits after the decimal point
--   String      maximum number of characters
--   </pre>
--   
--   The precision for Integral types is accomplished by zero-padding. If
--   both precision and zero-pad are given for an Integral field, the
--   zero-pad is ignored.
--   
--   Any precision is followed optionally for Integral types by a width
--   modifier; the only use of this modifier being to set the implicit size
--   of the operand for conversion of a negative operand to unsigned:
--   
--   <pre>
--   hh     Int8
--   h      Int16
--   l      Int32
--   ll     Int64
--   L      Int64
--   </pre>
--   
--   The specification ends with a format character:
--   
--   <pre>
--   c      character               Integral
--   d      decimal                 Integral
--   o      octal                   Integral
--   x      hexadecimal             Integral
--   X      hexadecimal             Integral
--   b      binary                  Integral
--   u      unsigned decimal        Integral
--   f      floating point          RealFloat
--   F      floating point          RealFloat
--   g      general format float    RealFloat
--   G      general format float    RealFloat
--   e      exponent format float   RealFloat
--   E      exponent format float   RealFloat
--   s      string                  String
--   v      default format          any type
--   </pre>
--   
--   The "%v" specifier is provided for all built-in types, and should be
--   provided for user-defined type formatters as well. It picks a "best"
--   representation for the given type. For the built-in types the "%v"
--   specifier is converted as follows:
--   
--   <pre>
--   c      Char
--   u      other unsigned Integral
--   d      other signed Integral
--   g      RealFloat
--   s      String
--   </pre>
--   
--   Mismatch between the argument types and the format string, as well as
--   any other syntactic or semantic errors in the format string, will
--   cause an exception to be thrown at runtime.
--   
--   Note that the formatting for <a>RealFloat</a> types is currently a bit
--   different from that of C <tt>printf(3)</tt>, conforming instead to
--   <a>showEFloat</a>, <a>showFFloat</a> and <a>showGFloat</a> (and their
--   alternate versions <a>showFFloatAlt</a> and <a>showGFloatAlt</a>).
--   This is hard to fix: the fixed versions would format in a
--   backward-incompatible way. In any case the Haskell behavior is
--   generally more sensible than the C behavior. A brief summary of some
--   key differences:
--   
--   <ul>
--   <li>Haskell <a>printf</a> never uses the default "6-digit" precision
--   used by C printf.</li>
--   <li>Haskell <a>printf</a> treats the "precision" specifier as
--   indicating the number of digits after the decimal point.</li>
--   <li>Haskell <a>printf</a> prints the exponent of e-format numbers
--   without a gratuitous plus sign, and with the minimum possible number
--   of digits.</li>
--   <li>Haskell <a>printf</a> will place a zero after a decimal point when
--   possible.</li>
--   </ul>
printf :: PrintfType r => String -> r

-- | Similar to <a>printf</a>, except that output is via the specified
--   <a>Handle</a>. The return type is restricted to <tt>(<a>IO</a>
--   a)</tt>.
hPrintf :: HPrintfType r => Handle -> String -> r

-- | <a>zipWithM_</a> is the extension of <a>zipWithM</a> which ignores the
--   final result.
zipWithM_ :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m ()

-- | The <a>zipWithM</a> function generalizes <a>zipWith</a> to arbitrary
--   applicative functors.
zipWithM :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m [c]

-- | The reverse of <a>when</a>.
unless :: Applicative f => Bool -> f () -> f ()

-- | Like <a>replicateM</a>, but discards the result.
--   
--   <h4><b>Examples</b></h4>
--   
--   <pre>
--   &gt;&gt;&gt; replicateM_ 3 (putStrLn "a")
--   a
--   a
--   a
--   </pre>
replicateM_ :: Applicative m => Int -> m a -> m ()

-- | <tt><a>replicateM</a> n act</tt> performs the action <tt>act</tt>
--   <tt>n</tt> times, and then returns the list of results:
--   
--   <h4><b>Examples</b></h4>
--   
--   <pre>
--   &gt;&gt;&gt; import Control.Monad.State
--   
--   &gt;&gt;&gt; runState (replicateM 3 $ state $ \s -&gt; (s, s + 1)) 1
--   ([1,2,3],4)
--   </pre>
replicateM :: Applicative m => Int -> m a -> m [a]

-- | Direct <a>MonadPlus</a> equivalent of <a>filter</a>.
--   
--   <h4><b>Examples</b></h4>
--   
--   The <a>filter</a> function is just <a>mfilter</a> specialized to the
--   list monad:
--   
--   <pre>
--   <a>filter</a> = ( <a>mfilter</a> :: (a -&gt; Bool) -&gt; [a] -&gt; [a] )
--   </pre>
--   
--   An example using <a>mfilter</a> with the <a>Maybe</a> monad:
--   
--   <pre>
--   &gt;&gt;&gt; mfilter odd (Just 1)
--   Just 1
--   
--   &gt;&gt;&gt; mfilter odd (Just 2)
--   Nothing
--   </pre>
mfilter :: MonadPlus m => (a -> Bool) -> m a -> m a

-- | The <a>mapAndUnzipM</a> function maps its first argument over a list,
--   returning the result as a pair of lists. This function is mainly used
--   with complicated data structures or a state monad.
mapAndUnzipM :: Applicative m => (a -> m (b, c)) -> [a] -> m ([b], [c])

-- | Repeat an action indefinitely.
--   
--   <h4><b>Examples</b></h4>
--   
--   A common use of <a>forever</a> is to process input from network
--   sockets, <a>Handle</a>s, and channels (e.g. <a>MVar</a> and
--   <a>Chan</a>).
--   
--   For example, here is how we might implement an <a>echo server</a>,
--   using <a>forever</a> both to listen for client connections on a
--   network socket and to echo client input on client connection handles:
--   
--   <pre>
--   echoServer :: Socket -&gt; IO ()
--   echoServer socket = <a>forever</a> $ do
--     client &lt;- accept socket
--     <a>forkFinally</a> (echo client) (\_ -&gt; hClose client)
--     where
--       echo :: Handle -&gt; IO ()
--       echo client = <a>forever</a> $
--         hGetLine client &gt;&gt;= hPutStrLn client
--   </pre>
--   
--   Note that "forever" isn't necessarily non-terminating. If the action
--   is in a <tt><a>MonadPlus</a></tt> and short-circuits after some number
--   of iterations. then <tt><a>forever</a></tt> actually returns
--   <a>mzero</a>, effectively short-circuiting its caller.
forever :: Applicative f => f a -> f b

-- | Like <a>foldM</a>, but discards the result.
foldM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m ()

-- | The <a>foldM</a> function is analogous to <a>foldl</a>, except that
--   its result is encapsulated in a monad. Note that <a>foldM</a> works
--   from left-to-right over the list arguments. This could be an issue
--   where <tt>(<a>&gt;&gt;</a>)</tt> and the `folded function' are not
--   commutative.
--   
--   <pre>
--   foldM f a1 [x1, x2, ..., xm]
--   
--   ==
--   
--   do
--     a2 &lt;- f a1 x1
--     a3 &lt;- f a2 x2
--     ...
--     f am xm
--   </pre>
--   
--   If right-to-left evaluation is required, the input list should be
--   reversed.
--   
--   Note: <a>foldM</a> is the same as <a>foldlM</a>
foldM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b

-- | This generalizes the list-based <a>filter</a> function.
filterM :: Applicative m => (a -> m Bool) -> [a] -> m [a]

-- | Left-to-right composition of Kleisli arrows.
--   
--   '<tt>(bs <a>&gt;=&gt;</a> cs) a</tt>' can be understood as the
--   <tt>do</tt> expression
--   
--   <pre>
--   do b &lt;- bs a
--      cs b
--   </pre>
(>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c
infixr 1 >=>

-- | Right-to-left composition of Kleisli arrows.
--   <tt>(<a>&gt;=&gt;</a>)</tt>, with the arguments flipped.
--   
--   Note how this operator resembles function composition
--   <tt>(<a>.</a>)</tt>:
--   
--   <pre>
--   (.)   ::            (b -&gt;   c) -&gt; (a -&gt;   b) -&gt; a -&gt;   c
--   (&lt;=&lt;) :: Monad m =&gt; (b -&gt; m c) -&gt; (a -&gt; m b) -&gt; a -&gt; m c
--   </pre>
(<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c
infixr 1 <=<

-- | Strict version of <a>&lt;$&gt;</a>.
(<$!>) :: Monad m => (a -> b) -> m a -> m b
infixl 4 <$!>

-- | Provides one possible concrete representation for <a>Version</a>. For
--   a version with <a>versionBranch</a> <tt>= [1,2,3]</tt> and
--   <a>versionTags</a> <tt>= ["tag1","tag2"]</tt>, the output will be
--   <tt>1.2.3-tag1-tag2</tt>.
showVersion :: Version -> String

-- | A parser for versions in the format produced by <a>showVersion</a>.
parseVersion :: ReadP Version

-- | like <a>trace</a>, but additionally prints a call stack if one is
--   available.
--   
--   In the current GHC implementation, the call stack is only available if
--   the program was compiled with <tt>-prof</tt>; otherwise
--   <a>traceStack</a> behaves exactly like <a>trace</a>. Entries in the
--   call stack correspond to <tt>SCC</tt> annotations, so it is a good
--   idea to use <tt>-fprof-auto</tt> or <tt>-fprof-auto-calls</tt> to add
--   SCC annotations automatically.
traceStack :: String -> a -> a

-- | Like <a>traceM</a>, but uses <a>show</a> on the argument to convert it
--   to a <a>String</a>.
--   
--   <pre>
--   &gt;&gt;&gt; :{
--   do
--       x &lt;- Just 3
--       traceShowM x
--       y &lt;- pure 12
--       traceShowM y
--       pure (x*2 + y)
--   :}
--   3
--   12
--   Just 18
--   </pre>
traceShowM :: (Show a, Applicative f) => a -> f ()

-- | Like <a>traceShow</a> but returns the shown value instead of a third
--   value.
--   
--   <pre>
--   &gt;&gt;&gt; traceShowId (1+2+3, "hello" ++ "world")
--   (6,"helloworld")
--   (6,"helloworld")
--   </pre>
traceShowId :: Show a => a -> a

-- | Like <a>trace</a>, but uses <a>show</a> on the argument to convert it
--   to a <a>String</a>.
--   
--   This makes it convenient for printing the values of interesting
--   variables or expressions inside a function. For example here we print
--   the value of the variables <tt>x</tt> and <tt>y</tt>:
--   
--   <pre>
--   &gt;&gt;&gt; let f x y = traceShow (x,y) (x + y) in f (1+2) 5
--   (3,5)
--   8
--   </pre>
traceShow :: Show a => a -> b -> b

-- | The <a>traceMarkerIO</a> function emits a marker to the eventlog, if
--   eventlog profiling is available and enabled at runtime.
--   
--   Compared to <a>traceMarker</a>, <a>traceMarkerIO</a> sequences the
--   event with respect to other IO actions.
traceMarkerIO :: String -> IO ()

-- | The <a>traceMarker</a> function emits a marker to the eventlog, if
--   eventlog profiling is available and enabled at runtime. The
--   <tt>String</tt> is the name of the marker. The name is just used in
--   the profiling tools to help you keep clear which marker is which.
--   
--   This function is suitable for use in pure code. In an IO context use
--   <a>traceMarkerIO</a> instead.
--   
--   Note that when using GHC's SMP runtime, it is possible (but rare) to
--   get duplicate events emitted if two CPUs simultaneously evaluate the
--   same thunk that uses <a>traceMarker</a>.
traceMarker :: String -> a -> a

-- | Like <a>trace</a> but returning unit in an arbitrary
--   <a>Applicative</a> context. Allows for convenient use in do-notation.
--   
--   Note that the application of <a>traceM</a> is not an action in the
--   <a>Applicative</a> context, as <a>traceIO</a> is in the <a>IO</a>
--   type. While the fresh bindings in the following example will force the
--   <a>traceM</a> expressions to be reduced every time the
--   <tt>do</tt>-block is executed, <tt>traceM "not crashed"</tt> would
--   only be reduced once, and the message would only be printed once. If
--   your monad is in <a>MonadIO</a>, <tt><a>liftIO</a> .
--   <a>traceIO</a></tt> may be a better option.
--   
--   <pre>
--   &gt;&gt;&gt; :{
--   do
--       x &lt;- Just 3
--       traceM ("x: " ++ show x)
--       y &lt;- pure 12
--       traceM ("y: " ++ show y)
--       pure (x*2 + y)
--   :}
--   x: 3
--   y: 12
--   Just 18
--   </pre>
traceM :: Applicative f => String -> f ()

-- | Like <a>trace</a> but returns the message instead of a third value.
--   
--   <pre>
--   &gt;&gt;&gt; traceId "hello"
--   hello
--   "hello"
--   </pre>
traceId :: String -> String

-- | The <a>traceIO</a> function outputs the trace message from the IO
--   monad. This sequences the output with respect to other IO actions.
traceIO :: String -> IO ()

-- | The <a>traceEventIO</a> function emits a message to the eventlog, if
--   eventlog profiling is available and enabled at runtime.
--   
--   Compared to <a>traceEvent</a>, <a>traceEventIO</a> sequences the event
--   with respect to other IO actions.
traceEventIO :: String -> IO ()

-- | The <a>traceEvent</a> function behaves like <a>trace</a> with the
--   difference that the message is emitted to the eventlog, if eventlog
--   profiling is available and enabled at runtime.
--   
--   It is suitable for use in pure code. In an IO context use
--   <a>traceEventIO</a> instead.
--   
--   Note that when using GHC's SMP runtime, it is possible (but rare) to
--   get duplicate events emitted if two CPUs simultaneously evaluate the
--   same thunk that uses <a>traceEvent</a>.
traceEvent :: String -> a -> a

putTraceMsg :: String -> IO ()

-- | Immediately flush the event log, if enabled.
flushEventLog :: IO ()

-- | The <a>isSubsequenceOf</a> function takes two lists and returns
--   <a>True</a> if all the elements of the first list occur, in order, in
--   the second. The elements do not have to occur consecutively.
--   
--   <tt><a>isSubsequenceOf</a> x y</tt> is equivalent to <tt><a>elem</a> x
--   (<a>subsequences</a> y)</tt>.
--   
--   <h4><b>Examples</b></h4>
--   
--   <pre>
--   &gt;&gt;&gt; isSubsequenceOf "GHC" "The Glorious Haskell Compiler"
--   True
--   
--   &gt;&gt;&gt; isSubsequenceOf ['a','d'..'z'] ['a'..'z']
--   True
--   
--   &gt;&gt;&gt; isSubsequenceOf [1..10] [10,9..0]
--   False
--   </pre>
isSubsequenceOf :: Eq a => [a] -> [a] -> Bool

-- | The <a>mapAccumR</a> function behaves like a combination of
--   <a>fmap</a> and <a>foldr</a>; it applies a function to each element of
--   a structure, passing an accumulating parameter from right to left, and
--   returning a final value of this accumulator together with the new
--   structure.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; mapAccumR (\a b -&gt; (a + b, a)) 0 [1..10]
--   (55,[54,52,49,45,40,34,27,19,10,0])
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; mapAccumR (\a b -&gt; (a &lt;&gt; show b, a)) "0" [1..5]
--   ("054321",["05432","0543","054","05","0"])
--   </pre>
mapAccumR :: Traversable t => (s -> a -> (s, b)) -> s -> t a -> (s, t b)

-- | The <a>mapAccumL</a> function behaves like a combination of
--   <a>fmap</a> and <a>foldl</a>; it applies a function to each element of
--   a structure, passing an accumulating parameter from left to right, and
--   returning a final value of this accumulator together with the new
--   structure.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; mapAccumL (\a b -&gt; (a + b, a)) 0 [1..10]
--   (55,[0,1,3,6,10,15,21,28,36,45])
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; mapAccumL (\a b -&gt; (a &lt;&gt; show b, a)) "0" [1..5]
--   ("012345",["0","01","012","0123","01234"])
--   </pre>
mapAccumL :: Traversable t => (s -> a -> (s, b)) -> s -> t a -> (s, t b)

-- | <a>forM</a> is <a>mapM</a> with its arguments flipped. For a version
--   that ignores the results see <a>forM_</a>.
forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b)

-- | <a>for</a> is <a>traverse</a> with its arguments flipped. For a
--   version that ignores the results see <a>for_</a>.
for :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b)

-- | This function may be used as a value for <a>foldMap</a> in a
--   <a>Foldable</a> instance.
--   
--   <pre>
--   <a>foldMapDefault</a> f ≡ <a>getConst</a> . <a>traverse</a> (<a>Const</a> . f)
--   </pre>
foldMapDefault :: (Traversable t, Monoid m) => (a -> m) -> t a -> m

-- | This function may be used as a value for <a>fmap</a> in a
--   <a>Functor</a> instance, provided that <a>traverse</a> is defined.
--   (Using <a>fmapDefault</a> with a <a>Traversable</a> instance defined
--   only by <a>sequenceA</a> will result in infinite recursion.)
--   
--   <pre>
--   <a>fmapDefault</a> f ≡ <a>runIdentity</a> . <a>traverse</a> (<a>Identity</a> . f)
--   </pre>
fmapDefault :: Traversable t => (a -> b) -> t a -> t b

-- | Lists, but with an <a>Applicative</a> functor based on zipping.
newtype ZipList a
ZipList :: [a] -> ZipList a
[getZipList] :: ZipList a -> [a]
newtype WrappedMonad (m :: Type -> Type) a
WrapMonad :: m a -> WrappedMonad (m :: Type -> Type) a
[unwrapMonad] :: WrappedMonad (m :: Type -> Type) a -> m a
newtype WrappedArrow (a :: Type -> Type -> Type) b c
WrapArrow :: a b c -> WrappedArrow (a :: Type -> Type -> Type) b c
[unwrapArrow] :: WrappedArrow (a :: Type -> Type -> Type) b c -> a b c

-- | One or none.
--   
--   It is useful for modelling any computation that is allowed to fail.
--   
--   <h4><b>Examples</b></h4>
--   
--   Using the <a>Alternative</a> instance of <a>Control.Monad.Except</a>,
--   the following functions:
--   
--   <pre>
--   &gt;&gt;&gt; import Control.Monad.Except
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; canFail = throwError "it failed" :: Except String Int
--   
--   &gt;&gt;&gt; final = return 42                :: Except String Int
--   </pre>
--   
--   Can be combined by allowing the first function to fail:
--   
--   <pre>
--   &gt;&gt;&gt; runExcept $ canFail *&gt; final
--   Left "it failed"
--   
--   &gt;&gt;&gt; runExcept $ optional canFail *&gt; final
--   Right 42
--   </pre>
optional :: Alternative f => f a -> f (Maybe a)

-- | Kleisli arrows of a monad.
newtype Kleisli (m :: Type -> Type) a b
Kleisli :: (a -> m b) -> Kleisli (m :: Type -> Type) a b
[runKleisli] :: Kleisli (m :: Type -> Type) a b -> a -> m b
class Arrow a => ArrowZero (a :: TYPE LiftedRep -> TYPE LiftedRep -> Type)
zeroArrow :: ArrowZero a => a b c

-- | A monoid on arrows.
class ArrowZero a => ArrowPlus (a :: TYPE LiftedRep -> TYPE LiftedRep -> Type)

-- | An associative operation with identity <a>zeroArrow</a>.
(<+>) :: ArrowPlus a => a b c -> a b c -> a b c
infixr 5 <+>

-- | The <a>ArrowApply</a> class is equivalent to <a>Monad</a>: any monad
--   gives rise to a <a>Kleisli</a> arrow, and any instance of
--   <a>ArrowApply</a> defines a monad.
newtype ArrowMonad (a :: Type -> Type -> Type) b
ArrowMonad :: a () b -> ArrowMonad (a :: Type -> Type -> Type) b

-- | The <a>loop</a> operator expresses computations in which an output
--   value is fed back as input, although the computation occurs only once.
--   It underlies the <tt>rec</tt> value recursion construct in arrow
--   notation. <a>loop</a> should satisfy the following laws:
--   
--   <ul>
--   <li><i><i>extension</i></i> <tt><a>loop</a> (<a>arr</a> f) =
--   <a>arr</a> (\ b -&gt; <a>fst</a> (<a>fix</a> (\ (c,d) -&gt; f
--   (b,d))))</tt></li>
--   <li><i><i>left tightening</i></i> <tt><a>loop</a> (<a>first</a> h
--   &gt;&gt;&gt; f) = h &gt;&gt;&gt; <a>loop</a> f</tt></li>
--   <li><i><i>right tightening</i></i> <tt><a>loop</a> (f &gt;&gt;&gt;
--   <a>first</a> h) = <a>loop</a> f &gt;&gt;&gt; h</tt></li>
--   <li><i><i>sliding</i></i> <tt><a>loop</a> (f &gt;&gt;&gt; <a>arr</a>
--   (<a>id</a> *** k)) = <a>loop</a> (<a>arr</a> (<a>id</a> *** k)
--   &gt;&gt;&gt; f)</tt></li>
--   <li><i><i>vanishing</i></i> <tt><a>loop</a> (<a>loop</a> f) =
--   <a>loop</a> (<a>arr</a> unassoc &gt;&gt;&gt; f &gt;&gt;&gt; <a>arr</a>
--   assoc)</tt></li>
--   <li><i><i>superposing</i></i> <tt><a>second</a> (<a>loop</a> f) =
--   <a>loop</a> (<a>arr</a> assoc &gt;&gt;&gt; <a>second</a> f
--   &gt;&gt;&gt; <a>arr</a> unassoc)</tt></li>
--   </ul>
--   
--   where
--   
--   <pre>
--   assoc ((a,b),c) = (a,(b,c))
--   unassoc (a,(b,c)) = ((a,b),c)
--   </pre>
class Arrow a => ArrowLoop (a :: TYPE LiftedRep -> TYPE LiftedRep -> Type)
loop :: ArrowLoop a => a (b, d) (c, d) -> a b c

-- | Choice, for arrows that support it. This class underlies the
--   <tt>if</tt> and <tt>case</tt> constructs in arrow notation.
--   
--   Instances should satisfy the following laws:
--   
--   <ul>
--   <li><pre><a>left</a> (<a>arr</a> f) = <a>arr</a> (<a>left</a>
--   f)</pre></li>
--   <li><pre><a>left</a> (f &gt;&gt;&gt; g) = <a>left</a> f &gt;&gt;&gt;
--   <a>left</a> g</pre></li>
--   <li><pre>f &gt;&gt;&gt; <a>arr</a> <a>Left</a> = <a>arr</a>
--   <a>Left</a> &gt;&gt;&gt; <a>left</a> f</pre></li>
--   <li><pre><a>left</a> f &gt;&gt;&gt; <a>arr</a> (<a>id</a> +++ g) =
--   <a>arr</a> (<a>id</a> +++ g) &gt;&gt;&gt; <a>left</a> f</pre></li>
--   <li><pre><a>left</a> (<a>left</a> f) &gt;&gt;&gt; <a>arr</a> assocsum
--   = <a>arr</a> assocsum &gt;&gt;&gt; <a>left</a> f</pre></li>
--   </ul>
--   
--   where
--   
--   <pre>
--   assocsum (Left (Left x)) = Left x
--   assocsum (Left (Right y)) = Right (Left y)
--   assocsum (Right z) = Right (Right z)
--   </pre>
--   
--   The other combinators have sensible default definitions, which may be
--   overridden for efficiency.
class Arrow a => ArrowChoice (a :: TYPE LiftedRep -> TYPE LiftedRep -> Type)

-- | Feed marked inputs through the argument arrow, passing the rest
--   through unchanged to the output.
left :: ArrowChoice a => a b c -> a (Either b d) (Either c d)

-- | A mirror image of <a>left</a>.
--   
--   The default definition may be overridden with a more efficient version
--   if desired.
right :: ArrowChoice a => a b c -> a (Either d b) (Either d c)

-- | Split the input between the two argument arrows, retagging and merging
--   their outputs. Note that this is in general not a functor.
--   
--   The default definition may be overridden with a more efficient version
--   if desired.
(+++) :: ArrowChoice a => a b c -> a b' c' -> a (Either b b') (Either c c')

-- | Fanin: Split the input between the two argument arrows and merge their
--   outputs.
--   
--   The default definition may be overridden with a more efficient version
--   if desired.
(|||) :: ArrowChoice a => a b d -> a c d -> a (Either b c) d
infixr 2 |||
infixr 2 +++

-- | Some arrows allow application of arrow inputs to other inputs.
--   Instances should satisfy the following laws:
--   
--   <ul>
--   <li><pre><a>first</a> (<a>arr</a> (\x -&gt; <a>arr</a> (\y -&gt;
--   (x,y)))) &gt;&gt;&gt; <a>app</a> = <a>id</a></pre></li>
--   <li><pre><a>first</a> (<a>arr</a> (g &gt;&gt;&gt;)) &gt;&gt;&gt;
--   <a>app</a> = <a>second</a> g &gt;&gt;&gt; <a>app</a></pre></li>
--   <li><pre><a>first</a> (<a>arr</a> (&gt;&gt;&gt; h)) &gt;&gt;&gt;
--   <a>app</a> = <a>app</a> &gt;&gt;&gt; h</pre></li>
--   </ul>
--   
--   Such arrows are equivalent to monads (see <a>ArrowMonad</a>).
class Arrow a => ArrowApply (a :: TYPE LiftedRep -> TYPE LiftedRep -> Type)
app :: ArrowApply a => a (a b c, b) c

-- | The basic arrow class.
--   
--   Instances should satisfy the following laws:
--   
--   <ul>
--   <li><pre><a>arr</a> id = <a>id</a></pre></li>
--   <li><pre><a>arr</a> (f &gt;&gt;&gt; g) = <a>arr</a> f &gt;&gt;&gt;
--   <a>arr</a> g</pre></li>
--   <li><pre><a>first</a> (<a>arr</a> f) = <a>arr</a> (<a>first</a>
--   f)</pre></li>
--   <li><pre><a>first</a> (f &gt;&gt;&gt; g) = <a>first</a> f &gt;&gt;&gt;
--   <a>first</a> g</pre></li>
--   <li><pre><a>first</a> f &gt;&gt;&gt; <a>arr</a> <a>fst</a> =
--   <a>arr</a> <a>fst</a> &gt;&gt;&gt; f</pre></li>
--   <li><pre><a>first</a> f &gt;&gt;&gt; <a>arr</a> (<a>id</a> *** g) =
--   <a>arr</a> (<a>id</a> *** g) &gt;&gt;&gt; <a>first</a> f</pre></li>
--   <li><pre><a>first</a> (<a>first</a> f) &gt;&gt;&gt; <a>arr</a> assoc =
--   <a>arr</a> assoc &gt;&gt;&gt; <a>first</a> f</pre></li>
--   </ul>
--   
--   where
--   
--   <pre>
--   assoc ((a,b),c) = (a,(b,c))
--   </pre>
--   
--   The other combinators have sensible default definitions, which may be
--   overridden for efficiency.
class Category a => Arrow (a :: TYPE LiftedRep -> TYPE LiftedRep -> Type)

-- | Lift a function to an arrow.
arr :: Arrow a => (b -> c) -> a b c

-- | Split the input between the two argument arrows and combine their
--   output. Note that this is in general not a functor.
--   
--   The default definition may be overridden with a more efficient version
--   if desired.
(***) :: Arrow a => a b c -> a b' c' -> a (b, b') (c, c')

-- | Fanout: send the input to both argument arrows and combine their
--   output.
--   
--   The default definition may be overridden with a more efficient version
--   if desired.
(&&&) :: Arrow a => a b c -> a b c' -> a b (c, c')
infixr 3 &&&
infixr 3 ***

-- | The identity arrow, which plays the role of <a>return</a> in arrow
--   notation.
returnA :: Arrow a => a b b

-- | Any instance of <a>ArrowApply</a> can be made into an instance of
--   <a>ArrowChoice</a> by defining <a>left</a> = <a>leftApp</a>.
leftApp :: ArrowApply a => a b c -> a (Either b d) (Either c d)

-- | Precomposition with a pure function.
(^>>) :: Arrow a => (b -> c) -> a c d -> a b d
infixr 1 ^>>

-- | Postcomposition with a pure function (right-to-left variant).
(^<<) :: Arrow a => (c -> d) -> a b c -> a b d
infixr 1 ^<<

-- | Postcomposition with a pure function.
(>>^) :: Arrow a => a b c -> (c -> d) -> a b d
infixr 1 >>^

-- | Precomposition with a pure function (right-to-left variant).
(<<^) :: Arrow a => a c d -> (b -> c) -> a b d
infixr 1 <<^

-- | Identity functor and monad. (a non-strict monad)
newtype Identity a
Identity :: a -> Identity a
[runIdentity] :: Identity a -> a

-- | The computation <a>writeFile</a> <tt>file str</tt> function writes the
--   string <tt>str</tt>, to the file <tt>file</tt>.
writeFile :: FilePath -> String -> IO ()

-- | The <a>readLn</a> function combines <a>getLine</a> and <a>readIO</a>.
readLn :: Read a => IO a

-- | The <a>readIO</a> function is similar to <a>read</a> except that it
--   signals parse failure to the <a>IO</a> monad instead of terminating
--   the program.
readIO :: Read a => String -> IO a

-- | The <a>readFile</a> function reads a file and returns the contents of
--   the file as a string. The file is read lazily, on demand, as with
--   <a>getContents</a>.
readFile :: FilePath -> IO String

-- | The same as <a>putStr</a>, but adds a newline character.
putStrLn :: String -> IO ()

-- | Write a string to the standard output device (same as <a>hPutStr</a>
--   <a>stdout</a>).
putStr :: String -> IO ()

-- | Write a character to the standard output device (same as
--   <a>hPutChar</a> <a>stdout</a>).
putChar :: Char -> IO ()

-- | The <a>interact</a> function takes a function of type
--   <tt>String-&gt;String</tt> as its argument. The entire input from the
--   standard input device is passed to this function as its argument, and
--   the resulting string is output on the standard output device.
interact :: (String -> String) -> IO ()

-- | Read a line from the standard input device (same as <a>hGetLine</a>
--   <a>stdin</a>).
getLine :: IO String

-- | The <a>getContents</a> operation returns all user input as a single
--   string, which is read lazily as it is needed (same as
--   <a>hGetContents</a> <a>stdin</a>).
getContents :: IO String

-- | Read a character from the standard input device (same as
--   <a>hGetChar</a> <a>stdin</a>).
getChar :: IO Char

-- | The computation <a>appendFile</a> <tt>file str</tt> function appends
--   the string <tt>str</tt>, to the file <tt>file</tt>.
--   
--   Note that <a>writeFile</a> and <a>appendFile</a> write a literal
--   string to a file. To write a value of any printable type, as with
--   <a>print</a>, use the <a>show</a> function to convert the value to a
--   string first.
--   
--   <pre>
--   main = appendFile "squares" (show [(x,x*x) | x &lt;- [0,0.1..2]])
--   </pre>
appendFile :: FilePath -> String -> IO ()

-- | Computation <a>hClose</a> <tt>hdl</tt> makes handle <tt>hdl</tt>
--   closed. Before the computation finishes, if <tt>hdl</tt> is writable
--   its buffer is flushed as for <a>hFlush</a>. Performing <a>hClose</a>
--   on a handle that has already been closed has no effect; doing so is
--   not an error. All other operations on a closed handle will fail. If
--   <a>hClose</a> fails for any reason, any further operations (apart from
--   <a>hClose</a>) on the handle will still fail as if <tt>hdl</tt> had
--   been successfully closed.
--   
--   <a>hClose</a> is an <i>interruptible operation</i> in the sense
--   described in <a>Control.Exception</a>. If <a>hClose</a> is interrupted
--   by an asynchronous exception in the process of flushing its buffers,
--   then the I/O device (e.g., file) will be closed anyway.
hClose :: Handle -> IO ()

-- | Suspends the current thread for a given number of microseconds (GHC
--   only).
--   
--   There is no guarantee that the thread will be rescheduled promptly
--   when the delay has expired, but the thread will never continue to run
--   <i>earlier</i> than specified.
threadDelay :: Int -> IO ()

-- | Switch the value of returned <a>TVar</a> from initial value
--   <a>False</a> to <a>True</a> after a given number of microseconds. The
--   caveats associated with <a>threadDelay</a> also apply.
registerDelay :: Int -> IO (TVar Bool)
ioManagerCapabilitiesChanged :: IO ()
ensureIOManagerIsRunning :: IO ()

-- | Close a file descriptor in a concurrency-safe way (GHC only). If you
--   are using <a>threadWaitRead</a> or <a>threadWaitWrite</a> to perform
--   blocking I/O, you <i>must</i> use this function to close file
--   descriptors, or blocked threads may not be woken.
--   
--   Any threads that are blocked on the file descriptor via
--   <a>threadWaitRead</a> or <a>threadWaitWrite</a> will be unblocked by
--   having IO exceptions thrown.
closeFdWith :: (Fd -> IO ()) -> Fd -> IO ()
type Signal = CInt
type HandlerFun = ForeignPtr Word8 -> IO ()
setHandler :: Signal -> Maybe (HandlerFun, Dynamic) -> IO (Maybe (HandlerFun, Dynamic))
runHandlers :: ForeignPtr Word8 -> Signal -> IO ()

-- | Like <a>withMVar</a>, but the <tt>IO</tt> action in the second
--   argument is executed with asynchronous exceptions masked.
withMVarMasked :: MVar a -> (a -> IO b) -> IO b

-- | <a>withMVar</a> is an exception-safe wrapper for operating on the
--   contents of an <a>MVar</a>. This operation is exception-safe: it will
--   replace the original contents of the <a>MVar</a> if an exception is
--   raised (see <a>Control.Exception</a>). However, it is only atomic if
--   there are no other producers for this <a>MVar</a>.
withMVar :: MVar a -> (a -> IO b) -> IO b

-- | Take a value from an <a>MVar</a>, put a new value into the <a>MVar</a>
--   and return the value taken. This function is atomic only if there are
--   no other producers for this <a>MVar</a>.
swapMVar :: MVar a -> a -> IO a

-- | An exception-safe wrapper for modifying the contents of an
--   <a>MVar</a>. Like <a>withMVar</a>, <a>modifyMVar</a> will replace the
--   original contents of the <a>MVar</a> if an exception is raised during
--   the operation. This function is only atomic if there are no other
--   producers for this <a>MVar</a>.
modifyMVar_ :: MVar a -> (a -> IO a) -> IO ()

-- | Like <a>modifyMVar_</a>, but the <tt>IO</tt> action in the second
--   argument is executed with asynchronous exceptions masked.
modifyMVarMasked_ :: MVar a -> (a -> IO a) -> IO ()

-- | Like <a>modifyMVar</a>, but the <tt>IO</tt> action in the second
--   argument is executed with asynchronous exceptions masked.
modifyMVarMasked :: MVar a -> (a -> IO (a, b)) -> IO b

-- | A slight variation on <a>modifyMVar_</a> that allows a value to be
--   returned (<tt>b</tt>) in addition to the modified value of the
--   <a>MVar</a>.
modifyMVar :: MVar a -> (a -> IO (a, b)) -> IO b

-- | Make a <a>Weak</a> pointer to an <a>MVar</a>, using the second
--   argument as a finalizer to run when <a>MVar</a> is garbage-collected
mkWeakMVar :: MVar a -> IO () -> IO (Weak (MVar a))
addMVarFinalizer :: MVar a -> IO () -> IO ()

-- | A slightly faster version of <a>fixIO</a> that may not be safe to use
--   with multiple threads. The unsafety arises when used like this:
--   
--   <pre>
--   unsafeFixIO $ \r -&gt; do
--      forkIO (print r)
--      return (...)
--   </pre>
--   
--   In this case, the child thread will receive a <tt>NonTermination</tt>
--   exception instead of waiting for the value of <tt>r</tt> to be
--   computed.
unsafeFixIO :: (a -> IO a) -> IO a

-- | You need this when using <a>catches</a>.
data Handler a
Handler :: (e -> IO a) -> Handler a

-- | Sometimes you want to catch two different sorts of exception. You
--   could do something like
--   
--   <pre>
--   f = expr `catch` \ (ex :: ArithException) -&gt; handleArith ex
--            `catch` \ (ex :: IOException)    -&gt; handleIO    ex
--   </pre>
--   
--   However, there are a couple of problems with this approach. The first
--   is that having two exception handlers is inefficient. However, the
--   more serious issue is that the second exception handler will catch
--   exceptions in the first, e.g. in the example above, if
--   <tt>handleArith</tt> throws an <tt>IOException</tt> then the second
--   exception handler will catch it.
--   
--   Instead, we provide a function <a>catches</a>, which would be used
--   thus:
--   
--   <pre>
--   f = expr `catches` [Handler (\ (ex :: ArithException) -&gt; handleArith ex),
--                       Handler (\ (ex :: IOException)    -&gt; handleIO    ex)]
--   </pre>
catches :: IO a -> [Handler a] -> IO a

-- | When invoked inside <a>mask</a>, this function allows a masked
--   asynchronous exception to be raised, if one exists. It is equivalent
--   to performing an interruptible operation (see #interruptible), but
--   does not involve any actual blocking.
--   
--   When called outside <a>mask</a>, or inside <a>uninterruptibleMask</a>,
--   this function has no effect.
allowInterrupt :: IO ()

-- | Allow the result of an <a>ST</a> computation to be used (lazily)
--   inside the computation.
--   
--   Note that if <tt>f</tt> is strict, <tt><a>fixST</a> f = _|_</tt>.
fixST :: (a -> ST s a) -> ST s a

-- | I/O error that is programmer-defined.
userErrorType :: IOErrorType

-- | The construct <a>tryIOError</a> <tt>comp</tt> exposes IO errors which
--   occur within a computation, and which are not fully handled.
--   
--   Non-I/O exceptions are not caught by this variant; to catch all
--   exceptions, use <a>try</a> from <a>Control.Exception</a>.
tryIOError :: IO a -> IO (Either IOError a)

-- | I/O error where the operation failed because the resource vanished.
--   This happens when, for example, attempting to write to a closed socket
--   or attempting to write to a named pipe that was deleted.
resourceVanishedErrorType :: IOErrorType

-- | I/O error where the operation failed because the user does not have
--   sufficient operating system privilege to perform that operation.
permissionErrorType :: IOErrorType

-- | Catch any <a>IOException</a> that occurs in the computation and throw
--   a modified version.
modifyIOError :: (IOError -> IOError) -> IO a -> IO a

-- | Construct an <a>IOException</a> of the given type where the second
--   argument describes the error location and the third and fourth
--   argument contain the file handle and file path of the file involved in
--   the error if applicable.
mkIOError :: IOErrorType -> String -> Maybe Handle -> Maybe FilePath -> IOError

-- | I/O error that is programmer-defined.
isUserErrorType :: IOErrorType -> Bool

-- | A programmer-defined error value constructed using <a>userError</a>.
isUserError :: IOError -> Bool

-- | I/O error where the operation failed because the resource vanished.
--   See <a>resourceVanishedErrorType</a>.
isResourceVanishedErrorType :: IOErrorType -> Bool

-- | An error indicating that the operation failed because the resource
--   vanished. See <a>resourceVanishedErrorType</a>.
isResourceVanishedError :: IOError -> Bool

-- | I/O error where the operation failed because the user does not have
--   sufficient operating system privilege to perform that operation.
isPermissionErrorType :: IOErrorType -> Bool

-- | An error indicating that an <a>IO</a> operation failed because the
--   user does not have sufficient operating system privilege to perform
--   that operation.
isPermissionError :: IOError -> Bool

-- | I/O error where the operation is not possible.
isIllegalOperationErrorType :: IOErrorType -> Bool

-- | An error indicating that an <a>IO</a> operation failed because the
--   operation was not possible. Any computation which returns an <a>IO</a>
--   result may fail with <a>isIllegalOperation</a>. In some cases, an
--   implementation will not be able to distinguish between the possible
--   error causes. In this case it should fail with
--   <a>isIllegalOperation</a>.
isIllegalOperation :: IOError -> Bool

-- | I/O error where the operation failed because the device is full.
isFullErrorType :: IOErrorType -> Bool

-- | An error indicating that an <a>IO</a> operation failed because the
--   device is full.
isFullError :: IOError -> Bool

-- | I/O error where the operation failed because the end of file has been
--   reached.
isEOFErrorType :: IOErrorType -> Bool

-- | An error indicating that an <a>IO</a> operation failed because the end
--   of file has been reached.
isEOFError :: IOError -> Bool

-- | I/O error where the operation failed because one of its arguments does
--   not exist.
isDoesNotExistErrorType :: IOErrorType -> Bool

-- | An error indicating that an <a>IO</a> operation failed because one of
--   its arguments does not exist.
isDoesNotExistError :: IOError -> Bool

-- | I/O error where the operation failed because one of its arguments is a
--   single-use resource, which is already being used.
isAlreadyInUseErrorType :: IOErrorType -> Bool

-- | An error indicating that an <a>IO</a> operation failed because one of
--   its arguments is a single-use resource, which is already being used
--   (for example, opening the same file twice for writing might give this
--   error).
isAlreadyInUseError :: IOError -> Bool

-- | I/O error where the operation failed because one of its arguments
--   already exists.
isAlreadyExistsErrorType :: IOErrorType -> Bool

-- | An error indicating that an <a>IO</a> operation failed because one of
--   its arguments already exists.
isAlreadyExistsError :: IOError -> Bool
ioeSetLocation :: IOError -> String -> IOError
ioeSetHandle :: IOError -> Handle -> IOError
ioeSetFileName :: IOError -> FilePath -> IOError
ioeSetErrorType :: IOError -> IOErrorType -> IOError
ioeSetErrorString :: IOError -> String -> IOError
ioeGetLocation :: IOError -> String
ioeGetHandle :: IOError -> Maybe Handle
ioeGetFileName :: IOError -> Maybe FilePath
ioeGetErrorType :: IOError -> IOErrorType
ioeGetErrorString :: IOError -> String

-- | I/O error where the operation is not possible.
illegalOperationErrorType :: IOErrorType

-- | I/O error where the operation failed because the device is full.
fullErrorType :: IOErrorType

-- | I/O error where the operation failed because the end of file has been
--   reached.
eofErrorType :: IOErrorType

-- | I/O error where the operation failed because one of its arguments does
--   not exist.
doesNotExistErrorType :: IOErrorType

-- | The <a>catchIOError</a> function establishes a handler that receives
--   any <a>IOException</a> raised in the action protected by
--   <a>catchIOError</a>. An <a>IOException</a> is caught by the most
--   recent handler established by one of the exception handling functions.
--   These handlers are not selective: all <a>IOException</a>s are caught.
--   Exception propagation must be explicitly provided in a handler by
--   re-raising any unwanted exceptions. For example, in
--   
--   <pre>
--   f = catchIOError g (\e -&gt; if IO.isEOFError e then return [] else ioError e)
--   </pre>
--   
--   the function <tt>f</tt> returns <tt>[]</tt> when an end-of-file
--   exception (cf. <a>isEOFError</a>) occurs in <tt>g</tt>; otherwise, the
--   exception is propagated to the next outer handler.
--   
--   When an exception propagates outside the main program, the Haskell
--   system prints the associated <a>IOException</a> value and exits the
--   program.
--   
--   Non-I/O exceptions are not caught by this variant; to catch all
--   exceptions, use <a>catch</a> from <a>Control.Exception</a>.
catchIOError :: IO a -> (IOError -> IO a) -> IO a

-- | Adds a location description and maybe a file path and file handle to
--   an <a>IOException</a>. If any of the file handle or file path is not
--   given the corresponding value in the <a>IOException</a> remains
--   unaltered.
annotateIOError :: IOError -> String -> Maybe Handle -> Maybe FilePath -> IOError

-- | I/O error where the operation failed because one of its arguments is a
--   single-use resource, which is already being used.
alreadyInUseErrorType :: IOErrorType

-- | I/O error where the operation failed because one of its arguments
--   already exists.
alreadyExistsErrorType :: IOErrorType

-- | An expression that didn't typecheck during compile time was called.
--   This is only possible with -fdefer-type-errors. The <tt>String</tt>
--   gives details about the failed type check.
newtype TypeError
TypeError :: String -> TypeError

-- | A record update was performed on a constructor without the appropriate
--   field. This can only happen with a datatype with multiple
--   constructors, where some fields are in one constructor but not
--   another. The <tt>String</tt> gives information about the source
--   location of the record update.
newtype RecUpdError
RecUpdError :: String -> RecUpdError

-- | A record selector was applied to a constructor without the appropriate
--   field. This can only happen with a datatype with multiple
--   constructors, where some fields are in one constructor but not
--   another. The <tt>String</tt> gives information about the source
--   location of the record selector.
newtype RecSelError
RecSelError :: String -> RecSelError

-- | An uninitialised record field was used. The <tt>String</tt> gives
--   information about the source location where the record was
--   constructed.
newtype RecConError
RecConError :: String -> RecConError

-- | A pattern match failed. The <tt>String</tt> gives information about
--   the source location of the pattern.
newtype PatternMatchFail
PatternMatchFail :: String -> PatternMatchFail

-- | Thrown when the runtime system detects that the computation is
--   guaranteed not to terminate. Note that there is no guarantee that the
--   runtime system will notice whether any given computation is guaranteed
--   to terminate or not.
data NonTermination
NonTermination :: NonTermination

-- | A class method without a definition (neither a default definition, nor
--   a definition in the appropriate instance) was called. The
--   <tt>String</tt> gives information about which method it was.
newtype NoMethodError
NoMethodError :: String -> NoMethodError

-- | Thrown when the program attempts to call <tt>atomically</tt>, from the
--   <tt>stm</tt> package, inside another call to <tt>atomically</tt>.
data NestedAtomically
NestedAtomically :: NestedAtomically

-- | A variant of <a>try</a> that takes an exception predicate to select
--   which exceptions are caught (c.f. <a>catchJust</a>). If the exception
--   does not match the predicate, it is re-thrown.
tryJust :: Exception e => (e -> Maybe b) -> IO a -> IO (Either b a)

-- | Similar to <a>catch</a>, but returns an <a>Either</a> result which is
--   <tt>(<a>Right</a> a)</tt> if no exception of type <tt>e</tt> was
--   raised, or <tt>(<a>Left</a> ex)</tt> if an exception of type
--   <tt>e</tt> was raised and its value is <tt>ex</tt>. If any other type
--   of exception is raised then it will be propagated up to the next
--   enclosing exception handler.
--   
--   <pre>
--   try a = catch (Right `liftM` a) (return . Left)
--   </pre>
try :: Exception e => IO a -> IO (Either e a)

-- | Like <a>finally</a>, but only performs the final action if there was
--   an exception raised by the computation.
onException :: IO a -> IO b -> IO a

-- | This function maps one exception into another as proposed in the paper
--   "A semantics for imprecise exceptions".
mapException :: (Exception e1, Exception e2) => (e1 -> e2) -> a -> a

-- | A version of <a>catchJust</a> with the arguments swapped around (see
--   <a>handle</a>).
handleJust :: Exception e => (e -> Maybe b) -> (b -> IO a) -> IO a -> IO a

-- | A version of <a>catch</a> with the arguments swapped around; useful in
--   situations where the code for the handler is shorter. For example:
--   
--   <pre>
--   do handle (\NonTermination -&gt; exitWith (ExitFailure 1)) $
--      ...
--   </pre>
handle :: Exception e => (e -> IO a) -> IO a -> IO a

-- | A specialised variant of <a>bracket</a> with just a computation to run
--   afterward.
finally :: IO a -> IO b -> IO a

-- | The function <a>catchJust</a> is like <a>catch</a>, but it takes an
--   extra argument which is an <i>exception predicate</i>, a function
--   which selects which type of exceptions we're interested in.
--   
--   <pre>
--   catchJust (\e -&gt; if isDoesNotExistErrorType (ioeGetErrorType e) then Just () else Nothing)
--             (readFile f)
--             (\_ -&gt; do hPutStrLn stderr ("No such file: " ++ show f)
--                       return "")
--   </pre>
--   
--   Any other exceptions which are not matched by the predicate are
--   re-raised, and may be caught by an enclosing <a>catch</a>,
--   <a>catchJust</a>, etc.
catchJust :: Exception e => (e -> Maybe b) -> IO a -> (b -> IO a) -> IO a

-- | A variant of <a>bracket</a> where the return value from the first
--   computation is not required.
bracket_ :: IO a -> IO b -> IO c -> IO c

-- | Like <a>bracket</a>, but only performs the final action if there was
--   an exception raised by the in-between computation.
bracketOnError :: IO a -> (a -> IO b) -> (a -> IO c) -> IO c

-- | When you want to acquire a resource, do some work with it, and then
--   release the resource, it is a good idea to use <a>bracket</a>, because
--   <a>bracket</a> will install the necessary exception handler to release
--   the resource in the event that an exception is raised during the
--   computation. If an exception is raised, then <a>bracket</a> will
--   re-raise the exception (after performing the release).
--   
--   A common example is opening a file:
--   
--   <pre>
--   bracket
--     (openFile "filename" ReadMode)
--     (hClose)
--     (\fileHandle -&gt; do { ... })
--   </pre>
--   
--   The arguments to <a>bracket</a> are in this order so that we can
--   partially apply it, e.g.:
--   
--   <pre>
--   withFile name mode = bracket (openFile name mode) hClose
--   </pre>
--   
--   Bracket wraps the release action with <a>mask</a>, which is sufficient
--   to ensure that the release action executes to completion when it does
--   not invoke any interruptible actions, even in the presence of
--   asynchronous exceptions. For example, <tt>hClose</tt> is
--   uninterruptible when it is not racing other uses of the handle.
--   Similarly, closing a socket (from "network" package) is also
--   uninterruptible under similar conditions. An example of an
--   interruptible action is <a>killThread</a>. Completion of interruptible
--   release actions can be ensured by wrapping them in in
--   <a>uninterruptibleMask_</a>, but this risks making the program
--   non-responsive to <tt>Control-C</tt>, or timeouts. Another option is
--   to run the release action asynchronously in its own thread:
--   
--   <pre>
--   void $ uninterruptibleMask_ $ forkIO $ do { ... }
--   </pre>
--   
--   The resource will be released as soon as possible, but the thread that
--   invoked bracket will not block in an uninterruptible state.
bracket :: IO a -> (a -> IO b) -> (a -> IO c) -> IO c

-- | The current status of a thread
data ThreadStatus

-- | the thread is currently runnable or running
ThreadRunning :: ThreadStatus

-- | the thread has finished
ThreadFinished :: ThreadStatus

-- | the thread is blocked on some resource
ThreadBlocked :: BlockReason -> ThreadStatus

-- | the thread received an uncaught exception
ThreadDied :: ThreadStatus

-- | A <a>ThreadId</a> is an abstract type representing a handle to a
--   thread. <a>ThreadId</a> is an instance of <a>Eq</a>, <a>Ord</a> and
--   <a>Show</a>, where the <a>Ord</a> instance implements an arbitrary
--   total ordering over <a>ThreadId</a>s. The <a>Show</a> instance lets
--   you convert an arbitrary-valued <a>ThreadId</a> to string form;
--   showing a <a>ThreadId</a> value is occasionally useful when debugging
--   or diagnosing the behaviour of a concurrent program.
--   
--   <i>Note</i>: in GHC, if you have a <a>ThreadId</a>, you essentially
--   have a pointer to the thread itself. This means the thread itself
--   can't be garbage collected until you drop the <a>ThreadId</a>. This
--   misfeature will hopefully be corrected at a later date.
data ThreadId
ThreadId :: ThreadId# -> ThreadId

-- | Shared memory locations that support atomic memory transactions.
data TVar a
TVar :: TVar# RealWorld a -> TVar a

-- | A monad supporting atomic memory transactions.
newtype STM a
STM :: (State# RealWorld -> (# State# RealWorld, a #)) -> STM a
data PrimMVar
data BlockReason

-- | blocked on <a>MVar</a>
BlockedOnMVar :: BlockReason

-- | blocked on a computation in progress by another thread
BlockedOnBlackHole :: BlockReason

-- | blocked in <a>throwTo</a>
BlockedOnException :: BlockReason

-- | blocked in <a>retry</a> in an STM transaction
BlockedOnSTM :: BlockReason

-- | currently in a foreign call
BlockedOnForeignCall :: BlockReason

-- | blocked on some other resource. Without <tt>-threaded</tt>, I/O and
--   <a>threadDelay</a> show up as <a>BlockedOnOther</a>, with
--   <tt>-threaded</tt> they show up as <a>BlockedOnMVar</a>.
BlockedOnOther :: BlockReason

-- | The <a>yield</a> action allows (forces, in a co-operative multitasking
--   implementation) a context-switch to any other currently runnable
--   threads (if any), and is occasionally useful when implementing
--   concurrency abstractions.
yield :: IO ()

-- | Write the supplied value into a <a>TVar</a>.
writeTVar :: TVar a -> a -> STM ()

-- | Unsafely performs IO in the STM monad. Beware: this is a highly
--   dangerous thing to do.
--   
--   <ul>
--   <li>The STM implementation will often run transactions multiple times,
--   so you need to be prepared for this if your IO has any side
--   effects.</li>
--   <li>The STM implementation will abort transactions that are known to
--   be invalid and need to be restarted. This may happen in the middle of
--   <a>unsafeIOToSTM</a>, so make sure you don't acquire any resources
--   that need releasing (exception handlers are ignored when aborting the
--   transaction). That includes doing any IO using Handles, for example.
--   Getting this wrong will probably lead to random deadlocks.</li>
--   <li>The transaction may have seen an inconsistent view of memory when
--   the IO runs. Invariants that you expect to be true throughout your
--   program may not be true inside a transaction, due to the way
--   transactions are implemented. Normally this wouldn't be visible to the
--   programmer, but using <a>unsafeIOToSTM</a> can expose it.</li>
--   </ul>
unsafeIOToSTM :: IO a -> STM a

-- | <a>throwTo</a> raises an arbitrary exception in the target thread (GHC
--   only).
--   
--   Exception delivery synchronizes between the source and target thread:
--   <a>throwTo</a> does not return until the exception has been raised in
--   the target thread. The calling thread can thus be certain that the
--   target thread has received the exception. Exception delivery is also
--   atomic with respect to other exceptions. Atomicity is a useful
--   property to have when dealing with race conditions: e.g. if there are
--   two threads that can kill each other, it is guaranteed that only one
--   of the threads will get to kill the other.
--   
--   Whatever work the target thread was doing when the exception was
--   raised is not lost: the computation is suspended until required by
--   another thread.
--   
--   If the target thread is currently making a foreign call, then the
--   exception will not be raised (and hence <a>throwTo</a> will not
--   return) until the call has completed. This is the case regardless of
--   whether the call is inside a <a>mask</a> or not. However, in GHC a
--   foreign call can be annotated as <tt>interruptible</tt>, in which case
--   a <a>throwTo</a> will cause the RTS to attempt to cause the call to
--   return; see the GHC documentation for more details.
--   
--   Important note: the behaviour of <a>throwTo</a> differs from that
--   described in the paper "Asynchronous exceptions in Haskell"
--   (<a>http://research.microsoft.com/~simonpj/Papers/asynch-exns.htm</a>).
--   In the paper, <a>throwTo</a> is non-blocking; but the library
--   implementation adopts a more synchronous design in which
--   <a>throwTo</a> does not return until the exception is received by the
--   target thread. The trade-off is discussed in Section 9 of the paper.
--   Like any blocking operation, <a>throwTo</a> is therefore interruptible
--   (see Section 5.3 of the paper). Unlike other interruptible operations,
--   however, <a>throwTo</a> is <i>always</i> interruptible, even if it
--   does not actually block.
--   
--   There is no guarantee that the exception will be delivered promptly,
--   although the runtime will endeavour to ensure that arbitrary delays
--   don't occur. In GHC, an exception can only be raised when a thread
--   reaches a <i>safe point</i>, where a safe point is where memory
--   allocation occurs. Some loops do not perform any memory allocation
--   inside the loop and therefore cannot be interrupted by a
--   <a>throwTo</a>.
--   
--   If the target of <a>throwTo</a> is the calling thread, then the
--   behaviour is the same as <a>throwIO</a>, except that the exception is
--   thrown as an asynchronous exception. This means that if there is an
--   enclosing pure computation, which would be the case if the current IO
--   operation is inside <a>unsafePerformIO</a> or
--   <a>unsafeInterleaveIO</a>, that computation is not permanently
--   replaced by the exception, but is suspended as if it had received an
--   asynchronous exception.
--   
--   Note that if <a>throwTo</a> is called with the current thread as the
--   target, the exception will be thrown even if the thread is currently
--   inside <a>mask</a> or <a>uninterruptibleMask</a>.
throwTo :: Exception e => ThreadId -> e -> IO ()

-- | A variant of <a>throw</a> that can only be used within the <a>STM</a>
--   monad.
--   
--   Throwing an exception in <tt>STM</tt> aborts the transaction and
--   propagates the exception. If the exception is caught via
--   <a>catchSTM</a>, only the changes enclosed by the catch are rolled
--   back; changes made outside of <a>catchSTM</a> persist.
--   
--   If the exception is not caught inside of the <a>STM</a>, it is
--   re-thrown by <a>atomically</a>, and the entire <a>STM</a> is rolled
--   back.
--   
--   Although <a>throwSTM</a> has a type that is an instance of the type of
--   <a>throw</a>, the two functions are subtly different:
--   
--   <pre>
--   throw e    `seq` x  ===&gt; throw e
--   throwSTM e `seq` x  ===&gt; x
--   </pre>
--   
--   The first example will cause the exception <tt>e</tt> to be raised,
--   whereas the second one won't. In fact, <a>throwSTM</a> will only cause
--   an exception to be raised when it is used within the <a>STM</a> monad.
--   The <a>throwSTM</a> variant should be used in preference to
--   <a>throw</a> to raise an exception within the <a>STM</a> monad because
--   it guarantees ordering with respect to other <a>STM</a> operations,
--   whereas <a>throw</a> does not.
throwSTM :: Exception e => e -> STM a
threadStatus :: ThreadId -> IO ThreadStatus

-- | Returns the number of the capability on which the thread is currently
--   running, and a boolean indicating whether the thread is locked to that
--   capability or not. A thread is locked to a capability if it was
--   created with <tt>forkOn</tt>.
threadCapability :: ThreadId -> IO (Int, Bool)
setUncaughtExceptionHandler :: (SomeException -> IO ()) -> IO ()

-- | Set the number of Haskell threads that can run truly simultaneously
--   (on separate physical processors) at any given time. The number passed
--   to <a>forkOn</a> is interpreted modulo this value. The initial value
--   is given by the <tt>+RTS -N</tt> runtime flag.
--   
--   This is also the number of threads that will participate in parallel
--   garbage collection. It is strongly recommended that the number of
--   capabilities is not set larger than the number of physical processor
--   cores, and it may often be beneficial to leave one or more cores free
--   to avoid contention with other processes in the machine.
setNumCapabilities :: Int -> IO ()

-- | Every thread has an allocation counter that tracks how much memory has
--   been allocated by the thread. The counter is initialized to zero, and
--   <a>setAllocationCounter</a> sets the current value. The allocation
--   counter counts *down*, so in the absence of a call to
--   <a>setAllocationCounter</a> its value is the negation of the number of
--   bytes of memory allocated by the thread.
--   
--   There are two things that you can do with this counter:
--   
--   <ul>
--   <li>Use it as a simple profiling mechanism, with
--   <a>getAllocationCounter</a>.</li>
--   <li>Use it as a resource limit. See <a>enableAllocationLimit</a>.</li>
--   </ul>
--   
--   Allocation accounting is accurate only to about 4Kbytes.
setAllocationCounter :: Int64 -> IO ()

-- | Internal function used by the RTS to run sparks.
runSparks :: IO ()

-- | Retry execution of the current memory transaction because it has seen
--   values in <a>TVar</a>s which mean that it should not continue (e.g.
--   the <a>TVar</a>s represent a shared buffer that is now empty). The
--   implementation may block the thread until one of the <a>TVar</a>s that
--   it has read from has been updated. (GHC only)
retry :: STM a
reportStackOverflow :: IO ()
reportHeapOverflow :: IO ()
reportError :: SomeException -> IO ()

-- | Return the current value stored in a <a>TVar</a>. This is equivalent
--   to
--   
--   <pre>
--   readTVarIO = atomically . readTVar
--   </pre>
--   
--   but works much faster, because it doesn't perform a complete
--   transaction, it just reads the current value of the <a>TVar</a>.
readTVarIO :: TVar a -> IO a

-- | Return the current value stored in a <a>TVar</a>.
readTVar :: TVar a -> STM a
pseq :: a -> b -> b
infixr 0 `pseq`
par :: a -> b -> b
infixr 0 `par`

-- | Returns the number of sparks currently in the local spark pool
numSparks :: IO Int

-- | the value passed to the <tt>+RTS -N</tt> flag. This is the number of
--   Haskell threads that can run truly simultaneously at any given time,
--   and is typically set to the number of physical processor cores on the
--   machine.
--   
--   Strictly speaking it is better to use <a>getNumCapabilities</a>,
--   because the number of capabilities might vary at runtime.
numCapabilities :: Int

-- | <tt>IO</tt> version of <a>newTVar</a>. This is useful for creating
--   top-level <a>TVar</a>s using <a>unsafePerformIO</a>, because using
--   <a>atomically</a> inside <a>unsafePerformIO</a> isn't possible.
newTVarIO :: a -> IO (TVar a)

-- | Create a new <a>TVar</a> holding a value supplied
newTVar :: a -> STM (TVar a)

-- | Make a StablePtr that can be passed to the C function
--   <tt>hs_try_putmvar()</tt>. The RTS wants a <a>StablePtr</a> to the
--   underlying <a>MVar#</a>, but a <a>StablePtr#</a> can only refer to
--   lifted types, so we have to cheat by coercing.
newStablePtrPrimMVar :: MVar () -> IO (StablePtr PrimMVar)

-- | Returns the <a>ThreadId</a> of the calling thread (GHC only).
myThreadId :: IO ThreadId

-- | Make a weak pointer to a <a>ThreadId</a>. It can be important to do
--   this if you want to hold a reference to a <a>ThreadId</a> while still
--   allowing the thread to receive the <tt>BlockedIndefinitely</tt> family
--   of exceptions (e.g. <a>BlockedIndefinitelyOnMVar</a>). Holding a
--   normal <a>ThreadId</a> reference will prevent the delivery of
--   <tt>BlockedIndefinitely</tt> exceptions because the reference could be
--   used as the target of <a>throwTo</a> at any time, which would unblock
--   the thread.
--   
--   Holding a <tt>Weak ThreadId</tt>, on the other hand, will not prevent
--   the thread from receiving <tt>BlockedIndefinitely</tt> exceptions. It
--   is still possible to throw an exception to a <tt>Weak ThreadId</tt>,
--   but the caller must use <tt>deRefWeak</tt> first to determine whether
--   the thread still exists.
mkWeakThreadId :: ThreadId -> IO (Weak ThreadId)

-- | <a>labelThread</a> stores a string as identifier for this thread. This
--   identifier will be used in the debugging output to make distinction of
--   different threads easier (otherwise you only have the thread state
--   object's address in the heap). It also emits an event to the RTS
--   eventlog.
--   
--   Other applications like the graphical Concurrent Haskell Debugger
--   (<a>http://www.informatik.uni-kiel.de/~fhu/chd/</a>) may choose to
--   overload <a>labelThread</a> for their purposes as well.
labelThread :: ThreadId -> String -> IO ()

-- | <a>killThread</a> raises the <a>ThreadKilled</a> exception in the
--   given thread (GHC only).
--   
--   <pre>
--   killThread tid = throwTo tid ThreadKilled
--   </pre>
killThread :: ThreadId -> IO ()
getUncaughtExceptionHandler :: IO (SomeException -> IO ())

-- | Returns the number of CPUs that the machine has
getNumProcessors :: IO Int

-- | Returns the number of Haskell threads that can run truly
--   simultaneously (on separate physical processors) at any given time. To
--   change this value, use <a>setNumCapabilities</a>.
getNumCapabilities :: IO Int

-- | Return the current value of the allocation counter for the current
--   thread.
getAllocationCounter :: IO Int64

-- | Like <a>forkIOWithUnmask</a>, but the child thread is pinned to the
--   given CPU, as with <a>forkOn</a>.
forkOnWithUnmask :: Int -> ((forall a. () => IO a -> IO a) -> IO ()) -> IO ThreadId

-- | Like <a>forkIO</a>, but lets you specify on which capability the
--   thread should run. Unlike a <a>forkIO</a> thread, a thread created by
--   <a>forkOn</a> will stay on the same capability for its entire lifetime
--   (<a>forkIO</a> threads can migrate between capabilities according to
--   the scheduling policy). <a>forkOn</a> is useful for overriding the
--   scheduling policy when you know in advance how best to distribute the
--   threads.
--   
--   The <a>Int</a> argument specifies a <i>capability number</i> (see
--   <a>getNumCapabilities</a>). Typically capabilities correspond to
--   physical processors, but the exact behaviour is
--   implementation-dependent. The value passed to <a>forkOn</a> is
--   interpreted modulo the total number of capabilities as returned by
--   <a>getNumCapabilities</a>.
--   
--   GHC note: the number of capabilities is specified by the <tt>+RTS
--   -N</tt> option when the program is started. Capabilities can be fixed
--   to actual processor cores with <tt>+RTS -qa</tt> if the underlying
--   operating system supports that, although in practice this is usually
--   unnecessary (and may actually degrade performance in some cases -
--   experimentation is recommended).
forkOn :: Int -> IO () -> IO ThreadId

-- | Like <a>forkIO</a>, but the child thread is passed a function that can
--   be used to unmask asynchronous exceptions. This function is typically
--   used in the following way
--   
--   <pre>
--   ... mask_ $ forkIOWithUnmask $ \unmask -&gt;
--                  catch (unmask ...) handler
--   </pre>
--   
--   so that the exception handler in the child thread is established with
--   asynchronous exceptions masked, meanwhile the main body of the child
--   thread is executed in the unmasked state.
--   
--   Note that the unmask function passed to the child thread should only
--   be used in that thread; the behaviour is undefined if it is invoked in
--   a different thread.
forkIOWithUnmask :: ((forall a. () => IO a -> IO a) -> IO ()) -> IO ThreadId

-- | Creates a new thread to run the <a>IO</a> computation passed as the
--   first argument, and returns the <a>ThreadId</a> of the newly created
--   thread.
--   
--   The new thread will be a lightweight, <i>unbound</i> thread. Foreign
--   calls made by this thread are not guaranteed to be made by any
--   particular OS thread; if you need foreign calls to be made by a
--   particular OS thread, then use <a>forkOS</a> instead.
--   
--   The new thread inherits the <i>masked</i> state of the parent (see
--   <a>mask</a>).
--   
--   The newly created thread has an exception handler that discards the
--   exceptions <a>BlockedIndefinitelyOnMVar</a>,
--   <a>BlockedIndefinitelyOnSTM</a>, and <a>ThreadKilled</a>, and passes
--   all other exceptions to the uncaught exception handler.
forkIO :: IO () -> IO ThreadId

-- | Enables the allocation counter to be treated as a limit for the
--   current thread. When the allocation limit is enabled, if the
--   allocation counter counts down below zero, the thread will be sent the
--   <a>AllocationLimitExceeded</a> asynchronous exception. When this
--   happens, the counter is reinitialised (by default to 100K, but tunable
--   with the <tt>+RTS -xq</tt> option) so that it can handle the exception
--   and perform any necessary clean up. If it exhausts this additional
--   allowance, another <a>AllocationLimitExceeded</a> exception is sent,
--   and so forth. Like other asynchronous exceptions, the
--   <a>AllocationLimitExceeded</a> exception is deferred while the thread
--   is inside <a>mask</a> or an exception handler in <a>catch</a>.
--   
--   Note that memory allocation is unrelated to <i>live memory</i>, also
--   known as <i>heap residency</i>. A thread can allocate a large amount
--   of memory and retain anything between none and all of it. It is better
--   to think of the allocation limit as a limit on <i>CPU time</i>, rather
--   than a limit on memory.
--   
--   Compared to using timeouts, allocation limits don't count time spent
--   blocked or in foreign calls.
enableAllocationLimit :: IO ()

-- | Disable allocation limit processing for the current thread.
disableAllocationLimit :: IO ()
childHandler :: SomeException -> IO ()

-- | Exception handling within STM actions.
--   
--   <tt><a>catchSTM</a> m f</tt> catches any exception thrown by
--   <tt>m</tt> using <a>throwSTM</a>, using the function <tt>f</tt> to
--   handle the exception. If an exception is thrown, any changes made by
--   <tt>m</tt> are rolled back, but changes prior to <tt>m</tt> persist.
catchSTM :: Exception e => STM a -> (e -> STM a) -> STM a

-- | Perform a series of STM actions atomically.
--   
--   Using <a>atomically</a> inside an <a>unsafePerformIO</a> or
--   <a>unsafeInterleaveIO</a> subverts some of guarantees that STM
--   provides. It makes it possible to run a transaction inside of another
--   transaction, depending on when the thunk is evaluated. If a nested
--   transaction is attempted, an exception is thrown by the runtime. It is
--   possible to safely use <a>atomically</a> inside <a>unsafePerformIO</a>
--   or <a>unsafeInterleaveIO</a>, but the typechecker does not rule out
--   programs that may attempt nested transactions, meaning that the
--   programmer must take special care to prevent these.
--   
--   However, there are functions for creating transactional variables that
--   can always be safely called in <a>unsafePerformIO</a>. See:
--   <a>newTVarIO</a>, <a>newTChanIO</a>, <a>newBroadcastTChanIO</a>,
--   <a>newTQueueIO</a>, <a>newTBQueueIO</a>, and <a>newTMVarIO</a>.
--   
--   Using <a>unsafePerformIO</a> inside of <a>atomically</a> is also
--   dangerous but for different reasons. See <a>unsafeIOToSTM</a> for more
--   on this.
atomically :: STM a -> IO a

-- | A value of type <a>Dynamic</a> is an object encapsulated together with
--   its type.
--   
--   A <a>Dynamic</a> may only represent a monomorphic value; an attempt to
--   create a value of type <a>Dynamic</a> from a polymorphically-typed
--   expression will result in an ambiguity error (see <a>toDyn</a>).
--   
--   <a>Show</a>ing a value of type <a>Dynamic</a> returns a pretty-printed
--   representation of the object's type; useful for debugging.
data Dynamic
[Dynamic] :: forall a. TypeRep a -> a -> Dynamic

-- | Converts a <a>Dynamic</a> object back into an ordinary Haskell value
--   of the correct type. See also <a>fromDyn</a>.
fromDynamic :: Typeable a => Dynamic -> Maybe a

-- | Converts a <a>Dynamic</a> object back into an ordinary Haskell value
--   of the correct type. See also <a>fromDynamic</a>.
fromDyn :: Typeable a => Dynamic -> a -> a
dynTypeRep :: Dynamic -> SomeTypeRep
dynApply :: Dynamic -> Dynamic -> Maybe Dynamic
dynApp :: Dynamic -> Dynamic -> Dynamic

-- | Superclass for asynchronous exceptions.
data SomeAsyncException
SomeAsyncException :: e -> SomeAsyncException

-- | An abstract type that contains a value for each variant of
--   <a>IOException</a>.
data IOErrorType
AlreadyExists :: IOErrorType
NoSuchThing :: IOErrorType
ResourceBusy :: IOErrorType
ResourceExhausted :: IOErrorType
EOF :: IOErrorType
IllegalOperation :: IOErrorType
PermissionDenied :: IOErrorType
UserError :: IOErrorType
UnsatisfiedConstraints :: IOErrorType
SystemError :: IOErrorType
ProtocolError :: IOErrorType
OtherError :: IOErrorType
InvalidArgument :: IOErrorType
InappropriateType :: IOErrorType
HardwareFault :: IOErrorType
UnsupportedOperation :: IOErrorType
TimeExpired :: IOErrorType
ResourceVanished :: IOErrorType
Interrupted :: IOErrorType

-- | The exception thrown when an infinite cycle is detected in
--   <a>fixIO</a>.
data FixIOException
FixIOException :: FixIOException

-- | Defines the exit codes that a program can return.
data ExitCode

-- | indicates successful termination;
ExitSuccess :: ExitCode

-- | indicates program failure with an exit code. The exact interpretation
--   of the code is operating-system dependent. In particular, some values
--   may be prohibited (e.g. 0 on a POSIX-compliant system).
ExitFailure :: Int -> ExitCode

-- | There are no runnable threads, so the program is deadlocked. The
--   <tt>Deadlock</tt> exception is raised in the main thread only.
data Deadlock
Deadlock :: Deadlock

-- | Compaction found an object that cannot be compacted. Functions cannot
--   be compacted, nor can mutable objects or pinned objects. See
--   <a>compact</a>.
newtype CompactionFailed
CompactionFailed :: String -> CompactionFailed

-- | The thread is waiting to retry an STM transaction, but there are no
--   other references to any <tt>TVar</tt>s involved, so it can't ever
--   continue.
data BlockedIndefinitelyOnSTM
BlockedIndefinitelyOnSTM :: BlockedIndefinitelyOnSTM

-- | The thread is blocked on an <tt>MVar</tt>, but there are no other
--   references to the <tt>MVar</tt> so it can't ever continue.
data BlockedIndefinitelyOnMVar
BlockedIndefinitelyOnMVar :: BlockedIndefinitelyOnMVar

-- | Asynchronous exceptions.
data AsyncException

-- | The current thread's stack exceeded its limit. Since an exception has
--   been raised, the thread's stack will certainly be below its limit
--   again, but the programmer should take remedial action immediately.
StackOverflow :: AsyncException

-- | The program's heap is reaching its limit, and the program should take
--   action to reduce the amount of live data it has. Notes:
--   
--   <ul>
--   <li>It is undefined which thread receives this exception. GHC
--   currently throws this to the same thread that receives
--   <a>UserInterrupt</a>, but this may change in the future.</li>
--   <li>The GHC RTS currently can only recover from heap overflow if it
--   detects that an explicit memory limit (set via RTS flags). has been
--   exceeded. Currently, failure to allocate memory from the operating
--   system results in immediate termination of the program.</li>
--   </ul>
HeapOverflow :: AsyncException

-- | This exception is raised by another thread calling <a>killThread</a>,
--   or by the system if it needs to terminate the thread for some reason.
ThreadKilled :: AsyncException

-- | This exception is raised by default in the main thread of the program
--   when the user requests to terminate the program via the usual
--   mechanism(s) (e.g. Control-C in the console).
UserInterrupt :: AsyncException

-- | <a>assert</a> was applied to <a>False</a>.
newtype AssertionFailed
AssertionFailed :: String -> AssertionFailed

-- | Exceptions generated by array operations
data ArrayException

-- | An attempt was made to index an array outside its declared bounds.
IndexOutOfBounds :: String -> ArrayException

-- | An attempt was made to evaluate an element of an array that had not
--   been initialized.
UndefinedElement :: String -> ArrayException

-- | This thread has exceeded its allocation limit. See
--   <a>setAllocationCounter</a> and <a>enableAllocationLimit</a>.
data AllocationLimitExceeded
AllocationLimitExceeded :: AllocationLimitExceeded
untangle :: Addr# -> String -> String
stackOverflow :: SomeException
ioException :: IOException -> IO a

-- | Raise an <a>IOException</a> in the <a>IO</a> monad.
ioError :: IOError -> IO a
heapOverflow :: SomeException
cannotCompactPinned :: SomeException
cannotCompactMutable :: SomeException
cannotCompactFunction :: SomeException
blockedIndefinitelyOnSTM :: SomeException
blockedIndefinitelyOnMVar :: SomeException

asyncExceptionToException :: Exception e => e -> SomeException

asyncExceptionFromException :: Exception e => SomeException -> Maybe e
allocationLimitExceeded :: SomeException

-- | Strict version of <a>modifyIORef</a>
modifyIORef' :: IORef a -> (a -> a) -> IO ()

-- | Mutate the contents of an <a>IORef</a>.
--   
--   Be warned that <a>modifyIORef</a> does not apply the function
--   strictly. This means if the program calls <a>modifyIORef</a> many
--   times, but seldom uses the value, thunks will pile up in memory
--   resulting in a space leak. This is a common mistake made when using an
--   IORef as a counter. For example, the following will likely produce a
--   stack overflow:
--   
--   <pre>
--   ref &lt;- newIORef 0
--   replicateM_ 1000000 $ modifyIORef ref (+1)
--   readIORef ref &gt;&gt;= print
--   </pre>
--   
--   To avoid this problem, use <a>modifyIORef'</a> instead.
modifyIORef :: IORef a -> (a -> a) -> IO ()

-- | Make a <a>Weak</a> pointer to an <a>IORef</a>, using the second
--   argument as a finalizer to run when <a>IORef</a> is garbage-collected
mkWeakIORef :: IORef a -> IO () -> IO (Weak (IORef a))

-- | Variant of <a>writeIORef</a> with the "barrier to reordering" property
--   that <a>atomicModifyIORef</a> has.
atomicWriteIORef :: IORef a -> a -> IO ()

-- | Atomically modifies the contents of an <a>IORef</a>.
--   
--   This function is useful for using <a>IORef</a> in a safe way in a
--   multithreaded program. If you only have one <a>IORef</a>, then using
--   <a>atomicModifyIORef</a> to access and modify it will prevent race
--   conditions.
--   
--   Extending the atomicity to multiple <a>IORef</a>s is problematic, so
--   it is recommended that if you need to do anything more complicated
--   then using <a>MVar</a> instead is a good idea.
--   
--   <a>atomicModifyIORef</a> does not apply the function strictly. This is
--   important to know even if all you are doing is replacing the value.
--   For example, this will leak memory:
--   
--   <pre>
--   ref &lt;- newIORef '1'
--   forever $ atomicModifyIORef ref (\_ -&gt; ('2', ()))
--   </pre>
--   
--   Use <a>atomicModifyIORef'</a> or <a>atomicWriteIORef</a> to avoid this
--   problem.
atomicModifyIORef :: IORef a -> (a -> (a, b)) -> IO b

-- | This variant of <a>newForeignPtr</a> adds a finalizer that expects an
--   environment in addition to the finalized pointer. The environment that
--   will be passed to the finalizer is fixed by the second argument to
--   <a>newForeignPtrEnv</a>.
newForeignPtrEnv :: FinalizerEnvPtr env a -> Ptr env -> Ptr a -> IO (ForeignPtr a)

-- | Turns a plain memory reference into a foreign pointer, and associates
--   a finalizer with the reference. The finalizer will be executed after
--   the last reference to the foreign object is dropped. There is no
--   guarantee of promptness, however the finalizer will be executed before
--   the program exits.
newForeignPtr :: FinalizerPtr a -> Ptr a -> IO (ForeignPtr a)

-- | This function is similar to <a>mallocArray0</a>, but yields a memory
--   area that has a finalizer attached that releases the memory area. As
--   with <a>mallocForeignPtr</a>, it is not guaranteed that the block of
--   memory was allocated by <a>malloc</a>.
mallocForeignPtrArray0 :: Storable a => Int -> IO (ForeignPtr a)

-- | This function is similar to <a>mallocArray</a>, but yields a memory
--   area that has a finalizer attached that releases the memory area. As
--   with <a>mallocForeignPtr</a>, it is not guaranteed that the block of
--   memory was allocated by <a>malloc</a>.
mallocForeignPtrArray :: Storable a => Int -> IO (ForeignPtr a)

-- | A finalizer is represented as a pointer to a foreign function that, at
--   finalisation time, gets as an argument a plain pointer variant of the
--   foreign pointer that the finalizer is associated with.
--   
--   Note that the foreign function <i>must</i> use the <tt>ccall</tt>
--   calling convention.
type FinalizerPtr a = FunPtr Ptr a -> IO ()
type FinalizerEnvPtr env a = FunPtr Ptr env -> Ptr a -> IO ()

-- | This is a way to look at the pointer living inside a foreign object.
--   This function takes a function which is applied to that pointer. The
--   resulting <a>IO</a> action is then executed. The foreign object is
--   kept alive at least during the whole action, even if it is not used
--   directly inside. Note that it is not safe to return the pointer from
--   the action and use it after the action completes. All uses of the
--   pointer should be inside the <a>withForeignPtr</a> bracket. The reason
--   for this unsafeness is the same as for <a>unsafeForeignPtrToPtr</a>
--   below: the finalizer may run earlier than expected, because the
--   compiler can only track usage of the <a>ForeignPtr</a> object, not a
--   <a>Ptr</a> object made from it.
--   
--   This function is normally used for marshalling data to or from the
--   object pointed to by the <a>ForeignPtr</a>, using the operations from
--   the <a>Storable</a> class.
withForeignPtr :: ForeignPtr a -> (Ptr a -> IO b) -> IO b

-- | This function ensures that the foreign object in question is alive at
--   the given place in the sequence of IO actions. However, this comes
--   with a significant caveat: the contract above does not hold if GHC can
--   demonstrate that the code preceeding <tt>touchForeignPtr</tt> diverges
--   (e.g. by looping infinitely or throwing an exception). For this
--   reason, you are strongly advised to use instead <a>withForeignPtr</a>
--   where possible.
--   
--   Also, note that this function should not be used to express
--   dependencies between finalizers on <a>ForeignPtr</a>s. For example, if
--   the finalizer for a <a>ForeignPtr</a> <tt>F1</tt> calls
--   <a>touchForeignPtr</a> on a second <a>ForeignPtr</a> <tt>F2</tt>, then
--   the only guarantee is that the finalizer for <tt>F2</tt> is never
--   started before the finalizer for <tt>F1</tt>. They might be started
--   together if for example both <tt>F1</tt> and <tt>F2</tt> are otherwise
--   unreachable, and in that case the scheduler might end up running the
--   finalizer for <tt>F2</tt> first.
--   
--   In general, it is not recommended to use finalizers on separate
--   objects with ordering constraints between them. To express the
--   ordering robustly requires explicit synchronisation using
--   <tt>MVar</tt>s between the finalizers, but even then the runtime
--   sometimes runs multiple finalizers sequentially in a single thread
--   (for performance reasons), so synchronisation between finalizers could
--   result in artificial deadlock. Another alternative is to use explicit
--   reference counting.
touchForeignPtr :: ForeignPtr a -> IO ()

-- | Advances the given address by the given offset in bytes.
--   
--   The new <a>ForeignPtr</a> shares the finalizer of the original,
--   equivalent from a finalization standpoint to just creating another
--   reference to the original. That is, the finalizer will not be called
--   before the new <a>ForeignPtr</a> is unreachable, nor will it be called
--   an additional time due to this call, and the finalizer will be called
--   with the same address that it would have had this call not happened,
--   *not* the new address.
plusForeignPtr :: ForeignPtr a -> Int -> ForeignPtr b

-- | Turns a plain memory reference into a foreign pointer that may be
--   associated with finalizers by using <a>addForeignPtrFinalizer</a>.
newForeignPtr_ :: Ptr a -> IO (ForeignPtr a)

-- | This function is similar to <a>mallocForeignPtr</a>, except that the
--   size of the memory required is given explicitly as a number of bytes.
mallocForeignPtrBytes :: Int -> IO (ForeignPtr a)

-- | Allocate some memory and return a <a>ForeignPtr</a> to it. The memory
--   will be released automatically when the <a>ForeignPtr</a> is
--   discarded.
--   
--   <a>mallocForeignPtr</a> is equivalent to
--   
--   <pre>
--   do { p &lt;- malloc; newForeignPtr finalizerFree p }
--   </pre>
--   
--   although it may be implemented differently internally: you may not
--   assume that the memory returned by <a>mallocForeignPtr</a> has been
--   allocated with <a>malloc</a>.
--   
--   GHC notes: <a>mallocForeignPtr</a> has a heavily optimised
--   implementation in GHC. It uses pinned memory in the garbage collected
--   heap, so the <a>ForeignPtr</a> does not require a finalizer to free
--   the memory. Use of <a>mallocForeignPtr</a> and associated functions is
--   strongly recommended in preference to <a>newForeignPtr</a> with a
--   finalizer.
mallocForeignPtr :: Storable a => IO (ForeignPtr a)

-- | Causes the finalizers associated with a foreign pointer to be run
--   immediately. The foreign pointer must not be used again after this
--   function is called. If the foreign pointer does not support
--   finalizers, this is a no-op.
finalizeForeignPtr :: ForeignPtr a -> IO ()

-- | This function casts a <a>ForeignPtr</a> parameterised by one type into
--   another type.
castForeignPtr :: ForeignPtr a -> ForeignPtr b

-- | Like <a>addForeignPtrFinalizer</a> but the finalizer is passed an
--   additional environment parameter.
addForeignPtrFinalizerEnv :: FinalizerEnvPtr env a -> Ptr env -> ForeignPtr a -> IO ()

-- | This function adds a finalizer to the given foreign object. The
--   finalizer will run <i>before</i> all other finalizers for the same
--   object which have already been registered.
addForeignPtrFinalizer :: FinalizerPtr a -> ForeignPtr a -> IO ()

-- | A mutable variable in the <a>IO</a> monad
data IORef a

-- | Write a new value into an <a>IORef</a>
writeIORef :: IORef a -> a -> IO ()

-- | Read the value of an <a>IORef</a>
readIORef :: IORef a -> IO a

-- | Build a new <a>IORef</a>
newIORef :: a -> IO (IORef a)

-- | Strict version of <a>atomicModifyIORef</a>. This forces both the value
--   stored in the <a>IORef</a> and the value returned. The new value is
--   installed in the <a>IORef</a> before the returned value is forced. So
--   
--   <pre>
--   atomicModifyIORef' ref (x -&gt; (x+1, undefined))
--   </pre>
--   
--   will increment the <a>IORef</a> and then throw an exception in the
--   calling thread.
atomicModifyIORef' :: IORef a -> (a -> (a, b)) -> IO b

-- | Describes the behaviour of a thread when an asynchronous exception is
--   received.
data MaskingState

-- | asynchronous exceptions are unmasked (the normal state)
Unmasked :: MaskingState

-- | the state during <a>mask</a>: asynchronous exceptions are masked, but
--   blocking operations may still be interrupted
MaskedInterruptible :: MaskingState

-- | the state during <a>uninterruptibleMask</a>: asynchronous exceptions
--   are masked, and blocking operations may not be interrupted
MaskedUninterruptible :: MaskingState

-- | File and directory names are values of type <a>String</a>, whose
--   precise meaning is operating system dependent. Files can be opened,
--   yielding a handle which can then be used to operate on the contents of
--   that file.
type FilePath = String

-- | Like <a>uninterruptibleMask</a>, but does not pass a <tt>restore</tt>
--   action to the argument.
uninterruptibleMask_ :: IO a -> IO a

-- | Like <a>mask</a>, but the masked computation is not interruptible (see
--   <a>Control.Exception#interruptible</a>). THIS SHOULD BE USED WITH
--   GREAT CARE, because if a thread executing in
--   <a>uninterruptibleMask</a> blocks for any reason, then the thread (and
--   possibly the program, if this is the main thread) will be unresponsive
--   and unkillable. This function should only be necessary if you need to
--   mask exceptions around an interruptible operation, and you can
--   guarantee that the interruptible operation will only block for a short
--   period of time.
uninterruptibleMask :: ((forall a. () => IO a -> IO a) -> IO b) -> IO b

-- | A variant of <a>throw</a> that can only be used within the <a>IO</a>
--   monad.
--   
--   Although <a>throwIO</a> has a type that is an instance of the type of
--   <a>throw</a>, the two functions are subtly different:
--   
--   <pre>
--   throw e   `seq` x  ===&gt; throw e
--   throwIO e `seq` x  ===&gt; x
--   </pre>
--   
--   The first example will cause the exception <tt>e</tt> to be raised,
--   whereas the second one won't. In fact, <a>throwIO</a> will only cause
--   an exception to be raised when it is used within the <a>IO</a> monad.
--   The <a>throwIO</a> variant should be used in preference to
--   <a>throw</a> to raise an exception within the <a>IO</a> monad because
--   it guarantees ordering with respect to other <a>IO</a> operations,
--   whereas <a>throw</a> does not.
throwIO :: Exception e => e -> IO a

-- | Embed a strict state thread in an <a>IO</a> action. The
--   <a>RealWorld</a> parameter indicates that the internal state used by
--   the <a>ST</a> computation is a special one supplied by the <a>IO</a>
--   monad, and thus distinct from those used by invocations of
--   <a>runST</a>.
stToIO :: ST RealWorld a -> IO a

-- | Like <a>mask</a>, but does not pass a <tt>restore</tt> action to the
--   argument.
mask_ :: IO a -> IO a

-- | Executes an IO computation with asynchronous exceptions <i>masked</i>.
--   That is, any thread which attempts to raise an exception in the
--   current thread with <a>throwTo</a> will be blocked until asynchronous
--   exceptions are unmasked again.
--   
--   The argument passed to <a>mask</a> is a function that takes as its
--   argument another function, which can be used to restore the prevailing
--   masking state within the context of the masked computation. For
--   example, a common way to use <a>mask</a> is to protect the acquisition
--   of a resource:
--   
--   <pre>
--   mask $ \restore -&gt; do
--       x &lt;- acquire
--       restore (do_something_with x) `onException` release
--       release
--   </pre>
--   
--   This code guarantees that <tt>acquire</tt> is paired with
--   <tt>release</tt>, by masking asynchronous exceptions for the critical
--   parts. (Rather than write this code yourself, it would be better to
--   use <a>bracket</a> which abstracts the general pattern).
--   
--   Note that the <tt>restore</tt> action passed to the argument to
--   <a>mask</a> does not necessarily unmask asynchronous exceptions, it
--   just restores the masking state to that of the enclosing context. Thus
--   if asynchronous exceptions are already masked, <a>mask</a> cannot be
--   used to unmask exceptions again. This is so that if you call a library
--   function with exceptions masked, you can be sure that the library call
--   will not be able to unmask exceptions again. If you are writing
--   library code and need to use asynchronous exceptions, the only way is
--   to create a new thread; see <a>forkIOWithUnmask</a>.
--   
--   Asynchronous exceptions may still be received while in the masked
--   state if the masked thread <i>blocks</i> in certain ways; see
--   <a>Control.Exception#interruptible</a>.
--   
--   Threads created by <a>forkIO</a> inherit the <a>MaskingState</a> from
--   the parent; that is, to start a thread in the
--   <a>MaskedInterruptible</a> state, use <tt>mask_ $ forkIO ...</tt>.
--   This is particularly useful if you need to establish an exception
--   handler in the forked thread before any asynchronous exceptions are
--   received. To create a new thread in an unmasked state use
--   <a>forkIOWithUnmask</a>.
mask :: ((forall a. () => IO a -> IO a) -> IO b) -> IO b

-- | Allow asynchronous exceptions to be raised even inside <a>mask</a>,
--   making the operation interruptible (see the discussion of
--   "Interruptible operations" in <a>Exception</a>).
--   
--   When called outside <a>mask</a>, or inside <a>uninterruptibleMask</a>,
--   this function has no effect.
interruptible :: IO a -> IO a

-- | Returns the <a>MaskingState</a> for the current thread.
getMaskingState :: IO MaskingState

-- | Evaluate the argument to weak head normal form.
--   
--   <a>evaluate</a> is typically used to uncover any exceptions that a
--   lazy value may contain, and possibly handle them.
--   
--   <a>evaluate</a> only evaluates to <i>weak head normal form</i>. If
--   deeper evaluation is needed, the <tt>force</tt> function from
--   <tt>Control.DeepSeq</tt> may be handy:
--   
--   <pre>
--   evaluate $ force x
--   </pre>
--   
--   There is a subtle difference between <tt><a>evaluate</a> x</tt> and
--   <tt><a>return</a> <a>$!</a> x</tt>, analogous to the difference
--   between <a>throwIO</a> and <a>throw</a>. If the lazy value <tt>x</tt>
--   throws an exception, <tt><a>return</a> <a>$!</a> x</tt> will fail to
--   return an <a>IO</a> action and will throw an exception instead.
--   <tt><a>evaluate</a> x</tt>, on the other hand, always produces an
--   <a>IO</a> action; that action will throw an exception upon
--   <i>execution</i> iff <tt>x</tt> throws an exception upon
--   <i>evaluation</i>.
--   
--   The practical implication of this difference is that due to the
--   <i>imprecise exceptions</i> semantics,
--   
--   <pre>
--   (return $! error "foo") &gt;&gt; error "bar"
--   </pre>
--   
--   may throw either <tt>"foo"</tt> or <tt>"bar"</tt>, depending on the
--   optimizations performed by the compiler. On the other hand,
--   
--   <pre>
--   evaluate (error "foo") &gt;&gt; error "bar"
--   </pre>
--   
--   is guaranteed to throw <tt>"foo"</tt>.
--   
--   The rule of thumb is to use <a>evaluate</a> to force or handle
--   exceptions in lazy values. If, on the other hand, you are forcing a
--   lazy value for efficiency reasons only and do not care about
--   exceptions, you may use <tt><a>return</a> <a>$!</a> x</tt>.
evaluate :: a -> IO a

-- | This is the simplest of the exception-catching functions. It takes a
--   single argument, runs it, and if an exception is raised the "handler"
--   is executed, with the value of the exception passed as an argument.
--   Otherwise, the result is returned as normal. For example:
--   
--   <pre>
--   catch (readFile f)
--         (\e -&gt; do let err = show (e :: IOException)
--                   hPutStr stderr ("Warning: Couldn't open " ++ f ++ ": " ++ err)
--                   return "")
--   </pre>
--   
--   Note that we have to give a type signature to <tt>e</tt>, or the
--   program will not typecheck as the type is ambiguous. While it is
--   possible to catch exceptions of any type, see the section "Catching
--   all exceptions" (in <a>Control.Exception</a>) for an explanation of
--   the problems with doing so.
--   
--   For catching exceptions in pure (non-<a>IO</a>) expressions, see the
--   function <a>evaluate</a>.
--   
--   Note that due to Haskell's unspecified evaluation order, an expression
--   may throw one of several possible exceptions: consider the expression
--   <tt>(error "urk") + (1 `div` 0)</tt>. Does the expression throw
--   <tt>ErrorCall "urk"</tt>, or <tt>DivideByZero</tt>?
--   
--   The answer is "it might throw either"; the choice is
--   non-deterministic. If you are catching any type of exception then you
--   might catch either. If you are calling <tt>catch</tt> with type <tt>IO
--   Int -&gt; (ArithException -&gt; IO Int) -&gt; IO Int</tt> then the
--   handler may get run with <tt>DivideByZero</tt> as an argument, or an
--   <tt>ErrorCall "urk"</tt> exception may be propagated further up. If
--   you call it again, you might get the opposite behaviour. This is ok,
--   because <a>catch</a> is an <a>IO</a> computation.
catch :: Exception e => IO a -> (e -> IO a) -> IO a

-- | Exceptions that occur in the <tt>IO</tt> monad. An
--   <tt>IOException</tt> records a more specific error type, a descriptive
--   string and maybe the handle that was used when the error was flagged.
data IOException
IOError :: Maybe Handle -> IOErrorType -> String -> String -> Maybe CInt -> Maybe FilePath -> IOException
[ioe_handle] :: IOException -> Maybe Handle
[ioe_type] :: IOException -> IOErrorType
[ioe_location] :: IOException -> String
[ioe_description] :: IOException -> String
[ioe_errno] :: IOException -> Maybe CInt
[ioe_filename] :: IOException -> Maybe FilePath

-- | The Haskell 2010 type for exceptions in the <a>IO</a> monad. Any I/O
--   operation may raise an <a>IOException</a> instead of returning a
--   result. For a more general type of exception, including also those
--   that arise in pure code, see <a>Exception</a>.
--   
--   In Haskell 2010, this is an opaque type.
type IOError = IOException

-- | Construct an <a>IOException</a> value with a string describing the
--   error. The <tt>fail</tt> method of the <a>IO</a> instance of the
--   <a>Monad</a> class raises a <a>userError</a>, thus:
--   
--   <pre>
--   instance Monad IO where
--     ...
--     fail s = ioError (userError s)
--   </pre>
userError :: String -> IOError
unsupportedOperation :: IOError

-- | This is thrown when the user calls <a>error</a>. The first
--   <tt>String</tt> is the argument given to <a>error</a>, second
--   <tt>String</tt> is the location.
data ErrorCall
ErrorCallWithLocation :: String -> String -> ErrorCall
pattern ErrorCall :: String -> ErrorCall

-- | Throw an exception. Exceptions may be thrown from purely functional
--   code, but may only be caught within the <a>IO</a> monad.
throw :: forall (r :: RuntimeRep) (a :: TYPE r) e. Exception e => e -> a

-- | Any type that you wish to throw or catch as an exception must be an
--   instance of the <tt>Exception</tt> class. The simplest case is a new
--   exception type directly below the root:
--   
--   <pre>
--   data MyException = ThisException | ThatException
--       deriving Show
--   
--   instance Exception MyException
--   </pre>
--   
--   The default method definitions in the <tt>Exception</tt> class do what
--   we need in this case. You can now throw and catch
--   <tt>ThisException</tt> and <tt>ThatException</tt> as exceptions:
--   
--   <pre>
--   *Main&gt; throw ThisException `catch` \e -&gt; putStrLn ("Caught " ++ show (e :: MyException))
--   Caught ThisException
--   </pre>
--   
--   In more complicated examples, you may wish to define a whole hierarchy
--   of exceptions:
--   
--   <pre>
--   ---------------------------------------------------------------------
--   -- Make the root exception type for all the exceptions in a compiler
--   
--   data SomeCompilerException = forall e . Exception e =&gt; SomeCompilerException e
--   
--   instance Show SomeCompilerException where
--       show (SomeCompilerException e) = show e
--   
--   instance Exception SomeCompilerException
--   
--   compilerExceptionToException :: Exception e =&gt; e -&gt; SomeException
--   compilerExceptionToException = toException . SomeCompilerException
--   
--   compilerExceptionFromException :: Exception e =&gt; SomeException -&gt; Maybe e
--   compilerExceptionFromException x = do
--       SomeCompilerException a &lt;- fromException x
--       cast a
--   
--   ---------------------------------------------------------------------
--   -- Make a subhierarchy for exceptions in the frontend of the compiler
--   
--   data SomeFrontendException = forall e . Exception e =&gt; SomeFrontendException e
--   
--   instance Show SomeFrontendException where
--       show (SomeFrontendException e) = show e
--   
--   instance Exception SomeFrontendException where
--       toException = compilerExceptionToException
--       fromException = compilerExceptionFromException
--   
--   frontendExceptionToException :: Exception e =&gt; e -&gt; SomeException
--   frontendExceptionToException = toException . SomeFrontendException
--   
--   frontendExceptionFromException :: Exception e =&gt; SomeException -&gt; Maybe e
--   frontendExceptionFromException x = do
--       SomeFrontendException a &lt;- fromException x
--       cast a
--   
--   ---------------------------------------------------------------------
--   -- Make an exception type for a particular frontend compiler exception
--   
--   data MismatchedParentheses = MismatchedParentheses
--       deriving Show
--   
--   instance Exception MismatchedParentheses where
--       toException   = frontendExceptionToException
--       fromException = frontendExceptionFromException
--   </pre>
--   
--   We can now catch a <tt>MismatchedParentheses</tt> exception as
--   <tt>MismatchedParentheses</tt>, <tt>SomeFrontendException</tt> or
--   <tt>SomeCompilerException</tt>, but not other types, e.g.
--   <tt>IOException</tt>:
--   
--   <pre>
--   *Main&gt; throw MismatchedParentheses `catch` \e -&gt; putStrLn ("Caught " ++ show (e :: MismatchedParentheses))
--   Caught MismatchedParentheses
--   *Main&gt; throw MismatchedParentheses `catch` \e -&gt; putStrLn ("Caught " ++ show (e :: SomeFrontendException))
--   Caught MismatchedParentheses
--   *Main&gt; throw MismatchedParentheses `catch` \e -&gt; putStrLn ("Caught " ++ show (e :: SomeCompilerException))
--   Caught MismatchedParentheses
--   *Main&gt; throw MismatchedParentheses `catch` \e -&gt; putStrLn ("Caught " ++ show (e :: IOException))
--   *** Exception: MismatchedParentheses
--   </pre>
class (Typeable e, Show e) => Exception e
toException :: Exception e => e -> SomeException
fromException :: Exception e => SomeException -> Maybe e

-- | Render this exception value in a human-friendly manner.
--   
--   Default implementation: <tt><a>show</a></tt>.
displayException :: Exception e => e -> String

-- | Arithmetic exceptions.
data ArithException
Overflow :: ArithException
Underflow :: ArithException
LossOfPrecision :: ArithException
DivideByZero :: ArithException
Denormal :: ArithException

RatioZeroDenominator :: ArithException

-- | A quantified type representation.
type TypeRep = SomeTypeRep

-- | Observe the type constructor of a quantified type representation.
typeRepTyCon :: TypeRep -> TyCon

-- | Takes a value of type <tt>a</tt> and returns a concrete representation
--   of that type.
typeRepFingerprint :: TypeRep -> Fingerprint

-- | Observe the argument types of a type representation
typeRepArgs :: TypeRep -> [TypeRep]

-- | Takes a value of type <tt>a</tt> and returns a concrete representation
--   of that type.
typeRep :: forall {k} proxy (a :: k). Typeable a => proxy a -> TypeRep
typeOf7 :: Typeable t => t a b c d e f g -> TypeRep
typeOf6 :: Typeable t => t a b c d e f -> TypeRep
typeOf5 :: Typeable t => t a b c d e -> TypeRep
typeOf4 :: Typeable t => t a b c d -> TypeRep
typeOf3 :: Typeable t => t a b c -> TypeRep
typeOf2 :: Typeable t => t a b -> TypeRep
typeOf1 :: Typeable t => t a -> TypeRep

-- | Observe a type representation for the type of a value.
typeOf :: Typeable a => a -> TypeRep

-- | Splits a type constructor application. Note that if the type
--   constructor is polymorphic, this will not return the kinds that were
--   used.
splitTyConApp :: TypeRep -> (TyCon, [TypeRep])

-- | Show a type representation
showsTypeRep :: TypeRep -> ShowS

-- | Force a <a>TypeRep</a> to normal form.
rnfTypeRep :: TypeRep -> ()

-- | Build a function type.
mkFunTy :: TypeRep -> TypeRep -> TypeRep

-- | Cast over <tt>k1 -&gt; k2 -&gt; k3</tt>
gcast2 :: forall {k1} {k2} {k3} c (t :: k2 -> k3 -> k1) (t' :: k2 -> k3 -> k1) (a :: k2) (b :: k3). (Typeable t, Typeable t') => c (t a b) -> Maybe (c (t' a b))

-- | Cast over <tt>k1 -&gt; k2</tt>
gcast1 :: forall {k1} {k2} c (t :: k2 -> k1) (t' :: k2 -> k1) (a :: k2). (Typeable t, Typeable t') => c (t a) -> Maybe (c (t' a))

-- | A flexible variation parameterised in a type constructor
gcast :: forall {k} (a :: k) (b :: k) c. (Typeable a, Typeable b) => c a -> Maybe (c b)

-- | Applies a type to a function type. Returns: <tt>Just u</tt> if the
--   first argument represents a function of type <tt>t -&gt; u</tt> and
--   the second argument represents a function of type <tt>t</tt>.
--   Otherwise, returns <tt>Nothing</tt>.
funResultTy :: TypeRep -> TypeRep -> Maybe TypeRep

-- | Extract a witness of equality of two types
eqT :: forall {k} (a :: k) (b :: k). (Typeable a, Typeable b) => Maybe (a :~: b)

-- | The type-safe cast operation
cast :: (Typeable a, Typeable b) => a -> Maybe b
tyConPackage :: TyCon -> String
tyConName :: TyCon -> String
tyConModule :: TyCon -> String
tyConFingerprint :: TyCon -> Fingerprint
trLiftedRep :: TypeRep ('BoxedRep 'Lifted)
rnfTyCon :: TyCon -> ()

-- | The <a>Const</a> functor.
newtype Const a (b :: k)
Const :: a -> Const a (b :: k)
[getConst] :: Const a (b :: k) -> a

-- | Map each element of a structure to an <a>Applicative</a> action,
--   evaluate these actions from left to right, and ignore the results. For
--   a version that doesn't ignore the results see <a>traverse</a>.
--   
--   <a>traverse_</a> is just like <a>mapM_</a>, but generalised to
--   <a>Applicative</a> actions.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; traverse_ print ["Hello", "world", "!"]
--   "Hello"
--   "world"
--   "!"
--   </pre>
traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f ()

-- | Evaluate each monadic action in the structure from left to right, and
--   ignore the results. For a version that doesn't ignore the results see
--   <a>sequence</a>.
--   
--   <a>sequence_</a> is just like <a>sequenceA_</a>, but specialised to
--   monadic actions.
sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()

-- | Evaluate each action in the structure from left to right, and ignore
--   the results. For a version that doesn't ignore the results see
--   <a>sequenceA</a>.
--   
--   <a>sequenceA_</a> is just like <a>sequence_</a>, but generalised to
--   <a>Applicative</a> actions.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; sequenceA_ [print "Hello", print "world", print "!"]
--   "Hello"
--   "world"
--   "!"
--   </pre>
sequenceA_ :: (Foldable t, Applicative f) => t (f a) -> f ()

-- | <a>or</a> returns the disjunction of a container of Bools. For the
--   result to be <a>False</a>, the container must be finite; <a>True</a>,
--   however, results from a <a>True</a> value finitely far from the left
--   end.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; or []
--   False
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; or [True]
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; or [False]
--   False
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; or [True, True, False]
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; or (True : repeat False) -- Infinite list [True,False,False,False,...
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; or (repeat False)
--   * Hangs forever *
--   </pre>
or :: Foldable t => t Bool -> Bool

-- | <a>notElem</a> is the negation of <a>elem</a>.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; 3 `notElem` []
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; 3 `notElem` [1,2]
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; 3 `notElem` [1,2,3,4,5]
--   False
--   </pre>
--   
--   For infinite structures, <a>notElem</a> terminates if the value exists
--   at a finite distance from the left side of the structure:
--   
--   <pre>
--   &gt;&gt;&gt; 3 `notElem` [1..]
--   False
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; 3 `notElem` ([4..] ++ [3])
--   * Hangs forever *
--   </pre>
notElem :: (Foldable t, Eq a) => a -> t a -> Bool
infix 4 `notElem`

-- | The sum of a collection of actions, generalizing <a>concat</a>.
--   
--   <a>msum</a> is just like <a>asum</a>, but specialised to
--   <a>MonadPlus</a>.
msum :: (Foldable t, MonadPlus m) => t (m a) -> m a

-- | The least element of a non-empty structure with respect to the given
--   comparison function.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; minimumBy (compare `on` length) ["Hello", "World", "!", "Longest", "bar"]
--   "!"
--   </pre>
--   
--   WARNING: This function is partial for possibly-empty structures like
--   lists.
minimumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a

-- | The largest element of a non-empty structure with respect to the given
--   comparison function.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; maximumBy (compare `on` length) ["Hello", "World", "!", "Longest", "bar"]
--   "Longest"
--   </pre>
--   
--   WARNING: This function is partial for possibly-empty structures like
--   lists.
maximumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a

-- | Map each element of a structure to a monadic action, evaluate these
--   actions from left to right, and ignore the results. For a version that
--   doesn't ignore the results see <a>mapM</a>.
--   
--   <a>mapM_</a> is just like <a>traverse_</a>, but specialised to monadic
--   actions.
mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()

-- | <a>for_</a> is <a>traverse_</a> with its arguments flipped. For a
--   version that doesn't ignore the results see <a>for</a>. This is
--   <a>forM_</a> generalised to <a>Applicative</a> actions.
--   
--   <a>for_</a> is just like <a>forM_</a>, but generalised to
--   <a>Applicative</a> actions.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; for_ [1..4] print
--   1
--   2
--   3
--   4
--   </pre>
for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f ()

-- | <a>forM_</a> is <a>mapM_</a> with its arguments flipped. For a version
--   that doesn't ignore the results see <a>forM</a>.
--   
--   <a>forM_</a> is just like <a>for_</a>, but specialised to monadic
--   actions.
forM_ :: (Foldable t, Monad m) => t a -> (a -> m b) -> m ()

-- | Right-to-left monadic fold over the elements of a structure.
--   
--   Given a structure <tt>t</tt> with elements <tt>(a, b, c, ..., x,
--   y)</tt>, the result of a fold with an operator function <tt>f</tt> is
--   equivalent to:
--   
--   <pre>
--   foldrM f z t = do
--       yy &lt;- f y z
--       xx &lt;- f x yy
--       ...
--       bb &lt;- f b cc
--       aa &lt;- f a bb
--       return aa -- Just @return z@ when the structure is empty
--   </pre>
--   
--   For a Monad <tt>m</tt>, given two functions <tt>f1 :: a -&gt; m b</tt>
--   and <tt>f2 :: b -&gt; m c</tt>, their Kleisli composition <tt>(f1
--   &gt;=&gt; f2) :: a -&gt; m c</tt> is defined by:
--   
--   <pre>
--   (f1 &gt;=&gt; f2) a = f1 a &gt;&gt;= f2
--   </pre>
--   
--   Another way of thinking about <tt>foldrM</tt> is that it amounts to an
--   application to <tt>z</tt> of a Kleisli composition:
--   
--   <pre>
--   foldrM f z t = f y &gt;=&gt; f x &gt;=&gt; ... &gt;=&gt; f b &gt;=&gt; f a $ z
--   </pre>
--   
--   The monadic effects of <tt>foldrM</tt> are sequenced from right to
--   left, and e.g. folds of infinite lists will diverge.
--   
--   If at some step the bind operator <tt>(<a>&gt;&gt;=</a>)</tt>
--   short-circuits (as with, e.g., <a>mzero</a> in a <a>MonadPlus</a>),
--   the evaluated effects will be from a tail of the element sequence. If
--   you want to evaluate the monadic effects in left-to-right order, or
--   perhaps be able to short-circuit after an initial sequence of
--   elements, you'll need to use <a>foldlM</a> instead.
--   
--   If the monadic effects don't short-circuit, the outermost application
--   of <tt>f</tt> is to the leftmost element <tt>a</tt>, so that, ignoring
--   effects, the result looks like a right fold:
--   
--   <pre>
--   a `f` (b `f` (c `f` (... (x `f` (y `f` z))))).
--   </pre>
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; let f i acc = do { print i ; return $ i : acc }
--   
--   &gt;&gt;&gt; foldrM f [] [0..3]
--   3
--   2
--   1
--   0
--   [0,1,2,3]
--   </pre>
foldrM :: (Foldable t, Monad m) => (a -> b -> m b) -> b -> t a -> m b

-- | Left-to-right monadic fold over the elements of a structure.
--   
--   Given a structure <tt>t</tt> with elements <tt>(a, b, ..., w, x,
--   y)</tt>, the result of a fold with an operator function <tt>f</tt> is
--   equivalent to:
--   
--   <pre>
--   foldlM f z t = do
--       aa &lt;- f z a
--       bb &lt;- f aa b
--       ...
--       xx &lt;- f ww x
--       yy &lt;- f xx y
--       return yy -- Just @return z@ when the structure is empty
--   </pre>
--   
--   For a Monad <tt>m</tt>, given two functions <tt>f1 :: a -&gt; m b</tt>
--   and <tt>f2 :: b -&gt; m c</tt>, their Kleisli composition <tt>(f1
--   &gt;=&gt; f2) :: a -&gt; m c</tt> is defined by:
--   
--   <pre>
--   (f1 &gt;=&gt; f2) a = f1 a &gt;&gt;= f2
--   </pre>
--   
--   Another way of thinking about <tt>foldlM</tt> is that it amounts to an
--   application to <tt>z</tt> of a Kleisli composition:
--   
--   <pre>
--   foldlM f z t =
--       flip f a &gt;=&gt; flip f b &gt;=&gt; ... &gt;=&gt; flip f x &gt;=&gt; flip f y $ z
--   </pre>
--   
--   The monadic effects of <tt>foldlM</tt> are sequenced from left to
--   right.
--   
--   If at some step the bind operator <tt>(<a>&gt;&gt;=</a>)</tt>
--   short-circuits (as with, e.g., <a>mzero</a> in a <a>MonadPlus</a>),
--   the evaluated effects will be from an initial segment of the element
--   sequence. If you want to evaluate the monadic effects in right-to-left
--   order, or perhaps be able to short-circuit after processing a tail of
--   the sequence of elements, you'll need to use <a>foldrM</a> instead.
--   
--   If the monadic effects don't short-circuit, the outermost application
--   of <tt>f</tt> is to the rightmost element <tt>y</tt>, so that,
--   ignoring effects, the result looks like a left fold:
--   
--   <pre>
--   ((((z `f` a) `f` b) ... `f` w) `f` x) `f` y
--   </pre>
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; let f a e = do { print e ; return $ e : a }
--   
--   &gt;&gt;&gt; foldlM f [] [0..3]
--   0
--   1
--   2
--   3
--   [3,2,1,0]
--   </pre>
foldlM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b

-- | The <a>find</a> function takes a predicate and a structure and returns
--   the leftmost element of the structure matching the predicate, or
--   <a>Nothing</a> if there is no such element.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; find (&gt; 42) [0, 5..]
--   Just 45
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; find (&gt; 12) [1..7]
--   Nothing
--   </pre>
find :: Foldable t => (a -> Bool) -> t a -> Maybe a

-- | Map a function over all the elements of a container and concatenate
--   the resulting lists.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; concatMap (take 3) [[1..], [10..], [100..], [1000..]]
--   [1,2,3,10,11,12,100,101,102,1000,1001,1002]
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; concatMap (take 3) (Just [1..])
--   [1,2,3]
--   </pre>
concatMap :: Foldable t => (a -> [b]) -> t a -> [b]

-- | The concatenation of all the elements of a container of lists.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; concat (Just [1, 2, 3])
--   [1,2,3]
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; concat (Left 42)
--   []
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; concat [[1, 2, 3], [4, 5], [6], []]
--   [1,2,3,4,5,6]
--   </pre>
concat :: Foldable t => t [a] -> [a]

-- | The sum of a collection of actions, generalizing <a>concat</a>.
--   
--   <a>asum</a> is just like <a>msum</a>, but generalised to
--   <a>Alternative</a>.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; asum [Just "Hello", Nothing, Just "World"]
--   Just "Hello"
--   </pre>
asum :: (Foldable t, Alternative f) => t (f a) -> f a

-- | Determines whether any element of the structure satisfies the
--   predicate.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; any (&gt; 3) []
--   False
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; any (&gt; 3) [1,2]
--   False
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; any (&gt; 3) [1,2,3,4,5]
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; any (&gt; 3) [1..]
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; any (&gt; 3) [0, -1..]
--   * Hangs forever *
--   </pre>
any :: Foldable t => (a -> Bool) -> t a -> Bool

-- | <a>and</a> returns the conjunction of a container of Bools. For the
--   result to be <a>True</a>, the container must be finite; <a>False</a>,
--   however, results from a <a>False</a> value finitely far from the left
--   end.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; and []
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; and [True]
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; and [False]
--   False
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; and [True, True, False]
--   False
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; and (False : repeat True) -- Infinite list [False,True,True,True,...
--   False
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; and (repeat True)
--   * Hangs forever *
--   </pre>
and :: Foldable t => t Bool -> Bool

-- | Determines whether all elements of the structure satisfy the
--   predicate.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; all (&gt; 3) []
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; all (&gt; 3) [1,2]
--   False
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; all (&gt; 3) [1,2,3,4,5]
--   False
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; all (&gt; 3) [1..]
--   False
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; all (&gt; 3) [4..]
--   * Hangs forever *
--   </pre>
all :: Foldable t => (a -> Bool) -> t a -> Bool

-- | The <a>zipWith7</a> function takes a function which combines seven
--   elements, as well as seven lists and returns a list of their
--   point-wise combination, analogous to <a>zipWith</a>. It is capable of
--   list fusion, but it is restricted to its first list argument and its
--   resulting list.
zipWith7 :: (a -> b -> c -> d -> e -> f -> g -> h) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [h]

-- | The <a>zipWith6</a> function takes a function which combines six
--   elements, as well as six lists and returns a list of their point-wise
--   combination, analogous to <a>zipWith</a>. It is capable of list
--   fusion, but it is restricted to its first list argument and its
--   resulting list.
zipWith6 :: (a -> b -> c -> d -> e -> f -> g) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g]

-- | The <a>zipWith5</a> function takes a function which combines five
--   elements, as well as five lists and returns a list of their point-wise
--   combination, analogous to <a>zipWith</a>. It is capable of list
--   fusion, but it is restricted to its first list argument and its
--   resulting list.
zipWith5 :: (a -> b -> c -> d -> e -> f) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f]

-- | The <a>zipWith4</a> function takes a function which combines four
--   elements, as well as four lists and returns a list of their point-wise
--   combination, analogous to <a>zipWith</a>. It is capable of list
--   fusion, but it is restricted to its first list argument and its
--   resulting list.
zipWith4 :: (a -> b -> c -> d -> e) -> [a] -> [b] -> [c] -> [d] -> [e]

-- | The <a>zip7</a> function takes seven lists and returns a list of
--   seven-tuples, analogous to <a>zip</a>. It is capable of list fusion,
--   but it is restricted to its first list argument and its resulting
--   list.
zip7 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [(a, b, c, d, e, f, g)]

-- | The <a>zip6</a> function takes six lists and returns a list of
--   six-tuples, analogous to <a>zip</a>. It is capable of list fusion, but
--   it is restricted to its first list argument and its resulting list.
zip6 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [(a, b, c, d, e, f)]

-- | The <a>zip5</a> function takes five lists and returns a list of
--   five-tuples, analogous to <a>zip</a>. It is capable of list fusion,
--   but it is restricted to its first list argument and its resulting
--   list.
zip5 :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a, b, c, d, e)]

-- | The <a>zip4</a> function takes four lists and returns a list of
--   quadruples, analogous to <a>zip</a>. It is capable of list fusion, but
--   it is restricted to its first list argument and its resulting list.
zip4 :: [a] -> [b] -> [c] -> [d] -> [(a, b, c, d)]

-- | <a>words</a> breaks a string up into a list of words, which were
--   delimited by white space.
--   
--   <pre>
--   &gt;&gt;&gt; words "Lorem ipsum\ndolor"
--   ["Lorem","ipsum","dolor"]
--   </pre>
words :: String -> [String]

-- | The <a>unzip7</a> function takes a list of seven-tuples and returns
--   seven lists, analogous to <a>unzip</a>.
unzip7 :: [(a, b, c, d, e, f, g)] -> ([a], [b], [c], [d], [e], [f], [g])

-- | The <a>unzip6</a> function takes a list of six-tuples and returns six
--   lists, analogous to <a>unzip</a>.
unzip6 :: [(a, b, c, d, e, f)] -> ([a], [b], [c], [d], [e], [f])

-- | The <a>unzip5</a> function takes a list of five-tuples and returns
--   five lists, analogous to <a>unzip</a>.
unzip5 :: [(a, b, c, d, e)] -> ([a], [b], [c], [d], [e])

-- | The <a>unzip4</a> function takes a list of quadruples and returns four
--   lists, analogous to <a>unzip</a>.
unzip4 :: [(a, b, c, d)] -> ([a], [b], [c], [d])

-- | <a>unwords</a> is an inverse operation to <a>words</a>. It joins words
--   with separating spaces.
--   
--   <pre>
--   &gt;&gt;&gt; unwords ["Lorem", "ipsum", "dolor"]
--   "Lorem ipsum dolor"
--   </pre>
unwords :: [String] -> String

-- | <a>unlines</a> is an inverse operation to <a>lines</a>. It joins
--   lines, after appending a terminating newline to each.
--   
--   <pre>
--   &gt;&gt;&gt; unlines ["Hello", "World", "!"]
--   "Hello\nWorld\n!\n"
--   </pre>
unlines :: [String] -> String

-- | The <a>unionBy</a> function is the non-overloaded version of
--   <a>union</a>.
unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]

-- | The <a>union</a> function returns the list union of the two lists. For
--   example,
--   
--   <pre>
--   &gt;&gt;&gt; "dog" `union` "cow"
--   "dogcw"
--   </pre>
--   
--   Duplicates, and elements of the first list, are removed from the the
--   second list, but if the first list contains duplicates, so will the
--   result. It is a special case of <a>unionBy</a>, which allows the
--   programmer to supply their own equality test.
union :: Eq a => [a] -> [a] -> [a]

-- | The <a>unfoldr</a> function is a `dual' to <a>foldr</a>: while
--   <a>foldr</a> reduces a list to a summary value, <a>unfoldr</a> builds
--   a list from a seed value. The function takes the element and returns
--   <a>Nothing</a> if it is done producing the list or returns <a>Just</a>
--   <tt>(a,b)</tt>, in which case, <tt>a</tt> is a prepended to the list
--   and <tt>b</tt> is used as the next element in a recursive call. For
--   example,
--   
--   <pre>
--   iterate f == unfoldr (\x -&gt; Just (x, f x))
--   </pre>
--   
--   In some cases, <a>unfoldr</a> can undo a <a>foldr</a> operation:
--   
--   <pre>
--   unfoldr f' (foldr f z xs) == xs
--   </pre>
--   
--   if the following holds:
--   
--   <pre>
--   f' (f x y) = Just (x,y)
--   f' z       = Nothing
--   </pre>
--   
--   A simple use of unfoldr:
--   
--   <pre>
--   &gt;&gt;&gt; unfoldr (\b -&gt; if b == 0 then Nothing else Just (b, b-1)) 10
--   [10,9,8,7,6,5,4,3,2,1]
--   </pre>
unfoldr :: (b -> Maybe (a, b)) -> b -> [a]

-- | The <a>transpose</a> function transposes the rows and columns of its
--   argument. For example,
--   
--   <pre>
--   &gt;&gt;&gt; transpose [[1,2,3],[4,5,6]]
--   [[1,4],[2,5],[3,6]]
--   </pre>
--   
--   If some of the rows are shorter than the following rows, their
--   elements are skipped:
--   
--   <pre>
--   &gt;&gt;&gt; transpose [[10,11],[20],[],[30,31,32]]
--   [[10,20,30],[11,31],[32]]
--   </pre>
transpose :: [[a]] -> [[a]]

-- | &lt;math&gt;. The <a>tails</a> function returns all final segments of
--   the argument, longest first. For example,
--   
--   <pre>
--   &gt;&gt;&gt; tails "abc"
--   ["abc","bc","c",""]
--   </pre>
--   
--   Note that <a>tails</a> has the following strictness property:
--   <tt>tails _|_ = _|_ : _|_</tt>
tails :: [a] -> [[a]]

-- | The <a>subsequences</a> function returns the list of all subsequences
--   of the argument.
--   
--   <pre>
--   &gt;&gt;&gt; subsequences "abc"
--   ["","a","b","ab","c","ac","bc","abc"]
--   </pre>
subsequences :: [a] -> [[a]]

-- | &lt;math&gt;. The <a>stripPrefix</a> function drops the given prefix
--   from a list. It returns <a>Nothing</a> if the list did not start with
--   the prefix given, or <a>Just</a> the list after the prefix, if it
--   does.
--   
--   <pre>
--   &gt;&gt;&gt; stripPrefix "foo" "foobar"
--   Just "bar"
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; stripPrefix "foo" "foo"
--   Just ""
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; stripPrefix "foo" "barfoo"
--   Nothing
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; stripPrefix "foo" "barfoobaz"
--   Nothing
--   </pre>
stripPrefix :: Eq a => [a] -> [a] -> Maybe [a]

-- | Sort a list by comparing the results of a key function applied to each
--   element. <tt>sortOn f</tt> is equivalent to <tt>sortBy (comparing
--   f)</tt>, but has the performance advantage of only evaluating
--   <tt>f</tt> once for each element in the input list. This is called the
--   decorate-sort-undecorate paradigm, or Schwartzian transform.
--   
--   Elements are arranged from lowest to highest, keeping duplicates in
--   the order they appeared in the input.
--   
--   <pre>
--   &gt;&gt;&gt; sortOn fst [(2, "world"), (4, "!"), (1, "Hello")]
--   [(1,"Hello"),(2,"world"),(4,"!")]
--   </pre>
sortOn :: Ord b => (a -> b) -> [a] -> [a]

-- | The <a>sortBy</a> function is the non-overloaded version of
--   <a>sort</a>.
--   
--   <pre>
--   &gt;&gt;&gt; sortBy (\(a,_) (b,_) -&gt; compare a b) [(2, "world"), (4, "!"), (1, "Hello")]
--   [(1,"Hello"),(2,"world"),(4,"!")]
--   </pre>
sortBy :: (a -> a -> Ordering) -> [a] -> [a]

-- | The <a>sort</a> function implements a stable sorting algorithm. It is
--   a special case of <a>sortBy</a>, which allows the programmer to supply
--   their own comparison function.
--   
--   Elements are arranged from lowest to highest, keeping duplicates in
--   the order they appeared in the input.
--   
--   <pre>
--   &gt;&gt;&gt; sort [1,6,4,3,2,5]
--   [1,2,3,4,5,6]
--   </pre>
sort :: Ord a => [a] -> [a]

-- | Produce singleton list.
--   
--   <pre>
--   &gt;&gt;&gt; singleton True
--   [True]
--   </pre>
singleton :: a -> [a]

-- | The <a>permutations</a> function returns the list of all permutations
--   of the argument.
--   
--   <pre>
--   &gt;&gt;&gt; permutations "abc"
--   ["abc","bac","cba","bca","cab","acb"]
--   </pre>
permutations :: [a] -> [[a]]

-- | The <a>partition</a> function takes a predicate and a list, and
--   returns the pair of lists of elements which do and do not satisfy the
--   predicate, respectively; i.e.,
--   
--   <pre>
--   partition p xs == (filter p xs, filter (not . p) xs)
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; partition (`elem` "aeiou") "Hello World!"
--   ("eoo","Hll Wrld!")
--   </pre>
partition :: (a -> Bool) -> [a] -> ([a], [a])

-- | The <a>nubBy</a> function behaves just like <a>nub</a>, except it uses
--   a user-supplied equality predicate instead of the overloaded <a>==</a>
--   function.
--   
--   <pre>
--   &gt;&gt;&gt; nubBy (\x y -&gt; mod x 3 == mod y 3) [1,2,4,5,6]
--   [1,2,6]
--   </pre>
nubBy :: (a -> a -> Bool) -> [a] -> [a]

-- | &lt;math&gt;. The <a>nub</a> function removes duplicate elements from
--   a list. In particular, it keeps only the first occurrence of each
--   element. (The name <a>nub</a> means `essence'.) It is a special case
--   of <a>nubBy</a>, which allows the programmer to supply their own
--   equality test.
--   
--   <pre>
--   &gt;&gt;&gt; nub [1,2,3,4,3,2,1,2,4,3,5]
--   [1,2,3,4,5]
--   </pre>
nub :: Eq a => [a] -> [a]

-- | <a>lines</a> breaks a string up into a list of strings at newline
--   characters. The resulting strings do not contain newlines.
--   
--   Note that after splitting the string at newline characters, the last
--   part of the string is considered a line even if it doesn't end with a
--   newline. For example,
--   
--   <pre>
--   &gt;&gt;&gt; lines ""
--   []
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; lines "\n"
--   [""]
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; lines "one"
--   ["one"]
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; lines "one\n"
--   ["one"]
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; lines "one\n\n"
--   ["one",""]
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; lines "one\ntwo"
--   ["one","two"]
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; lines "one\ntwo\n"
--   ["one","two"]
--   </pre>
--   
--   Thus <tt><a>lines</a> s</tt> contains at least as many elements as
--   newlines in <tt>s</tt>.
lines :: String -> [String]

-- | The <a>isSuffixOf</a> function takes two lists and returns <a>True</a>
--   iff the first list is a suffix of the second. The second list must be
--   finite.
--   
--   <pre>
--   &gt;&gt;&gt; "ld!" `isSuffixOf` "Hello World!"
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; "World" `isSuffixOf` "Hello World!"
--   False
--   </pre>
isSuffixOf :: Eq a => [a] -> [a] -> Bool

-- | &lt;math&gt;. The <a>isPrefixOf</a> function takes two lists and
--   returns <a>True</a> iff the first list is a prefix of the second.
--   
--   <pre>
--   &gt;&gt;&gt; "Hello" `isPrefixOf` "Hello World!"
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; "Hello" `isPrefixOf` "Wello Horld!"
--   False
--   </pre>
isPrefixOf :: Eq a => [a] -> [a] -> Bool

-- | The <a>isInfixOf</a> function takes two lists and returns <a>True</a>
--   iff the first list is contained, wholly and intact, anywhere within
--   the second.
--   
--   <pre>
--   &gt;&gt;&gt; isInfixOf "Haskell" "I really like Haskell."
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; isInfixOf "Ial" "I really like Haskell."
--   False
--   </pre>
isInfixOf :: Eq a => [a] -> [a] -> Bool

-- | &lt;math&gt;. The <a>intersperse</a> function takes an element and a
--   list and `intersperses' that element between the elements of the list.
--   For example,
--   
--   <pre>
--   &gt;&gt;&gt; intersperse ',' "abcde"
--   "a,b,c,d,e"
--   </pre>
intersperse :: a -> [a] -> [a]

-- | The <a>intersectBy</a> function is the non-overloaded version of
--   <a>intersect</a>.
intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]

-- | The <a>intersect</a> function takes the list intersection of two
--   lists. For example,
--   
--   <pre>
--   &gt;&gt;&gt; [1,2,3,4] `intersect` [2,4,6,8]
--   [2,4]
--   </pre>
--   
--   If the first list contains duplicates, so will the result.
--   
--   <pre>
--   &gt;&gt;&gt; [1,2,2,3,4] `intersect` [6,4,4,2]
--   [2,2,4]
--   </pre>
--   
--   It is a special case of <a>intersectBy</a>, which allows the
--   programmer to supply their own equality test. If the element is found
--   in both the first and the second list, the element from the first list
--   will be used.
intersect :: Eq a => [a] -> [a] -> [a]

-- | <a>intercalate</a> <tt>xs xss</tt> is equivalent to <tt>(<a>concat</a>
--   (<a>intersperse</a> xs xss))</tt>. It inserts the list <tt>xs</tt> in
--   between the lists in <tt>xss</tt> and concatenates the result.
--   
--   <pre>
--   &gt;&gt;&gt; intercalate ", " ["Lorem", "ipsum", "dolor"]
--   "Lorem, ipsum, dolor"
--   </pre>
intercalate :: [a] -> [[a]] -> [a]

-- | &lt;math&gt;. The non-overloaded version of <a>insert</a>.
insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a]

-- | &lt;math&gt;. The <a>insert</a> function takes an element and a list
--   and inserts the element into the list at the first position where it
--   is less than or equal to the next element. In particular, if the list
--   is sorted before the call, the result will also be sorted. It is a
--   special case of <a>insertBy</a>, which allows the programmer to supply
--   their own comparison function.
--   
--   <pre>
--   &gt;&gt;&gt; insert 4 [1,2,3,5,6,7]
--   [1,2,3,4,5,6,7]
--   </pre>
insert :: Ord a => a -> [a] -> [a]

-- | The <a>inits</a> function returns all initial segments of the
--   argument, shortest first. For example,
--   
--   <pre>
--   &gt;&gt;&gt; inits "abc"
--   ["","a","ab","abc"]
--   </pre>
--   
--   Note that <a>inits</a> has the following strictness property:
--   <tt>inits (xs ++ _|_) = inits xs ++ _|_</tt>
--   
--   In particular, <tt>inits _|_ = [] : _|_</tt>
inits :: [a] -> [[a]]

-- | The <a>groupBy</a> function is the non-overloaded version of
--   <a>group</a>.
groupBy :: (a -> a -> Bool) -> [a] -> [[a]]

-- | The <a>group</a> function takes a list and returns a list of lists
--   such that the concatenation of the result is equal to the argument.
--   Moreover, each sublist in the result contains only equal elements. For
--   example,
--   
--   <pre>
--   &gt;&gt;&gt; group "Mississippi"
--   ["M","i","ss","i","ss","i","pp","i"]
--   </pre>
--   
--   It is a special case of <a>groupBy</a>, which allows the programmer to
--   supply their own equality test.
group :: Eq a => [a] -> [[a]]

-- | The <a>genericTake</a> function is an overloaded version of
--   <a>take</a>, which accepts any <a>Integral</a> value as the number of
--   elements to take.
genericTake :: Integral i => i -> [a] -> [a]

-- | The <a>genericSplitAt</a> function is an overloaded version of
--   <a>splitAt</a>, which accepts any <a>Integral</a> value as the
--   position at which to split.
genericSplitAt :: Integral i => i -> [a] -> ([a], [a])

-- | The <a>genericReplicate</a> function is an overloaded version of
--   <a>replicate</a>, which accepts any <a>Integral</a> value as the
--   number of repetitions to make.
genericReplicate :: Integral i => i -> a -> [a]

-- | &lt;math&gt;. The <a>genericLength</a> function is an overloaded
--   version of <a>length</a>. In particular, instead of returning an
--   <a>Int</a>, it returns any type which is an instance of <a>Num</a>. It
--   is, however, less efficient than <a>length</a>.
--   
--   <pre>
--   &gt;&gt;&gt; genericLength [1, 2, 3] :: Int
--   3
--   
--   &gt;&gt;&gt; genericLength [1, 2, 3] :: Float
--   3.0
--   </pre>
genericLength :: Num i => [a] -> i

-- | The <a>genericIndex</a> function is an overloaded version of
--   <a>!!</a>, which accepts any <a>Integral</a> value as the index.
genericIndex :: Integral i => [a] -> i -> a

-- | The <a>genericDrop</a> function is an overloaded version of
--   <a>drop</a>, which accepts any <a>Integral</a> value as the number of
--   elements to drop.
genericDrop :: Integral i => i -> [a] -> [a]

-- | The <a>findIndices</a> function extends <a>findIndex</a>, by returning
--   the indices of all elements satisfying the predicate, in ascending
--   order.
--   
--   <pre>
--   &gt;&gt;&gt; findIndices (`elem` "aeiou") "Hello World!"
--   [1,4,7]
--   </pre>
findIndices :: (a -> Bool) -> [a] -> [Int]

-- | The <a>findIndex</a> function takes a predicate and a list and returns
--   the index of the first element in the list satisfying the predicate,
--   or <a>Nothing</a> if there is no such element.
--   
--   <pre>
--   &gt;&gt;&gt; findIndex isSpace "Hello World!"
--   Just 5
--   </pre>
findIndex :: (a -> Bool) -> [a] -> Maybe Int

-- | The <a>elemIndices</a> function extends <a>elemIndex</a>, by returning
--   the indices of all elements equal to the query element, in ascending
--   order.
--   
--   <pre>
--   &gt;&gt;&gt; elemIndices 'o' "Hello World"
--   [4,7]
--   </pre>
elemIndices :: Eq a => a -> [a] -> [Int]

-- | The <a>elemIndex</a> function returns the index of the first element
--   in the given list which is equal (by <a>==</a>) to the query element,
--   or <a>Nothing</a> if there is no such element.
--   
--   <pre>
--   &gt;&gt;&gt; elemIndex 4 [0..]
--   Just 4
--   </pre>
elemIndex :: Eq a => a -> [a] -> Maybe Int

-- | The <a>dropWhileEnd</a> function drops the largest suffix of a list in
--   which the given predicate holds for all elements. For example:
--   
--   <pre>
--   &gt;&gt;&gt; dropWhileEnd isSpace "foo\n"
--   "foo"
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; dropWhileEnd isSpace "foo bar"
--   "foo bar"
--   </pre>
--   
--   <pre>
--   dropWhileEnd isSpace ("foo\n" ++ undefined) == "foo" ++ undefined
--   </pre>
dropWhileEnd :: (a -> Bool) -> [a] -> [a]

-- | The <a>deleteFirstsBy</a> function takes a predicate and two lists and
--   returns the first list with the first occurrence of each element of
--   the second list removed.
deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]

-- | &lt;math&gt;. The <a>deleteBy</a> function behaves like <a>delete</a>,
--   but takes a user-supplied equality predicate.
--   
--   <pre>
--   &gt;&gt;&gt; deleteBy (&lt;=) 4 [1..10]
--   [1,2,3,5,6,7,8,9,10]
--   </pre>
deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]

-- | &lt;math&gt;. <a>delete</a> <tt>x</tt> removes the first occurrence of
--   <tt>x</tt> from its list argument. For example,
--   
--   <pre>
--   &gt;&gt;&gt; delete 'a' "banana"
--   "bnana"
--   </pre>
--   
--   It is a special case of <a>deleteBy</a>, which allows the programmer
--   to supply their own equality test.
delete :: Eq a => a -> [a] -> [a]

-- | The <a>\\</a> function is list difference (non-associative). In the
--   result of <tt>xs</tt> <a>\\</a> <tt>ys</tt>, the first occurrence of
--   each element of <tt>ys</tt> in turn (if any) has been removed from
--   <tt>xs</tt>. Thus
--   
--   <pre>
--   (xs ++ ys) \\ xs == ys.
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; "Hello World!" \\ "ell W"
--   "Hoorld!"
--   </pre>
--   
--   It is a special case of <a>deleteFirstsBy</a>, which allows the
--   programmer to supply their own equality test.
(\\) :: Eq a => [a] -> [a] -> [a]
infix 5 \\

-- | This data type witnesses the lifting of a <a>Monoid</a> into an
--   <a>Applicative</a> pointwise.
newtype Ap (f :: k -> Type) (a :: k)
Ap :: f a -> Ap (f :: k -> Type) (a :: k)
[getAp] :: Ap (f :: k -> Type) (a :: k) -> f a

-- | Monoid under addition.
--   
--   <pre>
--   &gt;&gt;&gt; getSum (Sum 1 &lt;&gt; Sum 2 &lt;&gt; mempty)
--   3
--   </pre>
newtype Sum a
Sum :: a -> Sum a
[getSum] :: Sum a -> a

-- | Monoid under multiplication.
--   
--   <pre>
--   &gt;&gt;&gt; getProduct (Product 3 &lt;&gt; Product 4 &lt;&gt; mempty)
--   12
--   </pre>
newtype Product a
Product :: a -> Product a
[getProduct] :: Product a -> a

-- | The monoid of endomorphisms under composition.
--   
--   <pre>
--   &gt;&gt;&gt; let computation = Endo ("Hello, " ++) &lt;&gt; Endo (++ "!")
--   
--   &gt;&gt;&gt; appEndo computation "Haskell"
--   "Hello, Haskell!"
--   </pre>
newtype Endo a
Endo :: (a -> a) -> Endo a
[appEndo] :: Endo a -> a -> a

-- | The dual of a <a>Monoid</a>, obtained by swapping the arguments of
--   <a>mappend</a>.
--   
--   <pre>
--   &gt;&gt;&gt; getDual (mappend (Dual "Hello") (Dual "World"))
--   "WorldHello"
--   </pre>
newtype Dual a
Dual :: a -> Dual a
[getDual] :: Dual a -> a

-- | Boolean monoid under disjunction (<a>||</a>).
--   
--   <pre>
--   &gt;&gt;&gt; getAny (Any True &lt;&gt; mempty &lt;&gt; Any False)
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; getAny (mconcat (map (\x -&gt; Any (even x)) [2,4,6,7,8]))
--   True
--   </pre>
newtype Any
Any :: Bool -> Any
[getAny] :: Any -> Bool
getAlt :: Alt f a -> f a

-- | Boolean monoid under conjunction (<a>&amp;&amp;</a>).
--   
--   <pre>
--   &gt;&gt;&gt; getAll (All True &lt;&gt; mempty &lt;&gt; All False)
--   False
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; getAll (mconcat (map (\x -&gt; All (even x)) [2,4,6,7,8]))
--   False
--   </pre>
newtype All
All :: Bool -> All
[getAll] :: All -> Bool

-- | This is a valid definition of <a>stimes</a> for a <a>Monoid</a>.
--   
--   Unlike the default definition of <a>stimes</a>, it is defined for 0
--   and so it should be preferred where possible.
stimesMonoid :: (Integral b, Monoid a) => b -> a -> a

-- | This is a valid definition of <a>stimes</a> for an idempotent
--   <a>Semigroup</a>.
--   
--   When <tt>x &lt;&gt; x = x</tt>, this definition should be preferred,
--   because it works in &lt;math&gt; rather than &lt;math&gt;.
stimesIdempotent :: Integral b => b -> a -> a

-- | The <a>Down</a> type allows you to reverse sort order conveniently. A
--   value of type <tt><a>Down</a> a</tt> contains a value of type
--   <tt>a</tt> (represented as <tt><a>Down</a> a</tt>).
--   
--   If <tt>a</tt> has an <tt><a>Ord</a></tt> instance associated with it
--   then comparing two values thus wrapped will give you the opposite of
--   their normal sort order. This is particularly useful when sorting in
--   generalised list comprehensions, as in: <tt>then sortWith by
--   <a>Down</a> x</tt>.
--   
--   <pre>
--   &gt;&gt;&gt; compare True False
--   GT
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; compare (Down True) (Down False)
--   LT
--   </pre>
--   
--   If <tt>a</tt> has a <tt><a>Bounded</a></tt> instance then the wrapped
--   instance also respects the reversed ordering by exchanging the values
--   of <tt><a>minBound</a></tt> and <tt><a>maxBound</a></tt>.
--   
--   <pre>
--   &gt;&gt;&gt; minBound :: Int
--   -9223372036854775808
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; minBound :: Down Int
--   Down 9223372036854775807
--   </pre>
--   
--   All other instances of <tt><a>Down</a> a</tt> behave as they do for
--   <tt>a</tt>.
newtype Down a
Down :: a -> Down a

[getDown] :: Down a -> a

-- | <pre>
--   comparing p x y = compare (p x) (p y)
--   </pre>
--   
--   Useful combinator for use in conjunction with the <tt>xxxBy</tt>
--   family of functions from <a>Data.List</a>, for example:
--   
--   <pre>
--   ... sortBy (comparing fst) ...
--   </pre>
comparing :: Ord a => (b -> a) -> b -> b -> Ordering

-- | <pre>
--   clamp (low, high) a = min high (max a low)
--   </pre>
--   
--   Function for ensursing the value <tt>a</tt> is within the inclusive
--   bounds given by <tt>low</tt> and <tt>high</tt>. If it is, <tt>a</tt>
--   is returned unchanged. The result is otherwise <tt>low</tt> if <tt>a
--   &lt;= low</tt>, or <tt>high</tt> if <tt>high &lt;= a</tt>.
--   
--   When clamp is used at Double and Float, it has NaN propagating
--   semantics in its second argument. That is, <tt>clamp (l,h) NaN =
--   NaN</tt>, but <tt>clamp (NaN, NaN) x = x</tt>.
--   
--   <pre>
--   &gt;&gt;&gt; clamp (0, 10) 2
--   2
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; clamp ('a', 'm') 'x'
--   'm'
--   </pre>
clamp :: Ord a => (a, a) -> a -> a

-- | An unsigned integral type that can be losslessly converted to and from
--   <tt>Ptr</tt>. This type is also compatible with the C99 type
--   <tt>uintptr_t</tt>, and can be marshalled to and from that type
--   safely.
newtype WordPtr
WordPtr :: Word -> WordPtr

-- | A signed integral type that can be losslessly converted to and from
--   <tt>Ptr</tt>. This type is also compatible with the C99 type
--   <tt>intptr_t</tt>, and can be marshalled to and from that type safely.
newtype IntPtr
IntPtr :: Int -> IntPtr

-- | casts a <tt>WordPtr</tt> to a <tt>Ptr</tt>
wordPtrToPtr :: WordPtr -> Ptr a

-- | casts a <tt>Ptr</tt> to a <tt>WordPtr</tt>
ptrToWordPtr :: Ptr a -> WordPtr

-- | casts a <tt>Ptr</tt> to an <tt>IntPtr</tt>
ptrToIntPtr :: Ptr a -> IntPtr

-- | casts an <tt>IntPtr</tt> to a <tt>Ptr</tt>
intPtrToPtr :: IntPtr -> Ptr a

-- | Release the storage associated with the given <a>FunPtr</a>, which
--   must have been obtained from a wrapper stub. This should be called
--   whenever the return value from a foreign import wrapper function is no
--   longer required; otherwise, the storage it uses will leak.
freeHaskellFunPtr :: FunPtr a -> IO ()

-- | The member functions of this class facilitate writing values of
--   primitive types to raw memory (which may have been allocated with the
--   above mentioned routines) and reading values from blocks of raw
--   memory. The class, furthermore, includes support for computing the
--   storage requirements and alignment restrictions of storable types.
--   
--   Memory addresses are represented as values of type <tt><a>Ptr</a>
--   a</tt>, for some <tt>a</tt> which is an instance of class
--   <a>Storable</a>. The type argument to <a>Ptr</a> helps provide some
--   valuable type safety in FFI code (you can't mix pointers of different
--   types without an explicit cast), while helping the Haskell type system
--   figure out which marshalling method is needed for a given pointer.
--   
--   All marshalling between Haskell and a foreign language ultimately
--   boils down to translating Haskell data structures into the binary
--   representation of a corresponding data structure of the foreign
--   language and vice versa. To code this marshalling in Haskell, it is
--   necessary to manipulate primitive data types stored in unstructured
--   memory blocks. The class <a>Storable</a> facilitates this manipulation
--   on all types for which it is instantiated, which are the standard
--   basic types of Haskell, the fixed size <tt>Int</tt> types
--   (<a>Int8</a>, <a>Int16</a>, <a>Int32</a>, <a>Int64</a>), the fixed
--   size <tt>Word</tt> types (<a>Word8</a>, <a>Word16</a>, <a>Word32</a>,
--   <a>Word64</a>), <a>StablePtr</a>, all types from
--   <a>Foreign.C.Types</a>, as well as <a>Ptr</a>.
class Storable a

-- | Computes the storage requirements (in bytes) of the argument. The
--   value of the argument is not used.
sizeOf :: Storable a => a -> Int

-- | Computes the alignment constraint of the argument. An alignment
--   constraint <tt>x</tt> is fulfilled by any address divisible by
--   <tt>x</tt>. The alignment must be a power of two if this instance is
--   to be used with <tt>alloca</tt> or <tt>allocaArray</tt>. The value of
--   the argument is not used.
alignment :: Storable a => a -> Int

-- | Read a value from a memory area regarded as an array of values of the
--   same kind. The first argument specifies the start address of the array
--   and the second the index into the array (the first element of the
--   array has index <tt>0</tt>). The following equality holds,
--   
--   <pre>
--   peekElemOff addr idx = IOExts.fixIO $ \result -&gt;
--     peek (addr `plusPtr` (idx * sizeOf result))
--   </pre>
--   
--   Note that this is only a specification, not necessarily the concrete
--   implementation of the function.
peekElemOff :: Storable a => Ptr a -> Int -> IO a

-- | Write a value to a memory area regarded as an array of values of the
--   same kind. The following equality holds:
--   
--   <pre>
--   pokeElemOff addr idx x = 
--     poke (addr `plusPtr` (idx * sizeOf x)) x
--   </pre>
pokeElemOff :: Storable a => Ptr a -> Int -> a -> IO ()

-- | Read a value from a memory location given by a base address and
--   offset. The following equality holds:
--   
--   <pre>
--   peekByteOff addr off = peek (addr `plusPtr` off)
--   </pre>
peekByteOff :: Storable a => Ptr b -> Int -> IO a

-- | Write a value to a memory location given by a base address and offset.
--   The following equality holds:
--   
--   <pre>
--   pokeByteOff addr off x = poke (addr `plusPtr` off) x
--   </pre>
pokeByteOff :: Storable a => Ptr b -> Int -> a -> IO ()

-- | Read a value from the given memory location.
--   
--   Note that the peek and poke functions might require properly aligned
--   addresses to function correctly. This is architecture dependent; thus,
--   portable code should ensure that when peeking or poking values of some
--   type <tt>a</tt>, the alignment constraint for <tt>a</tt>, as given by
--   the function <a>alignment</a> is fulfilled.
peek :: Storable a => Ptr a -> IO a

-- | Write the given value to the given memory location. Alignment
--   restrictions might apply; see <a>peek</a>.
poke :: Storable a => Ptr a -> a -> IO ()

-- | Dissolve the association between the stable pointer and the Haskell
--   value. Afterwards, if the stable pointer is passed to
--   <a>deRefStablePtr</a> or <a>freeStablePtr</a>, the behaviour is
--   undefined. However, the stable pointer may still be passed to
--   <a>castStablePtrToPtr</a>, but the <tt><a>Ptr</a> ()</tt> value
--   returned by <a>castStablePtrToPtr</a>, in this case, is undefined (in
--   particular, it may be <a>nullPtr</a>). Nevertheless, the call to
--   <a>castStablePtrToPtr</a> is guaranteed not to diverge.
freeStablePtr :: StablePtr a -> IO ()

-- | Obtain the Haskell value referenced by a stable pointer, i.e., the
--   same value that was passed to the corresponding call to
--   <a>newStablePtr</a>. If the argument to <a>deRefStablePtr</a> has
--   already been freed using <a>freeStablePtr</a>, the behaviour of
--   <a>deRefStablePtr</a> is undefined.
deRefStablePtr :: StablePtr a -> IO a

-- | Coerce a stable pointer to an address. No guarantees are made about
--   the resulting value, except that the original stable pointer can be
--   recovered by <a>castPtrToStablePtr</a>. In particular, the address may
--   not refer to an accessible memory location and any attempt to pass it
--   to the member functions of the class <a>Storable</a> leads to
--   undefined behaviour.
castStablePtrToPtr :: StablePtr a -> Ptr ()

-- | The inverse of <a>castStablePtrToPtr</a>, i.e., we have the identity
--   
--   <pre>
--   sp == castPtrToStablePtr (castStablePtrToPtr sp)
--   </pre>
--   
--   for any stable pointer <tt>sp</tt> on which <a>freeStablePtr</a> has
--   not been executed yet. Moreover, <a>castPtrToStablePtr</a> may only be
--   applied to pointers that have been produced by
--   <a>castStablePtrToPtr</a>.
castPtrToStablePtr :: Ptr () -> StablePtr a
unsafeCoerceUnlifted :: forall (a :: UnliftedType) (b :: UnliftedType). a -> b
unsafeCoerceAddr :: forall (a :: TYPE 'AddrRep) (b :: TYPE 'AddrRep). a -> b

-- | Coerce a value from one type to another, bypassing the type-checker.
--   
--   There are several legitimate ways to use <a>unsafeCoerce</a>:
--   
--   <ol>
--   <li>To coerce e.g. <tt>Int</tt> to <tt>HValue</tt>, put it in a list
--   of <tt>HValue</tt>, and then later coerce it back to <tt>Int</tt>
--   before using it.</li>
--   <li>To produce e.g. <tt>(a+b) :~: (b+a)</tt> from <tt>unsafeCoerce
--   Refl</tt>. Here the two sides really are the same type -- so nothing
--   unsafe is happening -- but GHC is not clever enough to see it.</li>
--   <li>In <tt>Data.Typeable</tt> we have</li>
--   </ol>
--   
--   <pre>
--   eqTypeRep :: forall k1 k2 (a :: k1) (b :: k2).
--                TypeRep a -&gt; TypeRep b -&gt; Maybe (a :~~: b)
--   eqTypeRep a b
--     | sameTypeRep a b = Just (unsafeCoerce HRefl)
--     | otherwise       = Nothing
--   
--   </pre>
--   
--   Here again, the <tt>unsafeCoerce HRefl</tt> is safe, because the two
--   types really are the same -- but the proof of that relies on the
--   complex, trusted implementation of <tt>Typeable</tt>.
--   
--   <ol>
--   <li>The "reflection trick", which takes advantage of the fact that in
--   <tt>class C a where { op :: ty }</tt>, we can safely coerce between
--   <tt>C a</tt> and <tt>ty</tt> (which have different kinds!) because
--   it's really just a newtype. Note: there is <i>no guarantee, at all</i>
--   that this behavior will be supported into perpetuity.</li>
--   </ol>
unsafeCoerce :: a -> b

-- | Monoid under bitwise XOR.
--   
--   <pre>
--   &gt;&gt;&gt; getXor (Xor 0xab &lt;&gt; Xor 0x12) :: Word8
--   185
--   </pre>
newtype Xor a
Xor :: a -> Xor a
[getXor] :: Xor a -> a

-- | Monoid under bitwise inclusive OR.
--   
--   <pre>
--   &gt;&gt;&gt; getIor (Ior 0xab &lt;&gt; Ior 0x12) :: Word8
--   187
--   </pre>
newtype Ior a
Ior :: a -> Ior a
[getIor] :: Ior a -> a

-- | Monoid under bitwise 'equality'; defined as <tt>1</tt> if the
--   corresponding bits match, and <tt>0</tt> otherwise.
--   
--   <pre>
--   &gt;&gt;&gt; getIff (Iff 0xab &lt;&gt; Iff 0x12) :: Word8
--   70
--   </pre>
newtype Iff a
Iff :: a -> Iff a
[getIff] :: Iff a -> a

-- | Monoid under bitwise AND.
--   
--   <pre>
--   &gt;&gt;&gt; getAnd (And 0xab &lt;&gt; And 0x12) :: Word8
--   2
--   </pre>
newtype And a
And :: a -> And a
[getAnd] :: And a -> a

-- | A more concise version of <tt>complement zeroBits</tt>.
--   
--   <pre>
--   &gt;&gt;&gt; complement (zeroBits :: Word) == (oneBits :: Word)
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; complement (oneBits :: Word) == (zeroBits :: Word)
--   True
--   </pre>
--   
--   <h1>Note</h1>
--   
--   The constraint on <a>oneBits</a> is arguably too strong. However, as
--   some types (such as <tt>Natural</tt>) have undefined
--   <a>complement</a>, this is the only safe choice.
oneBits :: FiniteBits a => a

-- | Selects Unicode space and separator characters.
--   
--   This function returns <a>True</a> if its argument has one of the
--   following <a>GeneralCategory</a>s, or <a>False</a> otherwise:
--   
--   <ul>
--   <li><a>Space</a></li>
--   <li><a>LineSeparator</a></li>
--   <li><a>ParagraphSeparator</a></li>
--   </ul>
--   
--   These classes are defined in the <a>Unicode Character Database</a>,
--   part of the Unicode standard. The same document defines what is and is
--   not a "Separator".
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; isSeparator 'a'
--   False
--   
--   &gt;&gt;&gt; isSeparator '6'
--   False
--   
--   &gt;&gt;&gt; isSeparator ' '
--   True
--   </pre>
--   
--   Warning: newlines and tab characters are not considered separators.
--   
--   <pre>
--   &gt;&gt;&gt; isSeparator '\n'
--   False
--   
--   &gt;&gt;&gt; isSeparator '\t'
--   False
--   </pre>
--   
--   But some more exotic characters are (like HTML's <tt>&amp;nbsp;</tt>):
--   
--   <pre>
--   &gt;&gt;&gt; isSeparator '\160'
--   True
--   </pre>
isSeparator :: Char -> Bool

-- | Selects Unicode numeric characters, including digits from various
--   scripts, Roman numerals, et cetera.
--   
--   This function returns <a>True</a> if its argument has one of the
--   following <a>GeneralCategory</a>s, or <a>False</a> otherwise:
--   
--   <ul>
--   <li><a>DecimalNumber</a></li>
--   <li><a>LetterNumber</a></li>
--   <li><a>OtherNumber</a></li>
--   </ul>
--   
--   These classes are defined in the <a>Unicode Character Database</a>,
--   part of the Unicode standard. The same document defines what is and is
--   not a "Number".
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; isNumber 'a'
--   False
--   
--   &gt;&gt;&gt; isNumber '%'
--   False
--   
--   &gt;&gt;&gt; isNumber '3'
--   True
--   </pre>
--   
--   ASCII <tt>'0'</tt> through <tt>'9'</tt> are all numbers:
--   
--   <pre>
--   &gt;&gt;&gt; and $ map isNumber ['0'..'9']
--   True
--   </pre>
--   
--   Unicode Roman numerals are "numbers" as well:
--   
--   <pre>
--   &gt;&gt;&gt; isNumber 'Ⅸ'
--   True
--   </pre>
isNumber :: Char -> Bool

-- | Selects Unicode mark characters, for example accents and the like,
--   which combine with preceding characters.
--   
--   This function returns <a>True</a> if its argument has one of the
--   following <a>GeneralCategory</a>s, or <a>False</a> otherwise:
--   
--   <ul>
--   <li><a>NonSpacingMark</a></li>
--   <li><a>SpacingCombiningMark</a></li>
--   <li><a>EnclosingMark</a></li>
--   </ul>
--   
--   These classes are defined in the <a>Unicode Character Database</a>,
--   part of the Unicode standard. The same document defines what is and is
--   not a "Mark".
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; isMark 'a'
--   False
--   
--   &gt;&gt;&gt; isMark '0'
--   False
--   </pre>
--   
--   Combining marks such as accent characters usually need to follow
--   another character before they become printable:
--   
--   <pre>
--   &gt;&gt;&gt; map isMark "ò"
--   [False,True]
--   </pre>
--   
--   Puns are not necessarily supported:
--   
--   <pre>
--   &gt;&gt;&gt; isMark '✓'
--   False
--   </pre>
isMark :: Char -> Bool

-- | Selects alphabetic Unicode characters (lower-case, upper-case and
--   title-case letters, plus letters of caseless scripts and modifiers
--   letters). This function is equivalent to <a>isAlpha</a>.
--   
--   This function returns <a>True</a> if its argument has one of the
--   following <a>GeneralCategory</a>s, or <a>False</a> otherwise:
--   
--   <ul>
--   <li><a>UppercaseLetter</a></li>
--   <li><a>LowercaseLetter</a></li>
--   <li><a>TitlecaseLetter</a></li>
--   <li><a>ModifierLetter</a></li>
--   <li><a>OtherLetter</a></li>
--   </ul>
--   
--   These classes are defined in the <a>Unicode Character Database</a>,
--   part of the Unicode standard. The same document defines what is and is
--   not a "Letter".
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; isLetter 'a'
--   True
--   
--   &gt;&gt;&gt; isLetter 'A'
--   True
--   
--   &gt;&gt;&gt; isLetter 'λ'
--   True
--   
--   &gt;&gt;&gt; isLetter '0'
--   False
--   
--   &gt;&gt;&gt; isLetter '%'
--   False
--   
--   &gt;&gt;&gt; isLetter '♥'
--   False
--   
--   &gt;&gt;&gt; isLetter '\31'
--   False
--   </pre>
--   
--   Ensure that <a>isLetter</a> and <a>isAlpha</a> are equivalent.
--   
--   <pre>
--   &gt;&gt;&gt; let chars = [(chr 0)..]
--   
--   &gt;&gt;&gt; let letters = map isLetter chars
--   
--   &gt;&gt;&gt; let alphas = map isAlpha chars
--   
--   &gt;&gt;&gt; letters == alphas
--   True
--   </pre>
isLetter :: Char -> Bool

-- | Convert a single digit <a>Char</a> to the corresponding <a>Int</a>.
--   This function fails unless its argument satisfies <a>isHexDigit</a>,
--   but recognises both upper- and lower-case hexadecimal digits (that is,
--   <tt>'0'</tt>..<tt>'9'</tt>, <tt>'a'</tt>..<tt>'f'</tt>,
--   <tt>'A'</tt>..<tt>'F'</tt>).
--   
--   <h4><b>Examples</b></h4>
--   
--   Characters <tt>'0'</tt> through <tt>'9'</tt> are converted properly to
--   <tt>0..9</tt>:
--   
--   <pre>
--   &gt;&gt;&gt; map digitToInt ['0'..'9']
--   [0,1,2,3,4,5,6,7,8,9]
--   </pre>
--   
--   Both upper- and lower-case <tt>'A'</tt> through <tt>'F'</tt> are
--   converted as well, to <tt>10..15</tt>.
--   
--   <pre>
--   &gt;&gt;&gt; map digitToInt ['a'..'f']
--   [10,11,12,13,14,15]
--   
--   &gt;&gt;&gt; map digitToInt ['A'..'F']
--   [10,11,12,13,14,15]
--   </pre>
--   
--   Anything else throws an exception:
--   
--   <pre>
--   &gt;&gt;&gt; digitToInt 'G'
--   *** Exception: Char.digitToInt: not a digit 'G'
--   
--   &gt;&gt;&gt; digitToInt '♥'
--   *** Exception: Char.digitToInt: not a digit '\9829'
--   </pre>
digitToInt :: Char -> Int

-- | equivalent to <a>readsPrec</a> with a precedence of 0.
reads :: Read a => ReadS a

-- | Parse a string using the <a>Read</a> instance. Succeeds if there is
--   exactly one valid result.
--   
--   <pre>
--   &gt;&gt;&gt; readMaybe "123" :: Maybe Int
--   Just 123
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; readMaybe "hello" :: Maybe Int
--   Nothing
--   </pre>
readMaybe :: Read a => String -> Maybe a

-- | Parse a string using the <a>Read</a> instance. Succeeds if there is
--   exactly one valid result. A <a>Left</a> value indicates a parse error.
--   
--   <pre>
--   &gt;&gt;&gt; readEither "123" :: Either String Int
--   Right 123
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; readEither "hello" :: Either String Int
--   Left "Prelude.read: no parse"
--   </pre>
readEither :: Read a => String -> Either String a

-- | The <a>read</a> function reads input from a string, which must be
--   completely consumed by the input process. <a>read</a> fails with an
--   <a>error</a> if the parse is unsuccessful, and it is therefore
--   discouraged from being used in real applications. Use <a>readMaybe</a>
--   or <a>readEither</a> for safe alternatives.
--   
--   <pre>
--   &gt;&gt;&gt; read "123" :: Int
--   123
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; read "hello" :: Int
--   *** Exception: Prelude.read: no parse
--   </pre>
read :: Read a => String -> a

-- | Extracts from a list of <a>Either</a> all the <a>Right</a> elements.
--   All the <a>Right</a> elements are extracted in order.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
--   
--   &gt;&gt;&gt; rights list
--   [3,7]
--   </pre>
rights :: [Either a b] -> [b]

-- | Partitions a list of <a>Either</a> into two lists. All the <a>Left</a>
--   elements are extracted, in order, to the first component of the
--   output. Similarly the <a>Right</a> elements are extracted to the
--   second component of the output.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
--   
--   &gt;&gt;&gt; partitionEithers list
--   (["foo","bar","baz"],[3,7])
--   </pre>
--   
--   The pair returned by <tt><a>partitionEithers</a> x</tt> should be the
--   same pair as <tt>(<a>lefts</a> x, <a>rights</a> x)</tt>:
--   
--   <pre>
--   &gt;&gt;&gt; let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
--   
--   &gt;&gt;&gt; partitionEithers list == (lefts list, rights list)
--   True
--   </pre>
partitionEithers :: [Either a b] -> ([a], [b])

-- | Extracts from a list of <a>Either</a> all the <a>Left</a> elements.
--   All the <a>Left</a> elements are extracted in order.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
--   
--   &gt;&gt;&gt; lefts list
--   ["foo","bar","baz"]
--   </pre>
lefts :: [Either a b] -> [a]

-- | Return <a>True</a> if the given value is a <a>Right</a>-value,
--   <a>False</a> otherwise.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; isRight (Left "foo")
--   False
--   
--   &gt;&gt;&gt; isRight (Right 3)
--   True
--   </pre>
--   
--   Assuming a <a>Left</a> value signifies some sort of error, we can use
--   <a>isRight</a> to write a very simple reporting function that only
--   outputs "SUCCESS" when a computation has succeeded.
--   
--   This example shows how <a>isRight</a> might be used to avoid pattern
--   matching when one does not care about the value contained in the
--   constructor:
--   
--   <pre>
--   &gt;&gt;&gt; import Control.Monad ( when )
--   
--   &gt;&gt;&gt; let report e = when (isRight e) $ putStrLn "SUCCESS"
--   
--   &gt;&gt;&gt; report (Left "parse error")
--   
--   &gt;&gt;&gt; report (Right 1)
--   SUCCESS
--   </pre>
isRight :: Either a b -> Bool

-- | Return <a>True</a> if the given value is a <a>Left</a>-value,
--   <a>False</a> otherwise.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; isLeft (Left "foo")
--   True
--   
--   &gt;&gt;&gt; isLeft (Right 3)
--   False
--   </pre>
--   
--   Assuming a <a>Left</a> value signifies some sort of error, we can use
--   <a>isLeft</a> to write a very simple error-reporting function that
--   does absolutely nothing in the case of success, and outputs "ERROR" if
--   any error occurred.
--   
--   This example shows how <a>isLeft</a> might be used to avoid pattern
--   matching when one does not care about the value contained in the
--   constructor:
--   
--   <pre>
--   &gt;&gt;&gt; import Control.Monad ( when )
--   
--   &gt;&gt;&gt; let report e = when (isLeft e) $ putStrLn "ERROR"
--   
--   &gt;&gt;&gt; report (Right 1)
--   
--   &gt;&gt;&gt; report (Left "parse error")
--   ERROR
--   </pre>
isLeft :: Either a b -> Bool

-- | Return the contents of a <a>Right</a>-value or a default value
--   otherwise.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; fromRight 1 (Right 3)
--   3
--   
--   &gt;&gt;&gt; fromRight 1 (Left "foo")
--   1
--   </pre>
fromRight :: b -> Either a b -> b

-- | Return the contents of a <a>Left</a>-value or a default value
--   otherwise.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; fromLeft 1 (Left 3)
--   3
--   
--   &gt;&gt;&gt; fromLeft 1 (Right "foo")
--   1
--   </pre>
fromLeft :: a -> Either a b -> a

-- | <a>Proxy</a> is a type that holds no data, but has a phantom parameter
--   of arbitrary type (or even kind). Its use is to provide type
--   information, even though there is no value available of that type (or
--   it may be too costly to create one).
--   
--   Historically, <tt><a>Proxy</a> :: <a>Proxy</a> a</tt> is a safer
--   alternative to the <tt><a>undefined</a> :: a</tt> idiom.
--   
--   <pre>
--   &gt;&gt;&gt; Proxy :: Proxy (Void, Int -&gt; Int)
--   Proxy
--   </pre>
--   
--   Proxy can even hold types of higher kinds,
--   
--   <pre>
--   &gt;&gt;&gt; Proxy :: Proxy Either
--   Proxy
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; Proxy :: Proxy Functor
--   Proxy
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; Proxy :: Proxy complicatedStructure
--   Proxy
--   </pre>
data Proxy (t :: k)
Proxy :: Proxy (t :: k)

-- | A concrete, promotable proxy type, for use at the kind level. There
--   are no instances for this because it is intended at the kind level
--   only
data KProxy t
KProxy :: KProxy t

-- | <a>asProxyTypeOf</a> is a type-restricted version of <a>const</a>. It
--   is usually used as an infix operator, and its typing forces its first
--   argument (which is usually overloaded) to have the same type as the
--   tag of the second.
--   
--   <pre>
--   &gt;&gt;&gt; import Data.Word
--   
--   &gt;&gt;&gt; :type asProxyTypeOf 123 (Proxy :: Proxy Word8)
--   asProxyTypeOf 123 (Proxy :: Proxy Word8) :: Word8
--   </pre>
--   
--   Note the lower-case <tt>proxy</tt> in the definition. This allows any
--   type constructor with just one argument to be passed to the function,
--   for example we could also write
--   
--   <pre>
--   &gt;&gt;&gt; import Data.Word
--   
--   &gt;&gt;&gt; :type asProxyTypeOf 123 (Just (undefined :: Word8))
--   asProxyTypeOf 123 (Just (undefined :: Word8)) :: Word8
--   </pre>
asProxyTypeOf :: a -> proxy a -> a

-- | A class for categories. Instances should satisfy the laws
--   
--   <ul>
--   <li><i>Right identity</i> <tt>f <a>.</a> <a>id</a> = f</tt></li>
--   <li><i>Left identity</i> <tt><a>id</a> <a>.</a> f = f</tt></li>
--   <li><i>Associativity</i> <tt>f <a>.</a> (g <a>.</a> h) = (f <a>.</a>
--   g) <a>.</a> h</tt></li>
--   </ul>
class Category (cat :: k -> k -> Type)

-- | the identity morphism
id :: forall (a :: k). Category cat => cat a a

-- | morphism composition
(.) :: forall (b :: k) (c :: k) (a :: k). Category cat => cat b c -> cat a b -> cat a c
infixr 9 .

-- | Left-to-right composition
(>>>) :: forall {k} cat (a :: k) (b :: k) (c :: k). Category cat => cat a b -> cat b c -> cat a c
infixr 1 >>>

-- | Right-to-left composition
(<<<) :: forall {k} cat (b :: k) (c :: k) (a :: k). Category cat => cat b c -> cat a b -> cat a c
infixr 1 <<<

-- | Kind heterogeneous propositional equality. Like <a>:~:</a>, <tt>a :~~:
--   b</tt> is inhabited by a terminating value if and only if <tt>a</tt>
--   is the same type as <tt>b</tt>.
data (a :: k1) :~~: (b :: k2)
[HRefl] :: forall {k1} (a :: k1). a :~~: a
infix 4 :~~:

-- | Propositional equality. If <tt>a :~: b</tt> is inhabited by some
--   terminating value, then the type <tt>a</tt> is the same as the type
--   <tt>b</tt>. To use this equality in practice, pattern-match on the
--   <tt>a :~: b</tt> to get out the <tt>Refl</tt> constructor; in the body
--   of the pattern-match, the compiler knows that <tt>a ~ b</tt>.
data (a :: k) :~: (b :: k)
[Refl] :: forall {k} (a :: k). a :~: a
infix 4 :~:

-- | Advances the given address by the given offset in bytes.
plusPtr :: Ptr a -> Int -> Ptr b

-- | The constant <a>nullPtr</a> contains a distinguished value of
--   <a>Ptr</a> that is not associated with a valid memory location.
nullPtr :: Ptr a

-- | The constant <a>nullFunPtr</a> contains a distinguished value of
--   <a>FunPtr</a> that is not associated with a valid memory location.
nullFunPtr :: FunPtr a

-- | Computes the offset required to get from the second to the first
--   argument. We have
--   
--   <pre>
--   p2 == p1 `plusPtr` (p2 `minusPtr` p1)
--   </pre>
minusPtr :: Ptr a -> Ptr b -> Int

-- | Casts a <a>Ptr</a> to a <a>FunPtr</a>.
--   
--   <i>Note:</i> this is valid only on architectures where data and
--   function pointers range over the same set of addresses, and should
--   only be used for bindings to external libraries whose interface
--   already relies on this assumption.
castPtrToFunPtr :: Ptr a -> FunPtr b

-- | The <a>castPtr</a> function casts a pointer from one type to another.
castPtr :: Ptr a -> Ptr b

-- | Casts a <a>FunPtr</a> to a <a>Ptr</a>.
--   
--   <i>Note:</i> this is valid only on architectures where data and
--   function pointers range over the same set of addresses, and should
--   only be used for bindings to external libraries whose interface
--   already relies on this assumption.
castFunPtrToPtr :: FunPtr a -> Ptr b

-- | Casts a <a>FunPtr</a> to a <a>FunPtr</a> of a different type.
castFunPtr :: FunPtr a -> FunPtr b

-- | Given an arbitrary address and an alignment constraint,
--   <a>alignPtr</a> yields the next higher address that fulfills the
--   alignment constraint. An alignment constraint <tt>x</tt> is fulfilled
--   by any address divisible by <tt>x</tt>. This operation is idempotent.
alignPtr :: Ptr a -> Int -> Ptr a

-- | Show <i>non-negative</i> <a>Integral</a> numbers in base 8.
showOct :: (Integral a, Show a) => a -> ShowS

-- | Shows a <i>non-negative</i> <a>Integral</a> number using the base
--   specified by the first argument, and the character representation
--   specified by the second.
showIntAtBase :: (Integral a, Show a) => a -> (Int -> Char) -> a -> ShowS

-- | Show <i>non-negative</i> <a>Integral</a> numbers in base 10.
showInt :: Integral a => a -> ShowS

-- | Show <i>non-negative</i> <a>Integral</a> numbers in base 16.
showHex :: (Integral a, Show a) => a -> ShowS

-- | Show a floating-point value in the hexadecimal format, similar to the
--   <tt>%a</tt> specifier in C's printf.
--   
--   <pre>
--   &gt;&gt;&gt; showHFloat (212.21 :: Double) ""
--   "0x1.a86b851eb851fp7"
--   
--   &gt;&gt;&gt; showHFloat (-12.76 :: Float) ""
--   "-0x1.9851ecp3"
--   
--   &gt;&gt;&gt; showHFloat (-0 :: Double) ""
--   "-0x0p+0"
--   </pre>
showHFloat :: RealFloat a => a -> ShowS

-- | Show a signed <a>RealFloat</a> value using standard decimal notation
--   for arguments whose absolute value lies between <tt>0.1</tt> and
--   <tt>9,999,999</tt>, and scientific notation otherwise.
--   
--   This behaves as <a>showFFloat</a>, except that a decimal point is
--   always guaranteed, even if not needed.
showGFloatAlt :: RealFloat a => Maybe Int -> a -> ShowS

-- | Show a signed <a>RealFloat</a> value using standard decimal notation
--   for arguments whose absolute value lies between <tt>0.1</tt> and
--   <tt>9,999,999</tt>, and scientific notation otherwise.
--   
--   In the call <tt><a>showGFloat</a> digs val</tt>, if <tt>digs</tt> is
--   <a>Nothing</a>, the value is shown to full precision; if <tt>digs</tt>
--   is <tt><a>Just</a> d</tt>, then at most <tt>d</tt> digits after the
--   decimal point are shown.
showGFloat :: RealFloat a => Maybe Int -> a -> ShowS

-- | Show a signed <a>RealFloat</a> value using standard decimal notation
--   (e.g. <tt>245000</tt>, <tt>0.0015</tt>).
--   
--   This behaves as <a>showFFloat</a>, except that a decimal point is
--   always guaranteed, even if not needed.
showFFloatAlt :: RealFloat a => Maybe Int -> a -> ShowS

-- | Show a signed <a>RealFloat</a> value using standard decimal notation
--   (e.g. <tt>245000</tt>, <tt>0.0015</tt>).
--   
--   In the call <tt><a>showFFloat</a> digs val</tt>, if <tt>digs</tt> is
--   <a>Nothing</a>, the value is shown to full precision; if <tt>digs</tt>
--   is <tt><a>Just</a> d</tt>, then at most <tt>d</tt> digits after the
--   decimal point are shown.
showFFloat :: RealFloat a => Maybe Int -> a -> ShowS

-- | Show a signed <a>RealFloat</a> value using scientific (exponential)
--   notation (e.g. <tt>2.45e2</tt>, <tt>1.5e-3</tt>).
--   
--   In the call <tt><a>showEFloat</a> digs val</tt>, if <tt>digs</tt> is
--   <a>Nothing</a>, the value is shown to full precision; if <tt>digs</tt>
--   is <tt><a>Just</a> d</tt>, then at most <tt>d</tt> digits after the
--   decimal point are shown.
showEFloat :: RealFloat a => Maybe Int -> a -> ShowS

-- | Show <i>non-negative</i> <a>Integral</a> numbers in base 2.
showBin :: (Integral a, Show a) => a -> ShowS

-- | Reads a <i>signed</i> <a>Real</a> value, given a reader for an
--   unsigned value.
readSigned :: Real a => ReadS a -> ReadS a

-- | Read an unsigned number in octal notation.
--   
--   <pre>
--   &gt;&gt;&gt; readOct "0644"
--   [(420,"")]
--   </pre>
readOct :: (Eq a, Num a) => ReadS a

-- | Reads an <i>unsigned</i> <a>Integral</a> value in an arbitrary base.
readInt :: Num a => a -> (Char -> Bool) -> (Char -> Int) -> ReadS a

-- | Read an unsigned number in hexadecimal notation. Both upper or lower
--   case letters are allowed.
--   
--   <pre>
--   &gt;&gt;&gt; readHex "deadbeef"
--   [(3735928559,"")]
--   </pre>
readHex :: (Eq a, Num a) => ReadS a

-- | Reads an <i>unsigned</i> <a>RealFrac</a> value, expressed in decimal
--   scientific notation.
readFloat :: RealFrac a => ReadS a

-- | Read an unsigned number in decimal notation.
--   
--   <pre>
--   &gt;&gt;&gt; readDec "0644"
--   [(644,"")]
--   </pre>
readDec :: (Eq a, Num a) => ReadS a

-- | Read an unsigned number in binary notation.
--   
--   <pre>
--   &gt;&gt;&gt; readBin "10011"
--   [(19,"")]
--   </pre>
readBin :: (Eq a, Num a) => ReadS a

-- | <tt><a>readParen</a> <a>True</a> p</tt> parses what <tt>p</tt> parses,
--   but surrounded with parentheses.
--   
--   <tt><a>readParen</a> <a>False</a> p</tt> parses what <tt>p</tt>
--   parses, but optionally surrounded with parentheses.
readParen :: Bool -> ReadS a -> ReadS a

-- | Read a string representation of a character, using Haskell
--   source-language escape conventions, and convert it to the character
--   that it encodes. For example:
--   
--   <pre>
--   readLitChar "\\nHello"  =  [('\n', "Hello")]
--   </pre>
readLitChar :: ReadS Char

-- | Read a string representation of a character, using Haskell
--   source-language escape conventions. For example:
--   
--   <pre>
--   lexLitChar  "\\nHello"  =  [("\\n", "Hello")]
--   </pre>
lexLitChar :: ReadS String

-- | Reads a non-empty string of decimal digits.
lexDigits :: ReadS String

-- | The <a>lex</a> function reads a single lexeme from the input,
--   discarding initial white space, and returning the characters that
--   constitute the lexeme. If the input string contains only white space,
--   <a>lex</a> returns a single successful `lexeme' consisting of the
--   empty string. (Thus <tt><a>lex</a> "" = [("","")]</tt>.) If there is
--   no legal lexeme at the beginning of the input string, <a>lex</a> fails
--   (i.e. returns <tt>[]</tt>).
--   
--   This lexer is not completely faithful to the Haskell lexical syntax in
--   the following respects:
--   
--   <ul>
--   <li>Qualified names are not handled properly</li>
--   <li>Octal and hexadecimal numerics are not recognized as a single
--   token</li>
--   <li>Comments are not treated properly</li>
--   </ul>
lex :: ReadS String
data ReadPrec a
readS_to_Prec :: (Int -> ReadS a) -> ReadPrec a
readPrec_to_S :: ReadPrec a -> Int -> ReadS a
readPrec_to_P :: ReadPrec a -> Int -> ReadP a
readP_to_Prec :: (Int -> ReadP a) -> ReadPrec a

-- | A parser for a type <tt>a</tt>, represented as a function that takes a
--   <a>String</a> and returns a list of possible parses as
--   <tt>(a,<a>String</a>)</tt> pairs.
--   
--   Note that this kind of backtracking parser is very inefficient;
--   reading a large structure may be quite slow (cf <a>ReadP</a>).
type ReadS a = String -> [(a, String)]
data ReadP a

-- | Converts a Haskell ReadS-style function into a parser. Warning: This
--   introduces local backtracking in the resulting parser, and therefore a
--   possible inefficiency.
readS_to_P :: ReadS a -> ReadP a

-- | Converts a parser into a Haskell ReadS-style function. This is the
--   main way in which you can "run" a <a>ReadP</a> parser: the expanded
--   type is <tt> readP_to_S :: ReadP a -&gt; String -&gt; [(a,String)]
--   </tt>
readP_to_S :: ReadP a -> ReadS a

-- | Show a signed <a>RealFloat</a> value to full precision using standard
--   decimal notation for arguments whose absolute value lies between
--   <tt>0.1</tt> and <tt>9,999,999</tt>, and scientific notation
--   otherwise.
showFloat :: RealFloat a => a -> ShowS

-- | Converts a <a>Rational</a> value into any type in class
--   <a>RealFloat</a>.
fromRat :: RealFloat a => Rational -> a

-- | <a>floatToDigits</a> takes a base and a non-negative <a>RealFloat</a>
--   number, and returns a list of digits and an exponent. In particular,
--   if <tt>x&gt;=0</tt>, and
--   
--   <pre>
--   floatToDigits base x = ([d1,d2,...,dn], e)
--   </pre>
--   
--   then
--   
--   <ol>
--   <li><pre>n &gt;= 1</pre></li>
--   <li><pre>x = 0.d1d2...dn * (base**e)</pre></li>
--   <li><pre>0 &lt;= di &lt;= base-1</pre></li>
--   </ol>
floatToDigits :: RealFloat a => Integer -> a -> ([Int], Int)

-- | Reverse order of bytes in <a>Word64</a>.
byteSwap64 :: Word64 -> Word64

-- | Reverse order of bytes in <a>Word32</a>.
byteSwap32 :: Word32 -> Word32

-- | Reverse order of bytes in <a>Word16</a>.
byteSwap16 :: Word16 -> Word16

-- | Reverse the order of the bits in a <a>Word8</a>.
bitReverse8 :: Word8 -> Word8

-- | Reverse the order of the bits in a <a>Word64</a>.
bitReverse64 :: Word64 -> Word64

-- | Reverse the order of the bits in a <a>Word32</a>.
bitReverse32 :: Word32 -> Word32

-- | Reverse the order of the bits in a <a>Word16</a>.
bitReverse16 :: Word16 -> Word16

-- | Unicode General Categories (column 2 of the UnicodeData table) in the
--   order they are listed in the Unicode standard (the Unicode Character
--   Database, in particular).
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; :t OtherLetter
--   OtherLetter :: GeneralCategory
--   </pre>
--   
--   <a>Eq</a> instance:
--   
--   <pre>
--   &gt;&gt;&gt; UppercaseLetter == UppercaseLetter
--   True
--   
--   &gt;&gt;&gt; UppercaseLetter == LowercaseLetter
--   False
--   </pre>
--   
--   <a>Ord</a> instance:
--   
--   <pre>
--   &gt;&gt;&gt; NonSpacingMark &lt;= MathSymbol
--   True
--   </pre>
--   
--   <a>Enum</a> instance:
--   
--   <pre>
--   &gt;&gt;&gt; enumFromTo ModifierLetter SpacingCombiningMark
--   [ModifierLetter,OtherLetter,NonSpacingMark,SpacingCombiningMark]
--   </pre>
--   
--   <a>Read</a> instance:
--   
--   <pre>
--   &gt;&gt;&gt; read "DashPunctuation" :: GeneralCategory
--   DashPunctuation
--   
--   &gt;&gt;&gt; read "17" :: GeneralCategory
--   *** Exception: Prelude.read: no parse
--   </pre>
--   
--   <a>Show</a> instance:
--   
--   <pre>
--   &gt;&gt;&gt; show EnclosingMark
--   "EnclosingMark"
--   </pre>
--   
--   <a>Bounded</a> instance:
--   
--   <pre>
--   &gt;&gt;&gt; minBound :: GeneralCategory
--   UppercaseLetter
--   
--   &gt;&gt;&gt; maxBound :: GeneralCategory
--   NotAssigned
--   </pre>
--   
--   <a>Ix</a> instance:
--   
--   <pre>
--   &gt;&gt;&gt; import Data.Ix ( index )
--   
--   &gt;&gt;&gt; index (OtherLetter,Control) FinalQuote
--   12
--   
--   &gt;&gt;&gt; index (OtherLetter,Control) Format
--   *** Exception: Error in array index
--   </pre>
data GeneralCategory

-- | Lu: Letter, Uppercase
UppercaseLetter :: GeneralCategory

-- | Ll: Letter, Lowercase
LowercaseLetter :: GeneralCategory

-- | Lt: Letter, Titlecase
TitlecaseLetter :: GeneralCategory

-- | Lm: Letter, Modifier
ModifierLetter :: GeneralCategory

-- | Lo: Letter, Other
OtherLetter :: GeneralCategory

-- | Mn: Mark, Non-Spacing
NonSpacingMark :: GeneralCategory

-- | Mc: Mark, Spacing Combining
SpacingCombiningMark :: GeneralCategory

-- | Me: Mark, Enclosing
EnclosingMark :: GeneralCategory

-- | Nd: Number, Decimal
DecimalNumber :: GeneralCategory

-- | Nl: Number, Letter
LetterNumber :: GeneralCategory

-- | No: Number, Other
OtherNumber :: GeneralCategory

-- | Pc: Punctuation, Connector
ConnectorPunctuation :: GeneralCategory

-- | Pd: Punctuation, Dash
DashPunctuation :: GeneralCategory

-- | Ps: Punctuation, Open
OpenPunctuation :: GeneralCategory

-- | Pe: Punctuation, Close
ClosePunctuation :: GeneralCategory

-- | Pi: Punctuation, Initial quote
InitialQuote :: GeneralCategory

-- | Pf: Punctuation, Final quote
FinalQuote :: GeneralCategory

-- | Po: Punctuation, Other
OtherPunctuation :: GeneralCategory

-- | Sm: Symbol, Math
MathSymbol :: GeneralCategory

-- | Sc: Symbol, Currency
CurrencySymbol :: GeneralCategory

-- | Sk: Symbol, Modifier
ModifierSymbol :: GeneralCategory

-- | So: Symbol, Other
OtherSymbol :: GeneralCategory

-- | Zs: Separator, Space
Space :: GeneralCategory

-- | Zl: Separator, Line
LineSeparator :: GeneralCategory

-- | Zp: Separator, Paragraph
ParagraphSeparator :: GeneralCategory

-- | Cc: Other, Control
Control :: GeneralCategory

-- | Cf: Other, Format
Format :: GeneralCategory

-- | Cs: Other, Surrogate
Surrogate :: GeneralCategory

-- | Co: Other, Private Use
PrivateUse :: GeneralCategory

-- | Cn: Other, Not Assigned
NotAssigned :: GeneralCategory

-- | Convert a letter to the corresponding upper-case letter, if any. Any
--   other character is returned unchanged.
toUpper :: Char -> Char

-- | Convert a letter to the corresponding title-case or upper-case letter,
--   if any. (Title case differs from upper case only for a small number of
--   ligature letters.) Any other character is returned unchanged.
toTitle :: Char -> Char

-- | Convert a letter to the corresponding lower-case letter, if any. Any
--   other character is returned unchanged.
toLower :: Char -> Char

-- | Selects upper-case or title-case alphabetic Unicode characters
--   (letters). Title case is used by a small number of letter ligatures
--   like the single-character form of <i>Lj</i>.
isUpper :: Char -> Bool

-- | Selects Unicode symbol characters, including mathematical and currency
--   symbols.
--   
--   This function returns <a>True</a> if its argument has one of the
--   following <a>GeneralCategory</a>s, or <a>False</a> otherwise:
--   
--   <ul>
--   <li><a>MathSymbol</a></li>
--   <li><a>CurrencySymbol</a></li>
--   <li><a>ModifierSymbol</a></li>
--   <li><a>OtherSymbol</a></li>
--   </ul>
--   
--   These classes are defined in the <a>Unicode Character Database</a>,
--   part of the Unicode standard. The same document defines what is and is
--   not a "Symbol".
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; isSymbol 'a'
--   False
--   
--   &gt;&gt;&gt; isSymbol '6'
--   False
--   
--   &gt;&gt;&gt; isSymbol '='
--   True
--   </pre>
--   
--   The definition of "math symbol" may be a little counter-intuitive
--   depending on one's background:
--   
--   <pre>
--   &gt;&gt;&gt; isSymbol '+'
--   True
--   
--   &gt;&gt;&gt; isSymbol '-'
--   False
--   </pre>
isSymbol :: Char -> Bool

-- | Returns <a>True</a> for any Unicode space character, and the control
--   characters <tt>\t</tt>, <tt>\n</tt>, <tt>\r</tt>, <tt>\f</tt>,
--   <tt>\v</tt>.
isSpace :: Char -> Bool

-- | Selects Unicode punctuation characters, including various kinds of
--   connectors, brackets and quotes.
--   
--   This function returns <a>True</a> if its argument has one of the
--   following <a>GeneralCategory</a>s, or <a>False</a> otherwise:
--   
--   <ul>
--   <li><a>ConnectorPunctuation</a></li>
--   <li><a>DashPunctuation</a></li>
--   <li><a>OpenPunctuation</a></li>
--   <li><a>ClosePunctuation</a></li>
--   <li><a>InitialQuote</a></li>
--   <li><a>FinalQuote</a></li>
--   <li><a>OtherPunctuation</a></li>
--   </ul>
--   
--   These classes are defined in the <a>Unicode Character Database</a>,
--   part of the Unicode standard. The same document defines what is and is
--   not a "Punctuation".
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; isPunctuation 'a'
--   False
--   
--   &gt;&gt;&gt; isPunctuation '7'
--   False
--   
--   &gt;&gt;&gt; isPunctuation '♥'
--   False
--   
--   &gt;&gt;&gt; isPunctuation '"'
--   True
--   
--   &gt;&gt;&gt; isPunctuation '?'
--   True
--   
--   &gt;&gt;&gt; isPunctuation '—'
--   True
--   </pre>
isPunctuation :: Char -> Bool

-- | Selects printable Unicode characters (letters, numbers, marks,
--   punctuation, symbols and spaces).
isPrint :: Char -> Bool

-- | Selects ASCII octal digits, i.e. <tt>'0'</tt>..<tt>'7'</tt>.
isOctDigit :: Char -> Bool

-- | Selects lower-case alphabetic Unicode characters (letters).
isLower :: Char -> Bool

-- | Selects the first 256 characters of the Unicode character set,
--   corresponding to the ISO 8859-1 (Latin-1) character set.
isLatin1 :: Char -> Bool

-- | Selects ASCII hexadecimal digits, i.e. <tt>'0'</tt>..<tt>'9'</tt>,
--   <tt>'a'</tt>..<tt>'f'</tt>, <tt>'A'</tt>..<tt>'F'</tt>.
isHexDigit :: Char -> Bool

-- | Selects ASCII digits, i.e. <tt>'0'</tt>..<tt>'9'</tt>.
isDigit :: Char -> Bool

-- | Selects control characters, which are the non-printing characters of
--   the Latin-1 subset of Unicode.
isControl :: Char -> Bool

-- | Selects ASCII upper-case letters, i.e. characters satisfying both
--   <a>isAscii</a> and <a>isUpper</a>.
isAsciiUpper :: Char -> Bool

-- | Selects ASCII lower-case letters, i.e. characters satisfying both
--   <a>isAscii</a> and <a>isLower</a>.
isAsciiLower :: Char -> Bool

-- | Selects the first 128 characters of the Unicode character set,
--   corresponding to the ASCII character set.
isAscii :: Char -> Bool

-- | Selects alphabetic or numeric Unicode characters.
--   
--   Note that numeric digits outside the ASCII range, as well as numeric
--   characters which aren't digits, are selected by this function but not
--   by <a>isDigit</a>. Such characters may be part of identifiers but are
--   not used by the printer and reader to represent numbers.
isAlphaNum :: Char -> Bool

-- | Selects alphabetic Unicode characters (lower-case, upper-case and
--   title-case letters, plus letters of caseless scripts and modifiers
--   letters). This function is equivalent to <a>isLetter</a>.
isAlpha :: Char -> Bool

-- | The Unicode general category of the character. This relies on the
--   <a>Enum</a> instance of <a>GeneralCategory</a>, which must remain in
--   the same order as the categories are presented in the Unicode
--   standard.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; generalCategory 'a'
--   LowercaseLetter
--   
--   &gt;&gt;&gt; generalCategory 'A'
--   UppercaseLetter
--   
--   &gt;&gt;&gt; generalCategory '0'
--   DecimalNumber
--   
--   &gt;&gt;&gt; generalCategory '%'
--   OtherPunctuation
--   
--   &gt;&gt;&gt; generalCategory '♥'
--   OtherSymbol
--   
--   &gt;&gt;&gt; generalCategory '\31'
--   Control
--   
--   &gt;&gt;&gt; generalCategory ' '
--   Space
--   </pre>
generalCategory :: Char -> GeneralCategory

-- | The <a>FiniteBits</a> class denotes types with a finite, fixed number
--   of bits.
class Bits b => FiniteBits b

-- | Return the number of bits in the type of the argument. The actual
--   value of the argument is ignored. Moreover, <a>finiteBitSize</a> is
--   total, in contrast to the deprecated <a>bitSize</a> function it
--   replaces.
--   
--   <pre>
--   <a>finiteBitSize</a> = <a>bitSize</a>
--   <a>bitSizeMaybe</a> = <a>Just</a> . <a>finiteBitSize</a>
--   </pre>
finiteBitSize :: FiniteBits b => b -> Int

-- | Count number of zero bits preceding the most significant set bit.
--   
--   <pre>
--   <a>countLeadingZeros</a> (<a>zeroBits</a> :: a) = finiteBitSize (<a>zeroBits</a> :: a)
--   </pre>
--   
--   <a>countLeadingZeros</a> can be used to compute log base 2 via
--   
--   <pre>
--   logBase2 x = <a>finiteBitSize</a> x - 1 - <a>countLeadingZeros</a> x
--   </pre>
--   
--   Note: The default implementation for this method is intentionally
--   naive. However, the instances provided for the primitive integral
--   types are implemented using CPU specific machine instructions.
countLeadingZeros :: FiniteBits b => b -> Int

-- | Count number of zero bits following the least significant set bit.
--   
--   <pre>
--   <a>countTrailingZeros</a> (<a>zeroBits</a> :: a) = finiteBitSize (<a>zeroBits</a> :: a)
--   <a>countTrailingZeros</a> . <a>negate</a> = <a>countTrailingZeros</a>
--   </pre>
--   
--   The related <a>find-first-set operation</a> can be expressed in terms
--   of <a>countTrailingZeros</a> as follows
--   
--   <pre>
--   findFirstSet x = 1 + <a>countTrailingZeros</a> x
--   </pre>
--   
--   Note: The default implementation for this method is intentionally
--   naive. However, the instances provided for the primitive integral
--   types are implemented using CPU specific machine instructions.
countTrailingZeros :: FiniteBits b => b -> Int

-- | The <a>Bits</a> class defines bitwise operations over integral types.
--   
--   <ul>
--   <li>Bits are numbered from 0 with bit 0 being the least significant
--   bit.</li>
--   </ul>
class Eq a => Bits a

-- | Bitwise "and"
(.&.) :: Bits a => a -> a -> a

-- | Bitwise "or"
(.|.) :: Bits a => a -> a -> a

-- | Bitwise "xor"
xor :: Bits a => a -> a -> a

-- | Reverse all the bits in the argument
complement :: Bits a => a -> a

-- | <tt><a>shift</a> x i</tt> shifts <tt>x</tt> left by <tt>i</tt> bits if
--   <tt>i</tt> is positive, or right by <tt>-i</tt> bits otherwise. Right
--   shifts perform sign extension on signed number types; i.e. they fill
--   the top bits with 1 if the <tt>x</tt> is negative and with 0
--   otherwise.
--   
--   An instance can define either this unified <a>shift</a> or
--   <a>shiftL</a> and <a>shiftR</a>, depending on which is more convenient
--   for the type in question.
shift :: Bits a => a -> Int -> a

-- | <tt><a>rotate</a> x i</tt> rotates <tt>x</tt> left by <tt>i</tt> bits
--   if <tt>i</tt> is positive, or right by <tt>-i</tt> bits otherwise.
--   
--   For unbounded types like <a>Integer</a>, <a>rotate</a> is equivalent
--   to <a>shift</a>.
--   
--   An instance can define either this unified <a>rotate</a> or
--   <a>rotateL</a> and <a>rotateR</a>, depending on which is more
--   convenient for the type in question.
rotate :: Bits a => a -> Int -> a

-- | <a>zeroBits</a> is the value with all bits unset.
--   
--   The following laws ought to hold (for all valid bit indices
--   <tt><i>n</i></tt>):
--   
--   <ul>
--   <li><pre><a>clearBit</a> <a>zeroBits</a> <i>n</i> ==
--   <a>zeroBits</a></pre></li>
--   <li><pre><a>setBit</a> <a>zeroBits</a> <i>n</i> == <a>bit</a>
--   <i>n</i></pre></li>
--   <li><pre><a>testBit</a> <a>zeroBits</a> <i>n</i> == False</pre></li>
--   <li><pre><a>popCount</a> <a>zeroBits</a> == 0</pre></li>
--   </ul>
--   
--   This method uses <tt><a>clearBit</a> (<a>bit</a> 0) 0</tt> as its
--   default implementation (which ought to be equivalent to
--   <a>zeroBits</a> for types which possess a 0th bit).
zeroBits :: Bits a => a

-- | <tt>bit <i>i</i></tt> is a value with the <tt><i>i</i></tt>th bit set
--   and all other bits clear.
--   
--   Can be implemented using <a>bitDefault</a> if <tt>a</tt> is also an
--   instance of <a>Num</a>.
--   
--   See also <a>zeroBits</a>.
bit :: Bits a => Int -> a

-- | <tt>x `setBit` i</tt> is the same as <tt>x .|. bit i</tt>
setBit :: Bits a => a -> Int -> a

-- | <tt>x `clearBit` i</tt> is the same as <tt>x .&amp;. complement (bit
--   i)</tt>
clearBit :: Bits a => a -> Int -> a

-- | <tt>x `complementBit` i</tt> is the same as <tt>x `xor` bit i</tt>
complementBit :: Bits a => a -> Int -> a

-- | <tt>x `testBit` i</tt> is the same as <tt>x .&amp;. bit n /= 0</tt>
--   
--   In other words it returns True if the bit at offset @n is set.
--   
--   Can be implemented using <a>testBitDefault</a> if <tt>a</tt> is also
--   an instance of <a>Num</a>.
testBit :: Bits a => a -> Int -> Bool

-- | Return the number of bits in the type of the argument. The actual
--   value of the argument is ignored. Returns Nothing for types that do
--   not have a fixed bitsize, like <a>Integer</a>.
bitSizeMaybe :: Bits a => a -> Maybe Int

-- | Return the number of bits in the type of the argument. The actual
--   value of the argument is ignored. The function <a>bitSize</a> is
--   undefined for types that do not have a fixed bitsize, like
--   <a>Integer</a>.
--   
--   Default implementation based upon <a>bitSizeMaybe</a> provided since
--   4.12.0.0.
bitSize :: Bits a => a -> Int

-- | Return <a>True</a> if the argument is a signed type. The actual value
--   of the argument is ignored
isSigned :: Bits a => a -> Bool

-- | Shift the argument left by the specified number of bits (which must be
--   non-negative). Some instances may throw an <a>Overflow</a> exception
--   if given a negative input.
--   
--   An instance can define either this and <a>shiftR</a> or the unified
--   <a>shift</a>, depending on which is more convenient for the type in
--   question.
shiftL :: Bits a => a -> Int -> a

-- | Shift the argument left by the specified number of bits. The result is
--   undefined for negative shift amounts and shift amounts greater or
--   equal to the <a>bitSize</a>.
--   
--   Defaults to <a>shiftL</a> unless defined explicitly by an instance.
unsafeShiftL :: Bits a => a -> Int -> a

-- | Shift the first argument right by the specified number of bits. The
--   result is undefined for negative shift amounts and shift amounts
--   greater or equal to the <a>bitSize</a>. Some instances may throw an
--   <a>Overflow</a> exception if given a negative input.
--   
--   Right shifts perform sign extension on signed number types; i.e. they
--   fill the top bits with 1 if the <tt>x</tt> is negative and with 0
--   otherwise.
--   
--   An instance can define either this and <a>shiftL</a> or the unified
--   <a>shift</a>, depending on which is more convenient for the type in
--   question.
shiftR :: Bits a => a -> Int -> a

-- | Shift the first argument right by the specified number of bits, which
--   must be non-negative and smaller than the number of bits in the type.
--   
--   Right shifts perform sign extension on signed number types; i.e. they
--   fill the top bits with 1 if the <tt>x</tt> is negative and with 0
--   otherwise.
--   
--   Defaults to <a>shiftR</a> unless defined explicitly by an instance.
unsafeShiftR :: Bits a => a -> Int -> a

-- | Rotate the argument left by the specified number of bits (which must
--   be non-negative).
--   
--   An instance can define either this and <a>rotateR</a> or the unified
--   <a>rotate</a>, depending on which is more convenient for the type in
--   question.
rotateL :: Bits a => a -> Int -> a

-- | Rotate the argument right by the specified number of bits (which must
--   be non-negative).
--   
--   An instance can define either this and <a>rotateL</a> or the unified
--   <a>rotate</a>, depending on which is more convenient for the type in
--   question.
rotateR :: Bits a => a -> Int -> a

-- | Return the number of set bits in the argument. This number is known as
--   the population count or the Hamming weight.
--   
--   Can be implemented using <a>popCountDefault</a> if <tt>a</tt> is also
--   an instance of <a>Num</a>.
popCount :: Bits a => a -> Int
infixl 6 `xor`
infixl 8 `shiftR`
infixl 8 `shiftL`
infixl 8 `shift`
infixl 8 `rotateR`
infixl 8 `rotateL`
infixl 8 `rotate`
infixl 7 .&.
infixl 5 .|.

-- | Attempt to convert an <a>Integral</a> type <tt>a</tt> to an
--   <a>Integral</a> type <tt>b</tt> using the size of the types as
--   measured by <a>Bits</a> methods.
--   
--   A simpler version of this function is:
--   
--   <pre>
--   toIntegral :: (Integral a, Integral b) =&gt; a -&gt; Maybe b
--   toIntegral x
--     | toInteger x == y = Just (fromInteger y)
--     | otherwise        = Nothing
--     where
--       y = toInteger x
--   </pre>
--   
--   This version requires going through <a>Integer</a>, which can be
--   inefficient. However, <tt>toIntegralSized</tt> is optimized to allow
--   GHC to statically determine the relative type sizes (as measured by
--   <a>bitSizeMaybe</a> and <a>isSigned</a>) and avoid going through
--   <a>Integer</a> for many types. (The implementation uses
--   <a>fromIntegral</a>, which is itself optimized with rules for
--   <tt>base</tt> types but may go through <a>Integer</a> for some type
--   pairs.)
toIntegralSized :: (Integral a, Integral b, Bits a, Bits b) => a -> Maybe b

-- | Default implementation for <a>testBit</a>.
--   
--   Note that: <tt>testBitDefault x i = (x .&amp;. bit i) /= 0</tt>
testBitDefault :: (Bits a, Num a) => a -> Int -> Bool

-- | Default implementation for <a>popCount</a>.
--   
--   This implementation is intentionally naive. Instances are expected to
--   provide an optimized implementation for their size.
popCountDefault :: (Bits a, Num a) => a -> Int

-- | Default implementation for <a>bit</a>.
--   
--   Note that: <tt>bitDefault i = 1 <a>shiftL</a> i</tt>
bitDefault :: (Bits a, Num a) => Int -> a

-- | Converts a possibly-negative <a>Real</a> value to a string.
showSigned :: Real a => (a -> ShowS) -> Int -> a -> ShowS
odd :: Integral a => a -> Bool

-- | Extract the numerator of the ratio in reduced form: the numerator and
--   denominator have no common factor and the denominator is positive.
numerator :: Ratio a -> a

-- | <tt><a>lcm</a> x y</tt> is the smallest positive integer that both
--   <tt>x</tt> and <tt>y</tt> divide.
lcm :: Integral a => a -> a -> a

-- | <tt><a>gcd</a> x y</tt> is the non-negative factor of both <tt>x</tt>
--   and <tt>y</tt> of which every common factor of <tt>x</tt> and
--   <tt>y</tt> is also a factor; for example <tt><a>gcd</a> 4 2 = 2</tt>,
--   <tt><a>gcd</a> (-4) 6 = 2</tt>, <tt><a>gcd</a> 0 4</tt> = <tt>4</tt>.
--   <tt><a>gcd</a> 0 0</tt> = <tt>0</tt>. (That is, the common divisor
--   that is "greatest" in the divisibility preordering.)
--   
--   Note: Since for signed fixed-width integer types, <tt><a>abs</a>
--   <a>minBound</a> &lt; 0</tt>, the result may be negative if one of the
--   arguments is <tt><a>minBound</a></tt> (and necessarily is if the other
--   is <tt>0</tt> or <tt><a>minBound</a></tt>) for such types.
gcd :: Integral a => a -> a -> a
even :: Integral a => a -> Bool

-- | Extract the denominator of the ratio in reduced form: the numerator
--   and denominator have no common factor and the denominator is positive.
denominator :: Ratio a -> a

-- | raise a number to an integral power
(^^) :: (Fractional a, Integral b) => a -> b -> a
infixr 8 ^^

-- | raise a number to a non-negative integral power
(^) :: (Num a, Integral b) => a -> b -> a
infixr 8 ^

-- | Forms the ratio of two integral numbers.
(%) :: Integral a => a -> a -> Ratio a
infixl 7 %

-- | The <a>toEnum</a> method restricted to the type <a>Char</a>.
chr :: Int -> Char

-- | a value of type <tt>STRef s a</tt> is a mutable variable in state
--   thread <tt>s</tt>, containing a value of type <tt>a</tt>
--   
--   <pre>
--   &gt;&gt;&gt; :{
--   runST (do
--       ref &lt;- newSTRef "hello"
--       x &lt;- readSTRef ref
--       writeSTRef ref (x ++ "world")
--       readSTRef ref )
--   :}
--   "helloworld"
--   </pre>
data STRef s a

-- | Write a new value into an <a>STRef</a>
writeSTRef :: STRef s a -> a -> ST s ()

-- | Read the value of an <a>STRef</a>
readSTRef :: STRef s a -> ST s a

-- | Build a new <a>STRef</a> in the current state thread
newSTRef :: a -> ST s (STRef s a)

-- | Return the value computed by a state thread. The <tt>forall</tt>
--   ensures that the internal state used by the <a>ST</a> computation is
--   inaccessible to the rest of the program.
runST :: (forall s. () => ST s a) -> a

-- | The <tt>shows</tt> functions return a function that prepends the
--   output <a>String</a> to an existing <a>String</a>. This allows
--   constant-time concatenation of results using function composition.
type ShowS = String -> String

-- | equivalent to <a>showsPrec</a> with a precedence of 0.
shows :: Show a => a -> ShowS

-- | utility function converting a <a>String</a> to a show function that
--   simply prepends the string unchanged.
showString :: String -> ShowS

-- | utility function that surrounds the inner show function with
--   parentheses when the <a>Bool</a> parameter is <a>True</a>.
showParen :: Bool -> ShowS -> ShowS

-- | Convert a character to a string using only printable characters, using
--   Haskell source-language escape conventions. For example:
--   
--   <pre>
--   showLitChar '\n' s  =  "\\n" ++ s
--   </pre>
showLitChar :: Char -> ShowS

-- | utility function converting a <a>Char</a> to a show function that
--   simply prepends the character unchanged.
showChar :: Char -> ShowS

-- | Convert an <a>Int</a> in the range <tt>0</tt>..<tt>15</tt> to the
--   corresponding single digit <a>Char</a>. This function fails on other
--   inputs, and generates lower-case hexadecimal digits.
intToDigit :: Int -> Char

-- | The <a>zipWith3</a> function takes a function which combines three
--   elements, as well as three lists and returns a list of the function
--   applied to corresponding elements, analogous to <a>zipWith</a>. It is
--   capable of list fusion, but it is restricted to its first list
--   argument and its resulting list.
--   
--   <pre>
--   zipWith3 (,,) xs ys zs == zip3 xs ys zs
--   zipWith3 f [x1,x2,x3..] [y1,y2,y3..] [z1,z2,z3..] == [f x1 y1 z1, f x2 y2 z2, f x3 y3 z3..]
--   </pre>
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]

-- | &lt;math&gt;. <a>zipWith</a> generalises <a>zip</a> by zipping with
--   the function given as the first argument, instead of a tupling
--   function.
--   
--   <pre>
--   zipWith (,) xs ys == zip xs ys
--   zipWith f [x1,x2,x3..] [y1,y2,y3..] == [f x1 y1, f x2 y2, f x3 y3..]
--   </pre>
--   
--   For example, <tt><a>zipWith</a> (+)</tt> is applied to two lists to
--   produce the list of corresponding sums:
--   
--   <pre>
--   &gt;&gt;&gt; zipWith (+) [1, 2, 3] [4, 5, 6]
--   [5,7,9]
--   </pre>
--   
--   <a>zipWith</a> is right-lazy:
--   
--   <pre>
--   &gt;&gt;&gt; let f = undefined
--   
--   &gt;&gt;&gt; zipWith f [] undefined
--   []
--   </pre>
--   
--   <a>zipWith</a> is capable of list fusion, but it is restricted to its
--   first list argument and its resulting list.
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]

-- | <a>zip3</a> takes three lists and returns a list of triples, analogous
--   to <a>zip</a>. It is capable of list fusion, but it is restricted to
--   its first list argument and its resulting list.
zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]

-- | The <a>unzip3</a> function takes a list of triples and returns three
--   lists, analogous to <a>unzip</a>.
--   
--   <pre>
--   &gt;&gt;&gt; unzip3 []
--   ([],[],[])
--   
--   &gt;&gt;&gt; unzip3 [(1, 'a', True), (2, 'b', False)]
--   ([1,2],"ab",[True,False])
--   </pre>
unzip3 :: [(a, b, c)] -> ([a], [b], [c])

-- | <a>unzip</a> transforms a list of pairs into a list of first
--   components and a list of second components.
--   
--   <pre>
--   &gt;&gt;&gt; unzip []
--   ([],[])
--   
--   &gt;&gt;&gt; unzip [(1, 'a'), (2, 'b')]
--   ([1,2],"ab")
--   </pre>
unzip :: [(a, b)] -> ([a], [b])

-- | &lt;math&gt;. Decompose a list into its head and tail.
--   
--   <ul>
--   <li>If the list is empty, returns <a>Nothing</a>.</li>
--   <li>If the list is non-empty, returns <tt><a>Just</a> (x, xs)</tt>,
--   where <tt>x</tt> is the head of the list and <tt>xs</tt> its
--   tail.</li>
--   </ul>
--   
--   <pre>
--   &gt;&gt;&gt; uncons []
--   Nothing
--   
--   &gt;&gt;&gt; uncons [1]
--   Just (1,[])
--   
--   &gt;&gt;&gt; uncons [1, 2, 3]
--   Just (1,[2,3])
--   </pre>
uncons :: [a] -> Maybe (a, [a])

-- | <a>takeWhile</a>, applied to a predicate <tt>p</tt> and a list
--   <tt>xs</tt>, returns the longest prefix (possibly empty) of
--   <tt>xs</tt> of elements that satisfy <tt>p</tt>.
--   
--   <pre>
--   &gt;&gt;&gt; takeWhile (&lt; 3) [1,2,3,4,1,2,3,4]
--   [1,2]
--   
--   &gt;&gt;&gt; takeWhile (&lt; 9) [1,2,3]
--   [1,2,3]
--   
--   &gt;&gt;&gt; takeWhile (&lt; 0) [1,2,3]
--   []
--   </pre>
takeWhile :: (a -> Bool) -> [a] -> [a]

-- | <a>take</a> <tt>n</tt>, applied to a list <tt>xs</tt>, returns the
--   prefix of <tt>xs</tt> of length <tt>n</tt>, or <tt>xs</tt> itself if
--   <tt>n &gt;= <a>length</a> xs</tt>.
--   
--   <pre>
--   &gt;&gt;&gt; take 5 "Hello World!"
--   "Hello"
--   
--   &gt;&gt;&gt; take 3 [1,2,3,4,5]
--   [1,2,3]
--   
--   &gt;&gt;&gt; take 3 [1,2]
--   [1,2]
--   
--   &gt;&gt;&gt; take 3 []
--   []
--   
--   &gt;&gt;&gt; take (-1) [1,2]
--   []
--   
--   &gt;&gt;&gt; take 0 [1,2]
--   []
--   </pre>
--   
--   It is an instance of the more general <a>genericTake</a>, in which
--   <tt>n</tt> may be of any integral type.
take :: Int -> [a] -> [a]

-- | &lt;math&gt;. Extract the elements after the head of a list, which
--   must be non-empty.
--   
--   <pre>
--   &gt;&gt;&gt; tail [1, 2, 3]
--   [2,3]
--   
--   &gt;&gt;&gt; tail [1]
--   []
--   
--   &gt;&gt;&gt; tail []
--   *** Exception: Prelude.tail: empty list
--   </pre>
tail :: [a] -> [a]

-- | <a>splitAt</a> <tt>n xs</tt> returns a tuple where first element is
--   <tt>xs</tt> prefix of length <tt>n</tt> and second element is the
--   remainder of the list:
--   
--   <pre>
--   &gt;&gt;&gt; splitAt 6 "Hello World!"
--   ("Hello ","World!")
--   
--   &gt;&gt;&gt; splitAt 3 [1,2,3,4,5]
--   ([1,2,3],[4,5])
--   
--   &gt;&gt;&gt; splitAt 1 [1,2,3]
--   ([1],[2,3])
--   
--   &gt;&gt;&gt; splitAt 3 [1,2,3]
--   ([1,2,3],[])
--   
--   &gt;&gt;&gt; splitAt 4 [1,2,3]
--   ([1,2,3],[])
--   
--   &gt;&gt;&gt; splitAt 0 [1,2,3]
--   ([],[1,2,3])
--   
--   &gt;&gt;&gt; splitAt (-1) [1,2,3]
--   ([],[1,2,3])
--   </pre>
--   
--   It is equivalent to <tt>(<a>take</a> n xs, <a>drop</a> n xs)</tt> when
--   <tt>n</tt> is not <tt>_|_</tt> (<tt>splitAt _|_ xs = _|_</tt>).
--   <a>splitAt</a> is an instance of the more general
--   <a>genericSplitAt</a>, in which <tt>n</tt> may be of any integral
--   type.
splitAt :: Int -> [a] -> ([a], [a])

-- | <a>span</a>, applied to a predicate <tt>p</tt> and a list <tt>xs</tt>,
--   returns a tuple where first element is longest prefix (possibly empty)
--   of <tt>xs</tt> of elements that satisfy <tt>p</tt> and second element
--   is the remainder of the list:
--   
--   <pre>
--   &gt;&gt;&gt; span (&lt; 3) [1,2,3,4,1,2,3,4]
--   ([1,2],[3,4,1,2,3,4])
--   
--   &gt;&gt;&gt; span (&lt; 9) [1,2,3]
--   ([1,2,3],[])
--   
--   &gt;&gt;&gt; span (&lt; 0) [1,2,3]
--   ([],[1,2,3])
--   </pre>
--   
--   <a>span</a> <tt>p xs</tt> is equivalent to <tt>(<a>takeWhile</a> p xs,
--   <a>dropWhile</a> p xs)</tt>
span :: (a -> Bool) -> [a] -> ([a], [a])

-- | &lt;math&gt;. <a>scanr1</a> is a variant of <a>scanr</a> that has no
--   starting value argument.
--   
--   <pre>
--   &gt;&gt;&gt; scanr1 (+) [1..4]
--   [10,9,7,4]
--   
--   &gt;&gt;&gt; scanr1 (+) []
--   []
--   
--   &gt;&gt;&gt; scanr1 (-) [1..4]
--   [-2,3,-1,4]
--   
--   &gt;&gt;&gt; scanr1 (&amp;&amp;) [True, False, True, True]
--   [False,False,True,True]
--   
--   &gt;&gt;&gt; scanr1 (||) [True, True, False, False]
--   [True,True,False,False]
--   
--   &gt;&gt;&gt; force $ scanr1 (+) [1..]
--   *** Exception: stack overflow
--   </pre>
scanr1 :: (a -> a -> a) -> [a] -> [a]

-- | &lt;math&gt;. <a>scanr</a> is the right-to-left dual of <a>scanl</a>.
--   Note that the order of parameters on the accumulating function are
--   reversed compared to <a>scanl</a>. Also note that
--   
--   <pre>
--   head (scanr f z xs) == foldr f z xs.
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; scanr (+) 0 [1..4]
--   [10,9,7,4,0]
--   
--   &gt;&gt;&gt; scanr (+) 42 []
--   [42]
--   
--   &gt;&gt;&gt; scanr (-) 100 [1..4]
--   [98,-97,99,-96,100]
--   
--   &gt;&gt;&gt; scanr (\nextChar reversedString -&gt; nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
--   ["abcdfoo","bcdfoo","cdfoo","dfoo","foo"]
--   
--   &gt;&gt;&gt; force $ scanr (+) 0 [1..]
--   *** Exception: stack overflow
--   </pre>
scanr :: (a -> b -> b) -> b -> [a] -> [b]

-- | &lt;math&gt;. <a>scanl1</a> is a variant of <a>scanl</a> that has no
--   starting value argument:
--   
--   <pre>
--   scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; scanl1 (+) [1..4]
--   [1,3,6,10]
--   
--   &gt;&gt;&gt; scanl1 (+) []
--   []
--   
--   &gt;&gt;&gt; scanl1 (-) [1..4]
--   [1,-1,-4,-8]
--   
--   &gt;&gt;&gt; scanl1 (&amp;&amp;) [True, False, True, True]
--   [True,False,False,False]
--   
--   &gt;&gt;&gt; scanl1 (||) [False, False, True, True]
--   [False,False,True,True]
--   
--   &gt;&gt;&gt; scanl1 (+) [1..]
--   * Hangs forever *
--   </pre>
scanl1 :: (a -> a -> a) -> [a] -> [a]

-- | &lt;math&gt;. A strict version of <a>scanl</a>.
scanl' :: (b -> a -> b) -> b -> [a] -> [b]

-- | &lt;math&gt;. <a>scanl</a> is similar to <a>foldl</a>, but returns a
--   list of successive reduced values from the left:
--   
--   <pre>
--   scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]
--   </pre>
--   
--   Note that
--   
--   <pre>
--   last (scanl f z xs) == foldl f z xs
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; scanl (+) 0 [1..4]
--   [0,1,3,6,10]
--   
--   &gt;&gt;&gt; scanl (+) 42 []
--   [42]
--   
--   &gt;&gt;&gt; scanl (-) 100 [1..4]
--   [100,99,97,94,90]
--   
--   &gt;&gt;&gt; scanl (\reversedString nextChar -&gt; nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
--   ["foo","afoo","bafoo","cbafoo","dcbafoo"]
--   
--   &gt;&gt;&gt; scanl (+) 0 [1..]
--   * Hangs forever *
--   </pre>
scanl :: (b -> a -> b) -> b -> [a] -> [b]

-- | <a>reverse</a> <tt>xs</tt> returns the elements of <tt>xs</tt> in
--   reverse order. <tt>xs</tt> must be finite.
--   
--   <pre>
--   &gt;&gt;&gt; reverse []
--   []
--   
--   &gt;&gt;&gt; reverse [42]
--   [42]
--   
--   &gt;&gt;&gt; reverse [2,5,7]
--   [7,5,2]
--   
--   &gt;&gt;&gt; reverse [1..]
--   * Hangs forever *
--   </pre>
reverse :: [a] -> [a]

-- | <a>replicate</a> <tt>n x</tt> is a list of length <tt>n</tt> with
--   <tt>x</tt> the value of every element. It is an instance of the more
--   general <a>genericReplicate</a>, in which <tt>n</tt> may be of any
--   integral type.
--   
--   <pre>
--   &gt;&gt;&gt; replicate 0 True
--   []
--   
--   &gt;&gt;&gt; replicate (-1) True
--   []
--   
--   &gt;&gt;&gt; replicate 4 True
--   [True,True,True,True]
--   </pre>
replicate :: Int -> a -> [a]

-- | <a>repeat</a> <tt>x</tt> is an infinite list, with <tt>x</tt> the
--   value of every element.
--   
--   <pre>
--   &gt;&gt;&gt; take 20 $ repeat 17
--   [17,17,17,17,17,17,17,17,17...
--   </pre>
repeat :: a -> [a]

-- | &lt;math&gt;. <a>lookup</a> <tt>key assocs</tt> looks up a key in an
--   association list.
--   
--   <pre>
--   &gt;&gt;&gt; lookup 2 []
--   Nothing
--   
--   &gt;&gt;&gt; lookup 2 [(1, "first")]
--   Nothing
--   
--   &gt;&gt;&gt; lookup 2 [(1, "first"), (2, "second"), (3, "third")]
--   Just "second"
--   </pre>
lookup :: Eq a => a -> [(a, b)] -> Maybe b

-- | &lt;math&gt;. Extract the last element of a list, which must be finite
--   and non-empty.
--   
--   <pre>
--   &gt;&gt;&gt; last [1, 2, 3]
--   3
--   
--   &gt;&gt;&gt; last [1..]
--   * Hangs forever *
--   
--   &gt;&gt;&gt; last []
--   *** Exception: Prelude.last: empty list
--   </pre>
last :: [a] -> a

-- | <a>iterate'</a> is the strict version of <a>iterate</a>.
--   
--   It forces the result of each application of the function to weak head
--   normal form (WHNF) before proceeding.
iterate' :: (a -> a) -> a -> [a]

-- | <a>iterate</a> <tt>f x</tt> returns an infinite list of repeated
--   applications of <tt>f</tt> to <tt>x</tt>:
--   
--   <pre>
--   iterate f x == [x, f x, f (f x), ...]
--   </pre>
--   
--   Note that <a>iterate</a> is lazy, potentially leading to thunk
--   build-up if the consumer doesn't force each iterate. See
--   <a>iterate'</a> for a strict variant of this function.
--   
--   <pre>
--   &gt;&gt;&gt; take 10 $ iterate not True
--   [True,False,True,False...
--   
--   &gt;&gt;&gt; take 10 $ iterate (+3) 42
--   [42,45,48,51,54,57,60,63...
--   </pre>
iterate :: (a -> a) -> a -> [a]

-- | &lt;math&gt;. Return all the elements of a list except the last one.
--   The list must be non-empty.
--   
--   <pre>
--   &gt;&gt;&gt; init [1, 2, 3]
--   [1,2]
--   
--   &gt;&gt;&gt; init [1]
--   []
--   
--   &gt;&gt;&gt; init []
--   *** Exception: Prelude.init: empty list
--   </pre>
init :: [a] -> [a]

-- | &lt;math&gt;. Extract the first element of a list, which must be
--   non-empty.
--   
--   <pre>
--   &gt;&gt;&gt; head [1, 2, 3]
--   1
--   
--   &gt;&gt;&gt; head [1..]
--   1
--   
--   &gt;&gt;&gt; head []
--   *** Exception: Prelude.head: empty list
--   </pre>
head :: [a] -> a

-- | A strict version of <a>foldl1</a>.
foldl1' :: (a -> a -> a) -> [a] -> a

-- | <a>dropWhile</a> <tt>p xs</tt> returns the suffix remaining after
--   <a>takeWhile</a> <tt>p xs</tt>.
--   
--   <pre>
--   &gt;&gt;&gt; dropWhile (&lt; 3) [1,2,3,4,5,1,2,3]
--   [3,4,5,1,2,3]
--   
--   &gt;&gt;&gt; dropWhile (&lt; 9) [1,2,3]
--   []
--   
--   &gt;&gt;&gt; dropWhile (&lt; 0) [1,2,3]
--   [1,2,3]
--   </pre>
dropWhile :: (a -> Bool) -> [a] -> [a]

-- | <a>drop</a> <tt>n xs</tt> returns the suffix of <tt>xs</tt> after the
--   first <tt>n</tt> elements, or <tt>[]</tt> if <tt>n &gt;= <a>length</a>
--   xs</tt>.
--   
--   <pre>
--   &gt;&gt;&gt; drop 6 "Hello World!"
--   "World!"
--   
--   &gt;&gt;&gt; drop 3 [1,2,3,4,5]
--   [4,5]
--   
--   &gt;&gt;&gt; drop 3 [1,2]
--   []
--   
--   &gt;&gt;&gt; drop 3 []
--   []
--   
--   &gt;&gt;&gt; drop (-1) [1,2]
--   [1,2]
--   
--   &gt;&gt;&gt; drop 0 [1,2]
--   [1,2]
--   </pre>
--   
--   It is an instance of the more general <a>genericDrop</a>, in which
--   <tt>n</tt> may be of any integral type.
drop :: Int -> [a] -> [a]

-- | <a>cycle</a> ties a finite list into a circular one, or equivalently,
--   the infinite repetition of the original list. It is the identity on
--   infinite lists.
--   
--   <pre>
--   &gt;&gt;&gt; cycle []
--   *** Exception: Prelude.cycle: empty list
--   
--   &gt;&gt;&gt; take 20 $ cycle [42]
--   [42,42,42,42,42,42,42,42,42,42...
--   
--   &gt;&gt;&gt; take 20 $ cycle [2, 5, 7]
--   [2,5,7,2,5,7,2,5,7,2,5,7...
--   </pre>
cycle :: [a] -> [a]

-- | <a>break</a>, applied to a predicate <tt>p</tt> and a list
--   <tt>xs</tt>, returns a tuple where first element is longest prefix
--   (possibly empty) of <tt>xs</tt> of elements that <i>do not satisfy</i>
--   <tt>p</tt> and second element is the remainder of the list:
--   
--   <pre>
--   &gt;&gt;&gt; break (&gt; 3) [1,2,3,4,1,2,3,4]
--   ([1,2,3],[4,1,2,3,4])
--   
--   &gt;&gt;&gt; break (&lt; 9) [1,2,3]
--   ([],[1,2,3])
--   
--   &gt;&gt;&gt; break (&gt; 9) [1,2,3]
--   ([1,2,3],[])
--   </pre>
--   
--   <a>break</a> <tt>p</tt> is equivalent to <tt><a>span</a> (<a>not</a> .
--   p)</tt>.
break :: (a -> Bool) -> [a] -> ([a], [a])

-- | List index (subscript) operator, starting from 0. It is an instance of
--   the more general <a>genericIndex</a>, which takes an index of any
--   integral type.
--   
--   <pre>
--   &gt;&gt;&gt; ['a', 'b', 'c'] !! 0
--   'a'
--   
--   &gt;&gt;&gt; ['a', 'b', 'c'] !! 2
--   'c'
--   
--   &gt;&gt;&gt; ['a', 'b', 'c'] !! 3
--   *** Exception: Prelude.!!: index too large
--   
--   &gt;&gt;&gt; ['a', 'b', 'c'] !! (-1)
--   *** Exception: Prelude.!!: negative index
--   </pre>
(!!) :: [a] -> Int -> a
infixl 9 !!

-- | The <a>maybeToList</a> function returns an empty list when given
--   <a>Nothing</a> or a singleton list when given <a>Just</a>.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; maybeToList (Just 7)
--   [7]
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; maybeToList Nothing
--   []
--   </pre>
--   
--   One can use <a>maybeToList</a> to avoid pattern matching when combined
--   with a function that (safely) works on lists:
--   
--   <pre>
--   &gt;&gt;&gt; import Text.Read ( readMaybe )
--   
--   &gt;&gt;&gt; sum $ maybeToList (readMaybe "3")
--   3
--   
--   &gt;&gt;&gt; sum $ maybeToList (readMaybe "")
--   0
--   </pre>
maybeToList :: Maybe a -> [a]

-- | The <a>maybe</a> function takes a default value, a function, and a
--   <a>Maybe</a> value. If the <a>Maybe</a> value is <a>Nothing</a>, the
--   function returns the default value. Otherwise, it applies the function
--   to the value inside the <a>Just</a> and returns the result.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; maybe False odd (Just 3)
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; maybe False odd Nothing
--   False
--   </pre>
--   
--   Read an integer from a string using <a>readMaybe</a>. If we succeed,
--   return twice the integer; that is, apply <tt>(*2)</tt> to it. If
--   instead we fail to parse an integer, return <tt>0</tt> by default:
--   
--   <pre>
--   &gt;&gt;&gt; import Text.Read ( readMaybe )
--   
--   &gt;&gt;&gt; maybe 0 (*2) (readMaybe "5")
--   10
--   
--   &gt;&gt;&gt; maybe 0 (*2) (readMaybe "")
--   0
--   </pre>
--   
--   Apply <a>show</a> to a <tt>Maybe Int</tt>. If we have <tt>Just n</tt>,
--   we want to show the underlying <a>Int</a> <tt>n</tt>. But if we have
--   <a>Nothing</a>, we return the empty string instead of (for example)
--   "Nothing":
--   
--   <pre>
--   &gt;&gt;&gt; maybe "" show (Just 5)
--   "5"
--   
--   &gt;&gt;&gt; maybe "" show Nothing
--   ""
--   </pre>
maybe :: b -> (a -> b) -> Maybe a -> b

-- | The <a>mapMaybe</a> function is a version of <a>map</a> which can
--   throw out elements. In particular, the functional argument returns
--   something of type <tt><a>Maybe</a> b</tt>. If this is <a>Nothing</a>,
--   no element is added on to the result list. If it is <tt><a>Just</a>
--   b</tt>, then <tt>b</tt> is included in the result list.
--   
--   <h4><b>Examples</b></h4>
--   
--   Using <tt><a>mapMaybe</a> f x</tt> is a shortcut for
--   <tt><a>catMaybes</a> $ <a>map</a> f x</tt> in most cases:
--   
--   <pre>
--   &gt;&gt;&gt; import Text.Read ( readMaybe )
--   
--   &gt;&gt;&gt; let readMaybeInt = readMaybe :: String -&gt; Maybe Int
--   
--   &gt;&gt;&gt; mapMaybe readMaybeInt ["1", "Foo", "3"]
--   [1,3]
--   
--   &gt;&gt;&gt; catMaybes $ map readMaybeInt ["1", "Foo", "3"]
--   [1,3]
--   </pre>
--   
--   If we map the <a>Just</a> constructor, the entire list should be
--   returned:
--   
--   <pre>
--   &gt;&gt;&gt; mapMaybe Just [1,2,3]
--   [1,2,3]
--   </pre>
mapMaybe :: (a -> Maybe b) -> [a] -> [b]

-- | The <a>listToMaybe</a> function returns <a>Nothing</a> on an empty
--   list or <tt><a>Just</a> a</tt> where <tt>a</tt> is the first element
--   of the list.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; listToMaybe []
--   Nothing
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; listToMaybe [9]
--   Just 9
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; listToMaybe [1,2,3]
--   Just 1
--   </pre>
--   
--   Composing <a>maybeToList</a> with <a>listToMaybe</a> should be the
--   identity on singleton/empty lists:
--   
--   <pre>
--   &gt;&gt;&gt; maybeToList $ listToMaybe [5]
--   [5]
--   
--   &gt;&gt;&gt; maybeToList $ listToMaybe []
--   []
--   </pre>
--   
--   But not on lists with more than one element:
--   
--   <pre>
--   &gt;&gt;&gt; maybeToList $ listToMaybe [1,2,3]
--   [1]
--   </pre>
listToMaybe :: [a] -> Maybe a

-- | The <a>isNothing</a> function returns <a>True</a> iff its argument is
--   <a>Nothing</a>.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; isNothing (Just 3)
--   False
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; isNothing (Just ())
--   False
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; isNothing Nothing
--   True
--   </pre>
--   
--   Only the outer constructor is taken into consideration:
--   
--   <pre>
--   &gt;&gt;&gt; isNothing (Just Nothing)
--   False
--   </pre>
isNothing :: Maybe a -> Bool

-- | The <a>isJust</a> function returns <a>True</a> iff its argument is of
--   the form <tt>Just _</tt>.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; isJust (Just 3)
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; isJust (Just ())
--   True
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; isJust Nothing
--   False
--   </pre>
--   
--   Only the outer constructor is taken into consideration:
--   
--   <pre>
--   &gt;&gt;&gt; isJust (Just Nothing)
--   True
--   </pre>
isJust :: Maybe a -> Bool

-- | The <a>fromMaybe</a> function takes a default value and a <a>Maybe</a>
--   value. If the <a>Maybe</a> is <a>Nothing</a>, it returns the default
--   value; otherwise, it returns the value contained in the <a>Maybe</a>.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; fromMaybe "" (Just "Hello, World!")
--   "Hello, World!"
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; fromMaybe "" Nothing
--   ""
--   </pre>
--   
--   Read an integer from a string using <a>readMaybe</a>. If we fail to
--   parse an integer, we want to return <tt>0</tt> by default:
--   
--   <pre>
--   &gt;&gt;&gt; import Text.Read ( readMaybe )
--   
--   &gt;&gt;&gt; fromMaybe 0 (readMaybe "5")
--   5
--   
--   &gt;&gt;&gt; fromMaybe 0 (readMaybe "")
--   0
--   </pre>
fromMaybe :: a -> Maybe a -> a

-- | The <a>fromJust</a> function extracts the element out of a <a>Just</a>
--   and throws an error if its argument is <a>Nothing</a>.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; fromJust (Just 1)
--   1
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; 2 * (fromJust (Just 10))
--   20
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; 2 * (fromJust Nothing)
--   *** Exception: Maybe.fromJust: Nothing
--   ...
--   </pre>
fromJust :: HasCallStack => Maybe a -> a

-- | The <a>catMaybes</a> function takes a list of <a>Maybe</a>s and
--   returns a list of all the <a>Just</a> values.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; catMaybes [Just 1, Nothing, Just 3]
--   [1,3]
--   </pre>
--   
--   When constructing a list of <a>Maybe</a> values, <a>catMaybes</a> can
--   be used to return all of the "success" results (if the list is the
--   result of a <a>map</a>, then <a>mapMaybe</a> would be more
--   appropriate):
--   
--   <pre>
--   &gt;&gt;&gt; import Text.Read ( readMaybe )
--   
--   &gt;&gt;&gt; [readMaybe x :: Maybe Int | x &lt;- ["1", "Foo", "3"] ]
--   [Just 1,Nothing,Just 3]
--   
--   &gt;&gt;&gt; catMaybes $ [readMaybe x :: Maybe Int | x &lt;- ["1", "Foo", "3"] ]
--   [1,3]
--   </pre>
catMaybes :: [Maybe a] -> [a]

-- | Case analysis for the <a>Bool</a> type. <tt><a>bool</a> x y p</tt>
--   evaluates to <tt>x</tt> when <tt>p</tt> is <a>False</a>, and evaluates
--   to <tt>y</tt> when <tt>p</tt> is <a>True</a>.
--   
--   This is equivalent to <tt>if p then y else x</tt>; that is, one can
--   think of it as an if-then-else construct with its arguments reordered.
--   
--   <h4><b>Examples</b></h4>
--   
--   Basic usage:
--   
--   <pre>
--   &gt;&gt;&gt; bool "foo" "bar" True
--   "bar"
--   
--   &gt;&gt;&gt; bool "foo" "bar" False
--   "foo"
--   </pre>
--   
--   Confirm that <tt><a>bool</a> x y p</tt> and <tt>if p then y else
--   x</tt> are equivalent:
--   
--   <pre>
--   &gt;&gt;&gt; let p = True; x = "bar"; y = "foo"
--   
--   &gt;&gt;&gt; bool x y p == if p then y else x
--   True
--   
--   &gt;&gt;&gt; let p = False
--   
--   &gt;&gt;&gt; bool x y p == if p then y else x
--   True
--   </pre>
bool :: a -> a -> Bool -> a

-- | <tt><a>on</a> b u x y</tt> runs the binary function <tt>b</tt>
--   <i>on</i> the results of applying unary function <tt>u</tt> to two
--   arguments <tt>x</tt> and <tt>y</tt>. From the opposite perspective, it
--   transforms two inputs and combines the outputs.
--   
--   <pre>
--   ((+) `<a>on</a>` f) x y = f x + f y
--   </pre>
--   
--   Typical usage: <tt><a>sortBy</a> (<a>compare</a> `on`
--   <a>fst</a>)</tt>.
--   
--   Algebraic properties:
--   
--   <ul>
--   <li><pre>(*) `on` <a>id</a> = (*) -- (if (*) ∉ {⊥, <a>const</a>
--   ⊥})</pre></li>
--   <li><pre>((*) `on` f) `on` g = (*) `on` (f . g)</pre></li>
--   <li><pre><a>flip</a> on f . <a>flip</a> on g = <a>flip</a> on (g .
--   f)</pre></li>
--   </ul>
on :: (b -> b -> c) -> (a -> b) -> a -> a -> c
infixl 0 `on`

-- | <tt><a>fix</a> f</tt> is the least fixed point of the function
--   <tt>f</tt>, i.e. the least defined <tt>x</tt> such that <tt>f x =
--   x</tt>.
--   
--   For example, we can write the factorial function using direct
--   recursion as
--   
--   <pre>
--   &gt;&gt;&gt; let fac n = if n &lt;= 1 then 1 else n * fac (n-1) in fac 5
--   120
--   </pre>
--   
--   This uses the fact that Haskell’s <tt>let</tt> introduces recursive
--   bindings. We can rewrite this definition using <a>fix</a>,
--   
--   <pre>
--   &gt;&gt;&gt; fix (\rec n -&gt; if n &lt;= 1 then 1 else n * rec (n-1)) 5
--   120
--   </pre>
--   
--   Instead of making a recursive call, we introduce a dummy parameter
--   <tt>rec</tt>; when used within <a>fix</a>, this parameter then refers
--   to <a>fix</a>’s argument, hence the recursion is reintroduced.
fix :: (a -> a) -> a

-- | <a>&amp;</a> is a reverse application operator. This provides
--   notational convenience. Its precedence is one higher than that of the
--   forward application operator <a>$</a>, which allows <a>&amp;</a> to be
--   nested in <a>$</a>.
--   
--   <pre>
--   &gt;&gt;&gt; 5 &amp; (+1) &amp; show
--   "6"
--   </pre>
(&) :: a -> (a -> b) -> b
infixl 1 &

-- | <tt><a>void</a> value</tt> discards or ignores the result of
--   evaluation, such as the return value of an <a>IO</a> action.
--   
--   <h4><b>Examples</b></h4>
--   
--   Replace the contents of a <tt><a>Maybe</a> <a>Int</a></tt> with unit:
--   
--   <pre>
--   &gt;&gt;&gt; void Nothing
--   Nothing
--   
--   &gt;&gt;&gt; void (Just 3)
--   Just ()
--   </pre>
--   
--   Replace the contents of an <tt><a>Either</a> <a>Int</a>
--   <a>Int</a></tt> with unit, resulting in an <tt><a>Either</a>
--   <a>Int</a> <tt>()</tt></tt>:
--   
--   <pre>
--   &gt;&gt;&gt; void (Left 8675309)
--   Left 8675309
--   
--   &gt;&gt;&gt; void (Right 8675309)
--   Right ()
--   </pre>
--   
--   Replace every element of a list with unit:
--   
--   <pre>
--   &gt;&gt;&gt; void [1,2,3]
--   [(),(),()]
--   </pre>
--   
--   Replace the second element of a pair with unit:
--   
--   <pre>
--   &gt;&gt;&gt; void (1,2)
--   (1,())
--   </pre>
--   
--   Discard the result of an <a>IO</a> action:
--   
--   <pre>
--   &gt;&gt;&gt; mapM print [1,2]
--   1
--   2
--   [(),()]
--   
--   &gt;&gt;&gt; void $ mapM print [1,2]
--   1
--   2
--   </pre>
void :: Functor f => f a -> f ()

-- | Flipped version of <a>&lt;$&gt;</a>.
--   
--   <pre>
--   (<a>&lt;&amp;&gt;</a>) = <a>flip</a> <a>fmap</a>
--   </pre>
--   
--   <h4><b>Examples</b></h4>
--   
--   Apply <tt>(+1)</tt> to a list, a <a>Just</a> and a <a>Right</a>:
--   
--   <pre>
--   &gt;&gt;&gt; Just 2 &lt;&amp;&gt; (+1)
--   Just 3
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; [1,2,3] &lt;&amp;&gt; (+1)
--   [2,3,4]
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; Right 3 &lt;&amp;&gt; (+1)
--   Right 4
--   </pre>
(<&>) :: Functor f => f a -> (a -> b) -> f b
infixl 1 <&>

-- | An infix synonym for <a>fmap</a>.
--   
--   The name of this operator is an allusion to <a>$</a>. Note the
--   similarities between their types:
--   
--   <pre>
--    ($)  ::              (a -&gt; b) -&gt;   a -&gt;   b
--   (&lt;$&gt;) :: Functor f =&gt; (a -&gt; b) -&gt; f a -&gt; f b
--   </pre>
--   
--   Whereas <a>$</a> is function application, <a>&lt;$&gt;</a> is function
--   application lifted over a <a>Functor</a>.
--   
--   <h4><b>Examples</b></h4>
--   
--   Convert from a <tt><a>Maybe</a> <a>Int</a></tt> to a <tt><a>Maybe</a>
--   <a>String</a></tt> using <a>show</a>:
--   
--   <pre>
--   &gt;&gt;&gt; show &lt;$&gt; Nothing
--   Nothing
--   
--   &gt;&gt;&gt; show &lt;$&gt; Just 3
--   Just "3"
--   </pre>
--   
--   Convert from an <tt><a>Either</a> <a>Int</a> <a>Int</a></tt> to an
--   <tt><a>Either</a> <a>Int</a></tt> <a>String</a> using <a>show</a>:
--   
--   <pre>
--   &gt;&gt;&gt; show &lt;$&gt; Left 17
--   Left 17
--   
--   &gt;&gt;&gt; show &lt;$&gt; Right 17
--   Right "17"
--   </pre>
--   
--   Double each element of a list:
--   
--   <pre>
--   &gt;&gt;&gt; (*2) &lt;$&gt; [1,2,3]
--   [2,4,6]
--   </pre>
--   
--   Apply <a>even</a> to the second element of a pair:
--   
--   <pre>
--   &gt;&gt;&gt; even &lt;$&gt; (2,2)
--   (2,True)
--   </pre>
(<$>) :: Functor f => (a -> b) -> f a -> f b
infixl 4 <$>

-- | Flipped version of <a>&lt;$</a>.
--   
--   <h4><b>Examples</b></h4>
--   
--   Replace the contents of a <tt><a>Maybe</a> <a>Int</a></tt> with a
--   constant <a>String</a>:
--   
--   <pre>
--   &gt;&gt;&gt; Nothing $&gt; "foo"
--   Nothing
--   
--   &gt;&gt;&gt; Just 90210 $&gt; "foo"
--   Just "foo"
--   </pre>
--   
--   Replace the contents of an <tt><a>Either</a> <a>Int</a>
--   <a>Int</a></tt> with a constant <a>String</a>, resulting in an
--   <tt><a>Either</a> <a>Int</a> <a>String</a></tt>:
--   
--   <pre>
--   &gt;&gt;&gt; Left 8675309 $&gt; "foo"
--   Left 8675309
--   
--   &gt;&gt;&gt; Right 8675309 $&gt; "foo"
--   Right "foo"
--   </pre>
--   
--   Replace each element of a list with a constant <a>String</a>:
--   
--   <pre>
--   &gt;&gt;&gt; [1,2,3] $&gt; "foo"
--   ["foo","foo","foo"]
--   </pre>
--   
--   Replace the second element of a pair with a constant <a>String</a>:
--   
--   <pre>
--   &gt;&gt;&gt; (1,2) $&gt; "foo"
--   (1,"foo")
--   </pre>
($>) :: Functor f => f a -> b -> f b
infixl 4 $>

-- | <a>uncurry</a> converts a curried function to a function on pairs.
--   
--   <h4><b>Examples</b></h4>
--   
--   <pre>
--   &gt;&gt;&gt; uncurry (+) (1,2)
--   3
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; uncurry ($) (show, 1)
--   "1"
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; map (uncurry max) [(1,2), (3,4), (6,8)]
--   [2,4,8]
--   </pre>
uncurry :: (a -> b -> c) -> (a, b) -> c

-- | Swap the components of a pair.
swap :: (a, b) -> (b, a)

-- | <a>curry</a> converts an uncurried function to a curried function.
--   
--   <h4><b>Examples</b></h4>
--   
--   <pre>
--   &gt;&gt;&gt; curry fst 1 2
--   1
--   </pre>
curry :: ((a, b) -> c) -> a -> b -> c

-- | A <a>Version</a> represents the version of a software entity.
--   
--   An instance of <a>Eq</a> is provided, which implements exact equality
--   modulo reordering of the tags in the <a>versionTags</a> field.
--   
--   An instance of <a>Ord</a> is also provided, which gives lexicographic
--   ordering on the <a>versionBranch</a> fields (i.e. 2.1 &gt; 2.0, 1.2.3
--   &gt; 1.2.2, etc.). This is expected to be sufficient for many uses,
--   but note that you may need to use a more specific ordering for your
--   versioning scheme. For example, some versioning schemes may include
--   pre-releases which have tags <tt>"pre1"</tt>, <tt>"pre2"</tt>, and so
--   on, and these would need to be taken into account when determining
--   ordering. In some cases, date ordering may be more appropriate, so the
--   application would have to look for <tt>date</tt> tags in the
--   <a>versionTags</a> field and compare those. The bottom line is, don't
--   always assume that <a>compare</a> and other <a>Ord</a> operations are
--   the right thing for every <a>Version</a>.
--   
--   Similarly, concrete representations of versions may differ. One
--   possible concrete representation is provided (see <a>showVersion</a>
--   and <a>parseVersion</a>), but depending on the application a different
--   concrete representation may be more appropriate.
data Version
Version :: [Int] -> [String] -> Version

-- | The numeric branch for this version. This reflects the fact that most
--   software versions are tree-structured; there is a main trunk which is
--   tagged with versions at various points (1,2,3...), and the first
--   branch off the trunk after version 3 is 3.1, the second branch off the
--   trunk after version 3 is 3.2, and so on. The tree can be branched
--   arbitrarily, just by adding more digits.
--   
--   We represent the branch as a list of <a>Int</a>, so version 3.2.1
--   becomes [3,2,1]. Lexicographic ordering (i.e. the default instance of
--   <a>Ord</a> for <tt>[Int]</tt>) gives the natural ordering of branches.
[versionBranch] :: Version -> [Int]

-- | A version can be tagged with an arbitrary list of strings. The
--   interpretation of the list of tags is entirely dependent on the entity
--   that this version applies to.
[versionTags] :: Version -> [String]

-- | Construct tag-less <a>Version</a>
makeVersion :: [Int] -> Version

-- | This is the "back door" into the <a>IO</a> monad, allowing <a>IO</a>
--   computation to be performed at any time. For this to be safe, the
--   <a>IO</a> computation should be free of side effects and independent
--   of its environment.
--   
--   If the I/O computation wrapped in <a>unsafePerformIO</a> performs side
--   effects, then the relative order in which those side effects take
--   place (relative to the main I/O trunk, or other calls to
--   <a>unsafePerformIO</a>) is indeterminate. Furthermore, when using
--   <a>unsafePerformIO</a> to cause side-effects, you should take the
--   following precautions to ensure the side effects are performed as many
--   times as you expect them to be. Note that these precautions are
--   necessary for GHC, but may not be sufficient, and other compilers may
--   require different precautions:
--   
--   <ul>
--   <li>Use <tt>{-# NOINLINE foo #-}</tt> as a pragma on any function
--   <tt>foo</tt> that calls <a>unsafePerformIO</a>. If the call is
--   inlined, the I/O may be performed more than once.</li>
--   <li>Use the compiler flag <tt>-fno-cse</tt> to prevent common
--   sub-expression elimination being performed on the module, which might
--   combine two side effects that were meant to be separate. A good
--   example is using multiple global variables (like <tt>test</tt> in the
--   example below).</li>
--   <li>Make sure that the either you switch off let-floating
--   (<tt>-fno-full-laziness</tt>), or that the call to
--   <a>unsafePerformIO</a> cannot float outside a lambda. For example, if
--   you say: <tt> f x = unsafePerformIO (newIORef []) </tt> you may get
--   only one reference cell shared between all calls to <tt>f</tt>. Better
--   would be <tt> f x = unsafePerformIO (newIORef [x]) </tt> because now
--   it can't float outside the lambda.</li>
--   </ul>
--   
--   It is less well known that <a>unsafePerformIO</a> is not type safe.
--   For example:
--   
--   <pre>
--   test :: IORef [a]
--   test = unsafePerformIO $ newIORef []
--   
--   main = do
--           writeIORef test [42]
--           bang &lt;- readIORef test
--           print (bang :: [Char])
--   </pre>
--   
--   This program will core dump. This problem with polymorphic references
--   is well known in the ML community, and does not arise with normal
--   monadic use of references. There is no easy way to make it impossible
--   once you use <a>unsafePerformIO</a>. Indeed, it is possible to write
--   <tt>coerce :: a -&gt; b</tt> with the help of <a>unsafePerformIO</a>.
--   So be careful!
unsafePerformIO :: IO a -> a

-- | <a>unsafeInterleaveIO</a> allows an <a>IO</a> computation to be
--   deferred lazily. When passed a value of type <tt>IO a</tt>, the
--   <a>IO</a> will only be performed when the value of the <tt>a</tt> is
--   demanded. This is used to implement lazy file reading, see
--   <a>hGetContents</a>.
unsafeInterleaveIO :: IO a -> IO a

-- | This version of <a>unsafePerformIO</a> is more efficient because it
--   omits the check that the IO is only being performed by a single
--   thread. Hence, when you use <a>unsafeDupablePerformIO</a>, there is a
--   possibility that the IO action may be performed multiple times (on a
--   multiprocessor), and you should therefore ensure that it gives the
--   same results each time. It may even happen that one of the duplicated
--   IO actions is only run partially, and then interrupted in the middle
--   without an exception being raised. Therefore, functions like
--   <a>bracket</a> cannot be used safely within
--   <a>unsafeDupablePerformIO</a>.
unsafeDupablePerformIO :: IO a -> a

-- | An <a>MVar</a> (pronounced "em-var") is a synchronising variable, used
--   for communication between concurrent threads. It can be thought of as
--   a box, which may be empty or full.
data MVar a

-- | A non-blocking version of <a>takeMVar</a>. The <a>tryTakeMVar</a>
--   function returns immediately, with <a>Nothing</a> if the <a>MVar</a>
--   was empty, or <tt><a>Just</a> a</tt> if the <a>MVar</a> was full with
--   contents <tt>a</tt>. After <a>tryTakeMVar</a>, the <a>MVar</a> is left
--   empty.
tryTakeMVar :: MVar a -> IO (Maybe a)

-- | A non-blocking version of <a>readMVar</a>. The <a>tryReadMVar</a>
--   function returns immediately, with <a>Nothing</a> if the <a>MVar</a>
--   was empty, or <tt><a>Just</a> a</tt> if the <a>MVar</a> was full with
--   contents <tt>a</tt>.
tryReadMVar :: MVar a -> IO (Maybe a)

-- | A non-blocking version of <a>putMVar</a>. The <a>tryPutMVar</a>
--   function attempts to put the value <tt>a</tt> into the <a>MVar</a>,
--   returning <a>True</a> if it was successful, or <a>False</a> otherwise.
tryPutMVar :: MVar a -> a -> IO Bool

-- | Return the contents of the <a>MVar</a>. If the <a>MVar</a> is
--   currently empty, <a>takeMVar</a> will wait until it is full. After a
--   <a>takeMVar</a>, the <a>MVar</a> is left empty.
--   
--   There are two further important properties of <a>takeMVar</a>:
--   
--   <ul>
--   <li><a>takeMVar</a> is single-wakeup. That is, if there are multiple
--   threads blocked in <a>takeMVar</a>, and the <a>MVar</a> becomes full,
--   only one thread will be woken up. The runtime guarantees that the
--   woken thread completes its <a>takeMVar</a> operation.</li>
--   <li>When multiple threads are blocked on an <a>MVar</a>, they are
--   woken up in FIFO order. This is useful for providing fairness
--   properties of abstractions built using <a>MVar</a>s.</li>
--   </ul>
takeMVar :: MVar a -> IO a

-- | Atomically read the contents of an <a>MVar</a>. If the <a>MVar</a> is
--   currently empty, <a>readMVar</a> will wait until it is full.
--   <a>readMVar</a> is guaranteed to receive the next <a>putMVar</a>.
--   
--   <a>readMVar</a> is multiple-wakeup, so when multiple readers are
--   blocked on an <a>MVar</a>, all of them are woken up at the same time.
--   
--   <i>Compatibility note:</i> Prior to base 4.7, <a>readMVar</a> was a
--   combination of <a>takeMVar</a> and <a>putMVar</a>. This mean that in
--   the presence of other threads attempting to <a>putMVar</a>,
--   <a>readMVar</a> could block. Furthermore, <a>readMVar</a> would not
--   receive the next <a>putMVar</a> if there was already a pending thread
--   blocked on <a>takeMVar</a>. The old behavior can be recovered by
--   implementing 'readMVar as follows:
--   
--   <pre>
--   readMVar :: MVar a -&gt; IO a
--   readMVar m =
--     mask_ $ do
--       a &lt;- takeMVar m
--       putMVar m a
--       return a
--   </pre>
readMVar :: MVar a -> IO a

-- | Put a value into an <a>MVar</a>. If the <a>MVar</a> is currently full,
--   <a>putMVar</a> will wait until it becomes empty.
--   
--   There are two further important properties of <a>putMVar</a>:
--   
--   <ul>
--   <li><a>putMVar</a> is single-wakeup. That is, if there are multiple
--   threads blocked in <a>putMVar</a>, and the <a>MVar</a> becomes empty,
--   only one thread will be woken up. The runtime guarantees that the
--   woken thread completes its <a>putMVar</a> operation.</li>
--   <li>When multiple threads are blocked on an <a>MVar</a>, they are
--   woken up in FIFO order. This is useful for providing fairness
--   properties of abstractions built using <a>MVar</a>s.</li>
--   </ul>
putMVar :: MVar a -> a -> IO ()

-- | Create an <a>MVar</a> which contains the supplied value.
newMVar :: a -> IO (MVar a)

-- | Create an <a>MVar</a> which is initially empty.
newEmptyMVar :: IO (MVar a)

-- | Check whether a given <a>MVar</a> is empty.
--   
--   Notice that the boolean value returned is just a snapshot of the state
--   of the MVar. By the time you get to react on its result, the MVar may
--   have been filled (or emptied) - so be extremely careful when using
--   this operation. Use <a>tryTakeMVar</a> instead if possible.
isEmptyMVar :: MVar a -> IO Bool

-- | the same as <tt><a>flip</a> (<a>-</a>)</tt>.
--   
--   Because <tt>-</tt> is treated specially in the Haskell grammar,
--   <tt>(-</tt> <i>e</i><tt>)</tt> is not a section, but an application of
--   prefix negation. However, <tt>(<a>subtract</a></tt>
--   <i>exp</i><tt>)</tt> is equivalent to the disallowed section.
subtract :: Num a => a -> a -> a

-- | Monads that also support choice and failure.
class (Alternative m, Monad m) => MonadPlus (m :: Type -> Type)

-- | The identity of <a>mplus</a>. It should also satisfy the equations
--   
--   <pre>
--   mzero &gt;&gt;= f  =  mzero
--   v &gt;&gt; mzero   =  mzero
--   </pre>
--   
--   The default definition is
--   
--   <pre>
--   mzero = <a>empty</a>
--   </pre>
mzero :: MonadPlus m => m a

-- | An associative operation. The default definition is
--   
--   <pre>
--   mplus = (<a>&lt;|&gt;</a>)
--   </pre>
mplus :: MonadPlus m => m a -> m a -> m a

-- | A monoid on applicative functors.
--   
--   If defined, <a>some</a> and <a>many</a> should be the least solutions
--   of the equations:
--   
--   <ul>
--   <li><pre><a>some</a> v = (:) <a>&lt;$&gt;</a> v <a>&lt;*&gt;</a>
--   <a>many</a> v</pre></li>
--   <li><pre><a>many</a> v = <a>some</a> v <a>&lt;|&gt;</a> <a>pure</a>
--   []</pre></li>
--   </ul>
class Applicative f => Alternative (f :: Type -> Type)

-- | The identity of <a>&lt;|&gt;</a>
empty :: Alternative f => f a

-- | An associative binary operation
(<|>) :: Alternative f => f a -> f a -> f a

-- | One or more.
some :: Alternative f => f a -> f [a]

-- | Zero or more.
many :: Alternative f => f a -> f [a]
infixl 3 <|>

-- | Conditional execution of <a>Applicative</a> expressions. For example,
--   
--   <pre>
--   when debug (putStrLn "Debugging")
--   </pre>
--   
--   will output the string <tt>Debugging</tt> if the Boolean value
--   <tt>debug</tt> is <a>True</a>, and otherwise do nothing.
when :: Applicative f => Bool -> f () -> f ()

-- | <tt><a>until</a> p f</tt> yields the result of applying <tt>f</tt>
--   until <tt>p</tt> holds.
until :: (a -> Bool) -> (a -> a) -> a -> a

-- | The <a>fromEnum</a> method restricted to the type <a>Char</a>.
ord :: Char -> Int

-- | Promote a function to a monad, scanning the monadic arguments from
--   left to right (cf. <a>liftM2</a>).
liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r

-- | Promote a function to a monad, scanning the monadic arguments from
--   left to right (cf. <a>liftM2</a>).
liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r

-- | Promote a function to a monad, scanning the monadic arguments from
--   left to right (cf. <a>liftM2</a>).
liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r

-- | Promote a function to a monad, scanning the monadic arguments from
--   left to right. For example,
--   
--   <pre>
--   liftM2 (+) [0,1] [0,2] = [0,2,1,3]
--   liftM2 (+) (Just 1) Nothing = Nothing
--   </pre>
liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r

-- | Lift a ternary function to actions.
liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d

-- | Lift a function to actions. Equivalent to Functor's <a>fmap</a> but
--   implemented using only <a>Applicative</a>'s methods: `liftA f a = pure
--   f <a>*</a> a`
--   
--   As such this function may be used to implement a <a>Functor</a>
--   instance from an <a>Applicative</a> one.
liftA :: Applicative f => (a -> b) -> f a -> f b

-- | <tt><a>flip</a> f</tt> takes its (first) two arguments in the reverse
--   order of <tt>f</tt>.
--   
--   <pre>
--   &gt;&gt;&gt; flip (++) "hello" "world"
--   "worldhello"
--   </pre>
flip :: (a -> b -> c) -> b -> a -> c

-- | <tt>const x</tt> is a unary function which evaluates to <tt>x</tt> for
--   all inputs.
--   
--   <pre>
--   &gt;&gt;&gt; const 42 "hello"
--   42
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; map (const 42) [0..3]
--   [42,42,42,42]
--   </pre>
const :: a -> b -> a

-- | <a>asTypeOf</a> is a type-restricted version of <a>const</a>. It is
--   usually used as an infix operator, and its typing forces its first
--   argument (which is usually overloaded) to have the same type as the
--   second.
asTypeOf :: a -> a -> a

-- | In many situations, the <a>liftM</a> operations can be replaced by
--   uses of <a>ap</a>, which promotes function application.
--   
--   <pre>
--   return f `ap` x1 `ap` ... `ap` xn
--   </pre>
--   
--   is equivalent to
--   
--   <pre>
--   liftMn f x1 x2 ... xn
--   </pre>
ap :: Monad m => m (a -> b) -> m a -> m b

-- | Same as <a>&gt;&gt;=</a>, but with the arguments interchanged.
(=<<) :: Monad m => (a -> m b) -> m a -> m b
infixr 1 =<<

-- | A variant of <a>&lt;*&gt;</a> with the arguments reversed.
(<**>) :: Applicative f => f a -> f (a -> b) -> f b
infixl 4 <**>

-- | Strict (call-by-value) application operator. It takes a function and
--   an argument, evaluates the argument to weak head normal form (WHNF),
--   then calls the function with that value.
($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
infixr 0 $!

-- | A special case of <a>error</a>. It is expected that compilers will
--   recognize this and insert error messages which are more appropriate to
--   the context in which <a>undefined</a> appears.
undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a

-- | A variant of <a>error</a> that does not produce a stack trace.
errorWithoutStackTrace :: forall (r :: RuntimeRep) (a :: TYPE r). [Char] -> a

-- | <a>error</a> stops execution and displays an error message.
error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a

-- | This is a valid definition of <a>stimes</a> for an idempotent
--   <a>Monoid</a>.
--   
--   When <tt>mappend x x = x</tt>, this definition should be preferred,
--   because it works in &lt;math&gt; rather than &lt;math&gt;
stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a

-- | The <tt>SomeException</tt> type is the root of the exception type
--   hierarchy. When an exception of type <tt>e</tt> is thrown, behind the
--   scenes it is encapsulated in a <tt>SomeException</tt>.
data SomeException
SomeException :: e -> SomeException

-- | Boolean "and", lazy in the second argument
(&&) :: Bool -> Bool -> Bool
infixr 3 &&

-- | Boolean "not"
not :: Bool -> Bool

-- | Boolean "or", lazy in the second argument
(||) :: Bool -> Bool -> Bool
infixr 2 ||

-- | Make a <a>Functor</a> over the second argument of a <a>Bifunctor</a>.
newtype WrappedBifunctor (p :: k -> k1 -> Type) (a :: k) (b :: k1)
WrapBifunctor :: p a b -> WrappedBifunctor (p :: k -> k1 -> Type) (a :: k) (b :: k1)
[unwrapBifunctor] :: WrappedBifunctor (p :: k -> k1 -> Type) (a :: k) (b :: k1) -> p a b
(<<$>>) :: (a -> b) -> a -> b
infixl 4 <<$>>

-- | A compact representation of a <a>Word8</a> vector.
--   
--   It has a lower memory overhead than a <a>ByteString</a> and does not
--   contribute to heap fragmentation. It can be converted to or from a
--   <a>ByteString</a> (at the cost of copying the string data). It
--   supports very few other operations.
--   
--   It is suitable for use as an internal representation for code that
--   needs to keep many short strings in memory, but it <i>should not</i>
--   be used as an interchange type. That is, it should not generally be
--   used in public APIs. The <a>ByteString</a> type is usually more
--   suitable for use in interfaces; it is more flexible and it supports a
--   wide range of operations.
data ShortByteString

-- | A space-efficient representation of a <a>Word8</a> vector, supporting
--   many efficient operations.
--   
--   A <a>ByteString</a> contains 8-bit bytes, or by using the operations
--   from <a>Data.ByteString.Char8</a> it can be interpreted as containing
--   8-bit characters.
data ByteString

-- | Lift a ternary function into a <a>Comonad</a> with zipping
liftW3 :: ComonadApply w => (a -> b -> c -> d) -> w a -> w b -> w c -> w d

-- | Lift a binary function into a <a>Comonad</a> with zipping
liftW2 :: ComonadApply w => (a -> b -> c) -> w a -> w b -> w c

-- | A variant of <a>&lt;@&gt;</a> with the arguments reversed.
(<@@>) :: ComonadApply w => w a -> w (a -> b) -> w b
infixl 4 <@@>

-- | Left-to-right <a>Cokleisli</a> composition
(=>=) :: Comonad w => (w a -> b) -> (w b -> c) -> w a -> c
infixr 1 =>=

-- | Right-to-left <a>Cokleisli</a> composition
(=<=) :: Comonad w => (w b -> c) -> (w a -> b) -> w a -> c
infixr 1 =<=

-- | <a>extend</a> in operator form
(<<=) :: Comonad w => (w a -> b) -> w a -> w b
infixr 1 <<=

-- | <a>extend</a> with the arguments swapped. Dual to <a>&gt;&gt;=</a> for
--   a <a>Monad</a>.
(=>>) :: Comonad w => w a -> (w a -> b) -> w b
infixl 1 =>>

-- | Comonadic fixed point à la Kenneth Foner:
--   
--   This is the <tt>evaluate</tt> function from his <a>"Getting a Quick
--   Fix on Comonads"</a> talk.
kfix :: ComonadApply w => w (w a -> a) -> w a

-- | Comonadic fixed point à la Dominic Orchard
cfix :: Comonad w => (w a -> a) -> w a

-- | Comonadic fixed point à la David Menendez
wfix :: Comonad w => w (w a -> a) -> a

-- | A suitable default definition for <a>fmap</a> for a <a>Comonad</a>.
--   Promotes a function to a comonad.
--   
--   You can only safely use <a>liftW</a> to define <a>fmap</a> if your
--   <a>Comonad</a> defines <a>extend</a>, not just <a>duplicate</a>, since
--   defining <a>extend</a> in terms of duplicate uses <a>fmap</a>!
--   
--   <pre>
--   <a>fmap</a> f = <a>liftW</a> f = <a>extend</a> (f . <a>extract</a>)
--   </pre>
liftW :: Comonad w => (a -> b) -> w a -> w b

-- | There are two ways to define a comonad:
--   
--   I. Provide definitions for <a>extract</a> and <a>extend</a> satisfying
--   these laws:
--   
--   <pre>
--   <a>extend</a> <a>extract</a>      = <a>id</a>
--   <a>extract</a> . <a>extend</a> f  = f
--   <a>extend</a> f . <a>extend</a> g = <a>extend</a> (f . <a>extend</a> g)
--   </pre>
--   
--   In this case, you may simply set <a>fmap</a> = <a>liftW</a>.
--   
--   These laws are directly analogous to the laws for monads and perhaps
--   can be made clearer by viewing them as laws stating that Cokleisli
--   composition must be associative, and has extract for a unit:
--   
--   <pre>
--   f <a>=&gt;=</a> <a>extract</a>   = f
--   <a>extract</a> <a>=&gt;=</a> f   = f
--   (f <a>=&gt;=</a> g) <a>=&gt;=</a> h = f <a>=&gt;=</a> (g <a>=&gt;=</a> h)
--   </pre>
--   
--   II. Alternately, you may choose to provide definitions for
--   <a>fmap</a>, <a>extract</a>, and <a>duplicate</a> satisfying these
--   laws:
--   
--   <pre>
--   <a>extract</a> . <a>duplicate</a>      = <a>id</a>
--   <a>fmap</a> <a>extract</a> . <a>duplicate</a> = <a>id</a>
--   <a>duplicate</a> . <a>duplicate</a>    = <a>fmap</a> <a>duplicate</a> . <a>duplicate</a>
--   </pre>
--   
--   In this case you may not rely on the ability to define <a>fmap</a> in
--   terms of <a>liftW</a>.
--   
--   You may of course, choose to define both <a>duplicate</a> <i>and</i>
--   <a>extend</a>. In that case you must also satisfy these laws:
--   
--   <pre>
--   <a>extend</a> f  = <a>fmap</a> f . <a>duplicate</a>
--   <a>duplicate</a> = <a>extend</a> id
--   <a>fmap</a> f    = <a>extend</a> (f . <a>extract</a>)
--   </pre>
--   
--   These are the default definitions of <a>extend</a> and
--   <a>duplicate</a> and the definition of <a>liftW</a> respectively.
class Functor w => Comonad (w :: Type -> Type)

-- | <pre>
--   <a>extract</a> . <a>fmap</a> f = f . <a>extract</a>
--   </pre>
extract :: Comonad w => w a -> a

-- | <pre>
--   <a>duplicate</a> = <a>extend</a> <a>id</a>
--   <a>fmap</a> (<a>fmap</a> f) . <a>duplicate</a> = <a>duplicate</a> . <a>fmap</a> f
--   </pre>
duplicate :: Comonad w => w a -> w (w a)

-- | <pre>
--   <a>extend</a> f = <a>fmap</a> f . <a>duplicate</a>
--   </pre>
extend :: Comonad w => (w a -> b) -> w a -> w b

-- | <tt>ComonadApply</tt> is to <tt>Comonad</tt> like <tt>Applicative</tt>
--   is to <tt>Monad</tt>.
--   
--   Mathematically, it is a strong lax symmetric semi-monoidal comonad on
--   the category <tt>Hask</tt> of Haskell types. That it to say that
--   <tt>w</tt> is a strong lax symmetric semi-monoidal functor on Hask,
--   where both <a>extract</a> and <a>duplicate</a> are symmetric monoidal
--   natural transformations.
--   
--   Laws:
--   
--   <pre>
--   (<a>.</a>) <a>&lt;$&gt;</a> u <a>&lt;@&gt;</a> v <a>&lt;@&gt;</a> w = u <a>&lt;@&gt;</a> (v <a>&lt;@&gt;</a> w)
--   <a>extract</a> (p <a>&lt;@&gt;</a> q) = <a>extract</a> p (<a>extract</a> q)
--   <a>duplicate</a> (p <a>&lt;@&gt;</a> q) = (<a>&lt;@&gt;</a>) <a>&lt;$&gt;</a> <a>duplicate</a> p <a>&lt;@&gt;</a> <a>duplicate</a> q
--   </pre>
--   
--   If our type is both a <a>ComonadApply</a> and <a>Applicative</a> we
--   further require
--   
--   <pre>
--   (<a>&lt;*&gt;</a>) = (<a>&lt;@&gt;</a>)
--   </pre>
--   
--   Finally, if you choose to define (<a>&lt;@</a>) and (<a>@&gt;</a>),
--   the results of your definitions should match the following laws:
--   
--   <pre>
--   a <a>@&gt;</a> b = <a>const</a> <a>id</a> <a>&lt;$&gt;</a> a <a>&lt;@&gt;</a> b
--   a <a>&lt;@</a> b = <a>const</a> <a>&lt;$&gt;</a> a <a>&lt;@&gt;</a> b
--   </pre>
class Comonad w => ComonadApply (w :: Type -> Type)
(<@>) :: ComonadApply w => w (a -> b) -> w a -> w b
(@>) :: ComonadApply w => w a -> w b -> w b
(<@) :: ComonadApply w => w a -> w b -> w a
infixl 4 <@
infixl 4 <@>
infixl 4 @>

-- | The <a>Cokleisli</a> <a>Arrow</a>s of a given <a>Comonad</a>
newtype Cokleisli (w :: k -> Type) (a :: k) b
Cokleisli :: (w a -> b) -> Cokleisli (w :: k -> Type) (a :: k) b
[runCokleisli] :: Cokleisli (w :: k -> Type) (a :: k) b -> w a -> b

-- | A map of integers to values <tt>a</tt>.
data IntMap a

-- | A set of integers.
data IntSet

-- | A Map from keys <tt>k</tt> to values <tt>a</tt>.
--   
--   The <a>Semigroup</a> operation for <a>Map</a> is <a>union</a>, which
--   prefers values from the left operand. If <tt>m1</tt> maps a key
--   <tt>k</tt> to a value <tt>a1</tt>, and <tt>m2</tt> maps the same key
--   to a different value <tt>a2</tt>, then their union <tt>m1 &lt;&gt;
--   m2</tt> maps <tt>k</tt> to <tt>a1</tt>.
data Map k a

-- | General-purpose finite sequences.
data Seq a

-- | A set of values <tt>a</tt>.
data Set a

-- | <pre>
--   <a>chosen</a> = <a>choose</a> <a>id</a>
--   </pre>
chosen :: Decidable f => f b -> f c -> f (Either b c)

-- | <pre>
--   <a>lost</a> = <a>lose</a> <a>id</a>
--   </pre>
lost :: Decidable f => f Void

-- | This is the divisible analogue of <a>liftA</a>. It gives a viable
--   default definition for <a>contramap</a> in terms of the members of
--   <a>Divisible</a>.
--   
--   <pre>
--   <a>liftD</a> f = <a>divide</a> ((,) () . f) <a>conquer</a>
--   </pre>
liftD :: Divisible f => (a -> b) -> f b -> f a

-- | Redundant, but provided for symmetry.
--   
--   <pre>
--   <a>conquered</a> = <a>conquer</a>
--   </pre>
conquered :: Divisible f => f ()

-- | <pre>
--   <a>divided</a> = <a>divide</a> <a>id</a>
--   </pre>
divided :: Divisible f => f a -> f b -> f (a, b)

-- | A <a>Divisible</a> contravariant functor is the contravariant analogue
--   of <a>Applicative</a>.
--   
--   Continuing the intuition that <a>Contravariant</a> functors consume
--   input, a <a>Divisible</a> contravariant functor also has the ability
--   to be composed "beside" another contravariant functor.
--   
--   Serializers provide a good example of <a>Divisible</a> contravariant
--   functors. To begin let's start with the type of serializers for
--   specific types:
--   
--   <pre>
--   newtype Serializer a = Serializer { runSerializer :: a -&gt; ByteString }
--   </pre>
--   
--   This is a contravariant functor:
--   
--   <pre>
--   instance Contravariant Serializer where
--     contramap f s = Serializer (runSerializer s . f)
--   </pre>
--   
--   That is, given a serializer for <tt>a</tt> (<tt>s :: Serializer
--   a</tt>), and a way to turn <tt>b</tt>s into <tt>a</tt>s (a mapping
--   <tt>f :: b -&gt; a</tt>), we have a serializer for <tt>b</tt>:
--   <tt>contramap f s :: Serializer b</tt>.
--   
--   Divisible gives us a way to combine two serializers that focus on
--   different parts of a structure. If we postulate the existance of two
--   primitive serializers - <tt>string :: Serializer String</tt> and
--   <tt>int :: Serializer Int</tt>, we would like to be able to combine
--   these into a serializer for pairs of <tt>String</tt>s and
--   <tt>Int</tt>s. How can we do this? Simply run both serializers and
--   combine their output!
--   
--   <pre>
--   data StringAndInt = StringAndInt String Int
--   
--   stringAndInt :: Serializer StringAndInt
--   stringAndInt = Serializer $ \(StringAndInt s i) -&gt;
--     let sBytes = runSerializer string s
--         iBytes = runSerializer int i
--     in sBytes &lt;&gt; iBytes
--   </pre>
--   
--   <a>divide</a> is a generalization by also taking a <a>contramap</a>
--   like function to split any <tt>a</tt> into a pair. This conveniently
--   allows you to target fields of a record, for instance, by extracting
--   the values under two fields and combining them into a tuple.
--   
--   To complete the example, here is how to write <tt>stringAndInt</tt>
--   using a <tt>Divisible</tt> instance:
--   
--   <pre>
--   instance Divisible Serializer where
--     conquer = Serializer (const mempty)
--   
--     divide toBC bSerializer cSerializer = Serializer $ \a -&gt;
--       case toBC a of
--         (b, c) -&gt;
--           let bBytes = runSerializer bSerializer b
--               cBytes = runSerializer cSerializer c
--           in bBytes &lt;&gt; cBytes
--   
--   stringAndInt :: Serializer StringAndInt
--   stringAndInt =
--     divide (\(StringAndInt s i) -&gt; (s, i)) string int
--   </pre>
class Contravariant f => Divisible (f :: Type -> Type)
divide :: Divisible f => (a -> (b, c)) -> f b -> f c -> f a

-- | Conquer acts as an identity for combining <tt>Divisible</tt> functors.
conquer :: Divisible f => f a

-- | A <a>Decidable</a> contravariant functor is the contravariant analogue
--   of <a>Alternative</a>.
--   
--   Noting the superclass constraint that <tt>f</tt> must also be
--   <a>Divisible</a>, a <tt>Decidable</tt> functor has the ability to "fan
--   out" input, under the intuition that contravariant functors consume
--   input.
--   
--   In the discussion for <tt>Divisible</tt>, an example was demonstrated
--   with <tt>Serializer</tt>s, that turn <tt>a</tt>s into
--   <tt>ByteString</tt>s. <tt>Divisible</tt> allowed us to serialize the
--   <i>product</i> of multiple values by concatenation. By making our
--   <tt>Serializer</tt> also <tt>Decidable</tt>- we now have the ability
--   to serialize the <i>sum</i> of multiple values - for example different
--   constructors in an ADT.
--   
--   Consider serializing arbitrary identifiers that can be either
--   <tt>String</tt>s or <tt>Int</tt>s:
--   
--   <pre>
--   data Identifier = StringId String | IntId Int
--   </pre>
--   
--   We know we have serializers for <tt>String</tt>s and <tt>Int</tt>s,
--   but how do we combine them into a <tt>Serializer</tt> for
--   <tt>Identifier</tt>? Essentially, our <tt>Serializer</tt> needs to
--   scrutinise the incoming value and choose how to serialize it:
--   
--   <pre>
--   identifier :: Serializer Identifier
--   identifier = Serializer $ \identifier -&gt;
--     case identifier of
--       StringId s -&gt; runSerializer string s
--       IntId i -&gt; runSerializer int i
--   </pre>
--   
--   It is exactly this notion of choice that <tt>Decidable</tt> encodes.
--   Hence if we add an instance of <tt>Decidable</tt> for
--   <tt>Serializer</tt>...
--   
--   <pre>
--   instance Decidable Serializer where
--     lose f = Serializer $ \a -&gt; absurd (f a)
--     choose split l r = Serializer $ \a -&gt;
--       either (runSerializer l) (runSerializer r) (split a)
--   </pre>
--   
--   Then our <tt>identifier</tt> <tt>Serializer</tt> is
--   
--   <pre>
--   identifier :: Serializer Identifier
--   identifier = choose toEither string int where
--     toEither (StringId s) = Left s
--     toEither (IntId i) = Right i
--   </pre>
class Divisible f => Decidable (f :: Type -> Type)

-- | Acts as identity to <a>choose</a>.
lose :: Decidable f => (a -> Void) -> f a
choose :: Decidable f => (a -> Either b c) -> f b -> f c -> f a

-- | A class of bifunctors that can be fully evaluated.
class NFData2 (p :: Type -> Type -> Type)

-- | <a>liftRnf2</a> should reduce its argument to normal form (that is,
--   fully evaluate all sub-components), given functions to reduce
--   <tt>a</tt> and <tt>b</tt> arguments respectively, and then return
--   <tt>()</tt>.
--   
--   <b>Note</b>: Unlike for the unary <a>liftRnf</a>, there is currently
--   no support for generically deriving <a>liftRnf2</a>.
liftRnf2 :: NFData2 p => (a -> ()) -> (b -> ()) -> p a b -> ()

-- | A class of functors that can be fully evaluated.
class NFData1 (f :: TYPE LiftedRep -> TYPE LiftedRep)

-- | <a>liftRnf</a> should reduce its argument to normal form (that is,
--   fully evaluate all sub-components), given an argument to reduce
--   <tt>a</tt> arguments, and then return <tt>()</tt>.
--   
--   See <a>rnf</a> for the generic deriving.
liftRnf :: NFData1 f => (a -> ()) -> f a -> ()

-- | A class of types that can be fully evaluated.
class NFData a

-- | <a>rnf</a> should reduce its argument to normal form (that is, fully
--   evaluate all sub-components), and then return <tt>()</tt>.
--   
--   <h3><a>Generic</a> <a>NFData</a> deriving</h3>
--   
--   Starting with GHC 7.2, you can automatically derive instances for
--   types possessing a <a>Generic</a> instance.
--   
--   Note: <a>Generic1</a> can be auto-derived starting with GHC 7.4
--   
--   <pre>
--   {-# LANGUAGE DeriveGeneric #-}
--   
--   import GHC.Generics (Generic, Generic1)
--   import Control.DeepSeq
--   
--   data Foo a = Foo a String
--                deriving (Eq, Generic, Generic1)
--   
--   instance NFData a =&gt; NFData (Foo a)
--   instance NFData1 Foo
--   
--   data Colour = Red | Green | Blue
--                 deriving Generic
--   
--   instance NFData Colour
--   </pre>
--   
--   Starting with GHC 7.10, the example above can be written more
--   concisely by enabling the new <tt>DeriveAnyClass</tt> extension:
--   
--   <pre>
--   {-# LANGUAGE DeriveGeneric, DeriveAnyClass #-}
--   
--   import GHC.Generics (Generic)
--   import Control.DeepSeq
--   
--   data Foo a = Foo a String
--                deriving (Eq, Generic, Generic1, NFData, NFData1)
--   
--   data Colour = Red | Green | Blue
--                 deriving (Generic, NFData)
--   </pre>
--   
--   <h3>Compatibility with previous <tt>deepseq</tt> versions</h3>
--   
--   Prior to version 1.4.0.0, the default implementation of the <a>rnf</a>
--   method was defined as
--   
--   <pre>
--   <a>rnf</a> a = <a>seq</a> a ()
--   </pre>
--   
--   However, starting with <tt>deepseq-1.4.0.0</tt>, the default
--   implementation is based on <tt>DefaultSignatures</tt> allowing for
--   more accurate auto-derived <a>NFData</a> instances. If you need the
--   previously used exact default <a>rnf</a> method implementation
--   semantics, use
--   
--   <pre>
--   instance NFData Colour where rnf x = seq x ()
--   </pre>
--   
--   or alternatively
--   
--   <pre>
--   instance NFData Colour where rnf = rwhnf
--   </pre>
--   
--   or
--   
--   <pre>
--   {-# LANGUAGE BangPatterns #-}
--   instance NFData Colour where rnf !_ = ()
--   </pre>
rnf :: NFData a => a -> ()

-- | Reduce to weak head normal form
--   
--   Equivalent to <tt>\x -&gt; <a>seq</a> x ()</tt>.
--   
--   Useful for defining <a>NFData</a> for types for which NF=WHNF holds.
--   
--   <pre>
--   data T = C1 | C2 | C3
--   instance NFData T where rnf = rwhnf
--   </pre>
rwhnf :: a -> ()

-- | Lift the standard <a>rnf</a> function through the type constructor.
rnf2 :: (NFData2 p, NFData a, NFData b) => p a b -> ()

-- | Lift the standard <a>rnf</a> function through the type constructor.
rnf1 :: (NFData1 f, NFData a) => f a -> ()

-- | a variant of <a>deepseq</a> that is useful in some circumstances:
--   
--   <pre>
--   force x = x `deepseq` x
--   </pre>
--   
--   <tt>force x</tt> fully evaluates <tt>x</tt>, and then returns it. Note
--   that <tt>force x</tt> only performs evaluation when the value of
--   <tt>force x</tt> itself is demanded, so essentially it turns shallow
--   evaluation into deep evaluation.
--   
--   <a>force</a> can be conveniently used in combination with
--   <tt>ViewPatterns</tt>:
--   
--   <pre>
--   {-# LANGUAGE BangPatterns, ViewPatterns #-}
--   import Control.DeepSeq
--   
--   someFun :: ComplexData -&gt; SomeResult
--   someFun (force -&gt; !arg) = {- 'arg' will be fully evaluated -}
--   </pre>
--   
--   Another useful application is to combine <a>force</a> with
--   <a>evaluate</a> in order to force deep evaluation relative to other
--   <a>IO</a> operations:
--   
--   <pre>
--   import Control.Exception (evaluate)
--   import Control.DeepSeq
--   
--   main = do
--     result &lt;- evaluate $ force $ pureComputation
--     {- 'result' will be fully evaluated at this point -}
--     return ()
--   </pre>
--   
--   Finally, here's an exception safe variant of the <tt>readFile'</tt>
--   example:
--   
--   <pre>
--   readFile' :: FilePath -&gt; IO String
--   readFile' fn = bracket (openFile fn ReadMode) hClose $ \h -&gt;
--                          evaluate . force =&lt;&lt; hGetContents h
--   </pre>
force :: NFData a => a -> a

-- | <a>deepseq</a>: fully evaluates the first argument, before returning
--   the second.
--   
--   The name <a>deepseq</a> is used to illustrate the relationship to
--   <a>seq</a>: where <a>seq</a> is shallow in the sense that it only
--   evaluates the top level of its argument, <a>deepseq</a> traverses the
--   entire data structure evaluating it completely.
--   
--   <a>deepseq</a> can be useful for forcing pending exceptions,
--   eradicating space leaks, or forcing lazy I/O to happen. It is also
--   useful in conjunction with parallel Strategies (see the
--   <tt>parallel</tt> package).
--   
--   There is no guarantee about the ordering of evaluation. The
--   implementation may evaluate the components of the structure in any
--   order or in parallel. To impose an actual order on evaluation, use
--   <tt>pseq</tt> from <a>Control.Parallel</a> in the <tt>parallel</tt>
--   package.
deepseq :: NFData a => a -> b -> b

-- | Deeply strict version of <a>&lt;$&gt;</a>.
(<$!!>) :: (Monad m, NFData b) => (a -> b) -> m a -> m b
infixl 4 <$!!>

-- | the deep analogue of <a>$!</a>. In the expression <tt>f $!! x</tt>,
--   <tt>x</tt> is fully evaluated before the function <tt>f</tt> is
--   applied to it.
($!!) :: NFData a => (a -> b) -> a -> b
infixr 0 $!!

-- | A difference list is an abstraction representing a list that supports
--   &lt;math&gt;(<tt>1</tt>) <a>append</a> and <a>snoc</a> operations,
--   making it useful for replacing frequent applications of <a>++</a> such
--   as logging and pretty printing (esp. if those uses of <a>++</a> are
--   left-nested).
data DList a

-- | Swap the <a>Left</a> and <a>Right</a> sides of an <a>Either</a>.
--   
--   <pre>
--   &gt;&gt;&gt; swapEither (Right 3)
--   Left 3
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; swapEither (Left "error")
--   Right "error"
--   </pre>
swapEither :: Either e a -> Either a e

-- | Generalize <tt>Either e</tt> as <tt>MonadError e m</tt>.
--   
--   If the argument has form <tt>Left e</tt>, an error is produced in the
--   monad via <a>throwError</a>. Otherwise, the <tt>Right a</tt> part is
--   forwarded.
eitherToError :: MonadError e m => Either e a -> m a

-- | Maybe produce a <a>Right</a>, otherwise produce a <a>Left</a>.
--   
--   <pre>
--   &gt;&gt;&gt; maybeToRight "default" (Just 12)
--   Right 12
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; maybeToRight "default" Nothing
--   Left "default"
--   </pre>
maybeToRight :: b -> Maybe a -> Either b a

-- | Maybe produce a <a>Left</a>, otherwise produce a <a>Right</a>.
--   
--   <pre>
--   &gt;&gt;&gt; maybeToLeft "default" (Just 12)
--   Left 12
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; maybeToLeft "default" Nothing
--   Right "default"
--   </pre>
maybeToLeft :: b -> Maybe a -> Either a b

-- | Maybe get the <a>Right</a> side of an <a>Either</a>.
--   
--   <pre>
--   <a>rightToMaybe</a> ≡ <a>either</a> (<a>const</a> <a>Nothing</a>) <a>Just</a>
--   </pre>
--   
--   Using <tt>Control.Lens</tt>:
--   
--   <pre>
--   <a>rightToMaybe</a> ≡ preview _Right
--   <a>rightToMaybe</a> x ≡ x^?_Right
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; rightToMaybe (Left 12)
--   Nothing
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; rightToMaybe (Right 12)
--   Just 12
--   </pre>
rightToMaybe :: Either a b -> Maybe b

-- | Maybe get the <a>Left</a> side of an <a>Either</a>.
--   
--   <pre>
--   <a>leftToMaybe</a> ≡ <a>either</a> <a>Just</a> (<a>const</a> <a>Nothing</a>)
--   </pre>
--   
--   Using <tt>Control.Lens</tt>:
--   
--   <pre>
--   <a>leftToMaybe</a> ≡ preview _Left
--   <a>leftToMaybe</a> x ≡ x^?_Left
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; leftToMaybe (Left 12)
--   Just 12
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; leftToMaybe (Right 12)
--   Nothing
--   </pre>
leftToMaybe :: Either a b -> Maybe a

-- | A synonym of <a>whenLeft</a>.
unlessRight :: Applicative m => Either a b -> (a -> m ()) -> m ()

-- | A synonym of <a>whenRight</a>.
unlessLeft :: Applicative m => Either a b -> (b -> m ()) -> m ()

-- | The <a>whenRight</a> function takes an <a>Either</a> value and a
--   function which returns a monad. The monad is only executed when the
--   given argument takes the form <tt><a>Right</a> _</tt>, otherwise it
--   does nothing.
--   
--   Using <tt>Data.Foldable</tt>:
--   
--   <pre>
--   <a>whenRight</a> ≡ <tt>forM_</tt>
--   </pre>
--   
--   Using <tt>Control.Lens</tt>:
--   
--   <pre>
--   <a>whenRight</a> ≡ forOf_ _Right
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; whenRight (Right 12) print
--   12
--   </pre>
whenRight :: Applicative m => Either a b -> (b -> m ()) -> m ()

-- | The <a>whenLeft</a> function takes an <a>Either</a> value and a
--   function which returns a monad. The monad is only executed when the
--   given argument takes the form <tt><a>Left</a> _</tt>, otherwise it
--   does nothing.
--   
--   Using <tt>Control.Lens</tt>:
--   
--   <pre>
--   <a>whenLeft</a> ≡ forOf_ _Left
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; whenLeft (Left 12) print
--   12
--   </pre>
whenLeft :: Applicative m => Either a b -> (a -> m ()) -> m ()

-- | The <a>mapBoth</a> function takes two functions and applies the first
--   if iff the value takes the form <tt><a>Left</a> _</tt> and the second
--   if the value takes the form <tt><a>Right</a> _</tt>.
--   
--   Using <tt>Data.Bifunctor</tt>:
--   
--   <pre>
--   <a>mapBoth</a> = bimap
--   </pre>
--   
--   Using <tt>Control.Arrow</tt>:
--   
--   <pre>
--   <a>mapBoth</a> = (<a>+++</a>)
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; mapBoth (*2) (*3) (Left 4)
--   Left 8
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; mapBoth (*2) (*3) (Right 4)
--   Right 12
--   </pre>
mapBoth :: (a -> c) -> (b -> d) -> Either a b -> Either c d

-- | Extracts the element out of a <a>Right</a> and throws an error if its
--   argument take the form <tt><a>Left</a> _</tt>.
--   
--   Using <tt>Control.Lens</tt>:
--   
--   <pre>
--   <a>fromRight'</a> x ≡ x^?!_Right
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; fromRight' (Right 12)
--   12
--   </pre>
fromRight' :: Either a b -> b

-- | Extracts the element out of a <a>Left</a> and throws an error if its
--   argument take the form <tt><a>Right</a> _</tt>.
--   
--   Using <tt>Control.Lens</tt>:
--   
--   <pre>
--   <a>fromLeft'</a> x ≡ x^?!_Left
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; fromLeft' (Left 12)
--   12
--   </pre>
fromLeft' :: Either a b -> a

-- | The parameterizable maybe monad, obtained by composing an arbitrary
--   monad with the <a>Maybe</a> monad.
--   
--   Computations are actions that may produce a value or exit.
--   
--   The <a>return</a> function yields a computation that produces that
--   value, while <tt>&gt;&gt;=</tt> sequences two subcomputations, exiting
--   if either computation does.
newtype MaybeT (m :: Type -> Type) a
MaybeT :: m (Maybe a) -> MaybeT (m :: Type -> Type) a

-- | A monad transformer that adds exceptions to other monads.
--   
--   <tt>ExceptT</tt> constructs a monad parameterized over two things:
--   
--   <ul>
--   <li>e - The exception type.</li>
--   <li>m - The inner monad.</li>
--   </ul>
--   
--   The <a>return</a> function yields a computation that produces the
--   given value, while <tt>&gt;&gt;=</tt> sequences two subcomputations,
--   exiting on the first exception.
newtype ExceptT e (m :: Type -> Type) a
ExceptT :: m (Either e a) -> ExceptT e (m :: Type -> Type) a

-- | Lazily generate all elements of a <a>Cyclic</a> group using its
--   <a>generator</a>.
--   
--   <i>Note:</i> Fuses, terminates if the underlying group is finite.
generated' :: (Eq a, Cyclic a) => [a]

-- | Generate all elements of a <a>Cyclic</a> group using its
--   <a>generator</a>.
--   
--   <i>Note:</i> Fuses, does not terminate even for finite groups.
generated :: Cyclic a => [a]

-- | A <a>Group</a> is a <a>Monoid</a> plus a function, <a>invert</a>, such
--   that:
--   
--   <pre>
--   a &lt;&gt; invert a == mempty
--   </pre>
--   
--   <pre>
--   invert a &lt;&gt; a == mempty
--   </pre>
class Monoid m => Group m
invert :: Group m => m -> m

-- | Group subtraction: <tt>x ~~ y == x &lt;&gt; invert y</tt>
(~~) :: Group m => m -> m -> m

-- | <pre>
--   <a>pow</a> a n == a &lt;&gt; a &lt;&gt; ... &lt;&gt; a
--   </pre>
--   
--   <pre>
--   (n lots of a)
--   </pre>
--   
--   If n is negative, the result is inverted.
pow :: (Group m, Integral x) => m -> x -> m
infixl 7 ~~

-- | An <a>Abelian</a> group is a <a>Group</a> that follows the rule:
--   
--   <pre>
--   a &lt;&gt; b == b &lt;&gt; a
--   </pre>
class Group g => Abelian g

-- | A <a>Group</a> G is <a>Cyclic</a> if there exists an element x of G
--   such that for all y in G, there exists an n, such that
--   
--   <pre>
--   y = pow x n
--   </pre>
class Group a => Cyclic a

-- | The generator of the <a>Cyclic</a> group.
generator :: Cyclic a => a

-- | <a>Hashed</a> cannot be <a>Traversable</a>
traverseHashed :: (Hashable b, Functor f) => (a -> f b) -> Hashed a -> f (Hashed b)

-- | <a>Hashed</a> cannot be <a>Functor</a>
mapHashed :: Hashable b => (a -> b) -> Hashed a -> Hashed b

-- | <a>hash</a> has <a>Eq</a> requirement.
hashedHash :: Hashed a -> Int

-- | Unwrap hashed value.
unhashed :: Hashed a -> a

-- | Wrap a hashable value, caching the <a>hash</a> function result.
hashed :: Hashable a => a -> Hashed a

-- | Compute a hash value for the content of this <a>ByteArray#</a>,
--   beginning at the specified offset, using specified number of bytes.
hashByteArray :: ByteArray# -> Int -> Int -> Int

-- | Compute a hash value for the content of this pointer.
hashPtr :: Ptr a -> Int -> IO Int

-- | Transform a value into a <a>Hashable</a> value, then hash the
--   transformed value using the given salt.
--   
--   This is a useful shorthand in cases where a type can easily be mapped
--   to another type that is already an instance of <a>Hashable</a>.
--   Example:
--   
--   <pre>
--   data Foo = Foo | Bar
--            deriving (Enum)
--   
--   instance Hashable Foo where
--       hashWithSalt = hashUsing fromEnum
--   </pre>
hashUsing :: Hashable b => (a -> b) -> Int -> a -> Int

-- | The class of types that can be converted to a hash value.
--   
--   Minimal implementation: <a>hashWithSalt</a>.
--   
--   <i>Note:</i> the hash is not guaranteed to be stable across library
--   versions, operating systems or architectures. For stable hashing use
--   named hashes: SHA256, CRC32 etc.
--   
--   If you are looking for <a>Hashable</a> instance in <tt>time</tt>
--   package, check <a>time-compat</a>
class Eq a => Hashable a

-- | Return a hash value for the argument, using the given salt.
--   
--   The general contract of <a>hashWithSalt</a> is:
--   
--   <ul>
--   <li>If two values are equal according to the <a>==</a> method, then
--   applying the <a>hashWithSalt</a> method on each of the two values
--   <i>must</i> produce the same integer result if the same salt is used
--   in each case.</li>
--   <li>It is <i>not</i> required that if two values are unequal according
--   to the <a>==</a> method, then applying the <a>hashWithSalt</a> method
--   on each of the two values must produce distinct integer results.
--   However, the programmer should be aware that producing distinct
--   integer results for unequal values may improve the performance of
--   hashing-based data structures.</li>
--   <li>This method can be used to compute different hash values for the
--   same input by providing a different salt in each application of the
--   method. This implies that any instance that defines
--   <a>hashWithSalt</a> <i>must</i> make use of the salt in its
--   implementation.</li>
--   <li><a>hashWithSalt</a> may return negative <a>Int</a> values.</li>
--   </ul>
hashWithSalt :: Hashable a => Int -> a -> Int

-- | Like <a>hashWithSalt</a>, but no salt is used. The default
--   implementation uses <a>hashWithSalt</a> with some default salt.
--   Instances might want to implement this method to provide a more
--   efficient implementation than the default implementation.
hash :: Hashable a => a -> Int
infixl 0 `hashWithSalt`

-- | A hashable value along with the result of the <a>hash</a> function.
data Hashed a

-- | Compute a hash value for the content of this <a>ByteArray#</a>, using
--   an initial salt.
--   
--   This function can for example be used to hash non-contiguous segments
--   of memory as if they were one contiguous segment, by using the output
--   of one hash as the salt for the next.
hashByteArrayWithSalt :: ByteArray# -> Int -> Int -> Salt -> Salt

-- | Compute a hash value for the content of this pointer, using an initial
--   salt.
--   
--   This function can for example be used to hash non-contiguous segments
--   of memory as if they were one contiguous segment, by using the output
--   of one hash as the salt for the next.
hashPtrWithSalt :: Ptr a -> Int -> Salt -> IO Salt

-- | Formally, the class <a>Profunctor</a> represents a profunctor from
--   <tt>Hask</tt> -&gt; <tt>Hask</tt>.
--   
--   Intuitively it is a bifunctor where the first argument is
--   contravariant and the second argument is covariant.
--   
--   You can define a <a>Profunctor</a> by either defining <a>dimap</a> or
--   by defining both <a>lmap</a> and <a>rmap</a>.
--   
--   If you supply <a>dimap</a>, you should ensure that:
--   
--   <pre>
--   <a>dimap</a> <a>id</a> <a>id</a> ≡ <a>id</a>
--   </pre>
--   
--   If you supply <a>lmap</a> and <a>rmap</a>, ensure:
--   
--   <pre>
--   <a>lmap</a> <a>id</a> ≡ <a>id</a>
--   <a>rmap</a> <a>id</a> ≡ <a>id</a>
--   </pre>
--   
--   If you supply both, you should also ensure:
--   
--   <pre>
--   <a>dimap</a> f g ≡ <a>lmap</a> f <a>.</a> <a>rmap</a> g
--   </pre>
--   
--   These ensure by parametricity:
--   
--   <pre>
--   <a>dimap</a> (f <a>.</a> g) (h <a>.</a> i) ≡ <a>dimap</a> g h <a>.</a> <a>dimap</a> f i
--   <a>lmap</a> (f <a>.</a> g) ≡ <a>lmap</a> g <a>.</a> <a>lmap</a> f
--   <a>rmap</a> (f <a>.</a> g) ≡ <a>rmap</a> f <a>.</a> <a>rmap</a> g
--   </pre>
class Profunctor (p :: Type -> Type -> Type)

-- | Map over both arguments at the same time.
--   
--   <pre>
--   <a>dimap</a> f g ≡ <a>lmap</a> f <a>.</a> <a>rmap</a> g
--   </pre>
dimap :: Profunctor p => (a -> b) -> (c -> d) -> p b c -> p a d

-- | Map the first argument contravariantly.
--   
--   <pre>
--   <a>lmap</a> f ≡ <a>dimap</a> f <a>id</a>
--   </pre>
lmap :: Profunctor p => (a -> b) -> p b c -> p a c

-- | Map the second argument covariantly.
--   
--   <pre>
--   <a>rmap</a> ≡ <a>dimap</a> <a>id</a>
--   </pre>
rmap :: Profunctor p => (b -> c) -> p a b -> p a c

-- | Strictly map the second argument argument covariantly with a function
--   that is assumed operationally to be a cast, such as a newtype
--   constructor.
--   
--   <i>Note:</i> This operation is explicitly <i>unsafe</i> since an
--   implementation may choose to use <tt>unsafeCoerce</tt> to implement
--   this combinator and it has no way to validate that your function meets
--   the requirements.
--   
--   If you implement this combinator with <tt>unsafeCoerce</tt>, then you
--   are taking upon yourself the obligation that you don't use GADT-like
--   tricks to distinguish values.
--   
--   If you import <a>Data.Profunctor.Unsafe</a> you are taking upon
--   yourself the obligation that you will only call this with a first
--   argument that is operationally identity.
--   
--   The semantics of this function with respect to bottoms should match
--   the default definition:
--   
--   <pre>
--   (<a>#.</a>) ≡ \_ -&gt; \p -&gt; p `seq` <a>rmap</a> <a>coerce</a> p
--   </pre>
(#.) :: forall a b c q. (Profunctor p, Coercible c b) => q b c -> p a b -> p a c

-- | Strictly map the first argument argument contravariantly with a
--   function that is assumed operationally to be a cast, such as a newtype
--   constructor.
--   
--   <i>Note:</i> This operation is explicitly <i>unsafe</i> since an
--   implementation may choose to use <tt>unsafeCoerce</tt> to implement
--   this combinator and it has no way to validate that your function meets
--   the requirements.
--   
--   If you implement this combinator with <tt>unsafeCoerce</tt>, then you
--   are taking upon yourself the obligation that you don't use GADT-like
--   tricks to distinguish values.
--   
--   If you import <a>Data.Profunctor.Unsafe</a> you are taking upon
--   yourself the obligation that you will only call this with a second
--   argument that is operationally identity.
--   
--   <pre>
--   (<a>.#</a>) ≡ \p -&gt; p `seq` \f -&gt; <a>lmap</a> <a>coerce</a> p
--   </pre>
(.#) :: forall a b c q. (Profunctor p, Coercible b a) => p b c -> q a b -> p a c
infixr 9 #.
infixl 8 .#

-- | A generic implementation of <a>invmap</a>.
genericInvmap :: (Generic1 f, Invariant (Rep1 f)) => (a -> b) -> (b -> a) -> f a -> f b

-- | Every <a>Profunctor</a> is also an <a>Invariant2</a> functor.
invmap2Profunctor :: Profunctor f => (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> f a b -> f c d

-- | Every <a>Bifunctor</a> is also an <a>Invariant2</a> functor.
invmap2Bifunctor :: Bifunctor f => (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> f a b -> f c d

-- | An <a>Arrow</a> with the same input and output types can be seen as an
--   <a>Invariant</a> functor.
invmapArrow :: Arrow arr => (a -> b) -> (b -> a) -> arr a a -> arr b b

-- | A <a>Profunctor</a> with the same input and output types can be seen
--   as an <a>Invariant</a> functor.
invmapProfunctor :: Profunctor p => (a -> b) -> (b -> a) -> p a a -> p b b

-- | Every <a>Contravariant</a> functor is also an <a>Invariant</a>
--   functor.
invmapContravariant :: Contravariant f => (a -> b) -> (b -> a) -> f a -> f b

-- | Every <a>Functor</a> is also an <a>Invariant</a> functor.
invmapFunctor :: Functor f => (a -> b) -> (b -> a) -> f a -> f b

-- | Any <tt>* -&gt; *</tt> type parametric in the argument permits an
--   instance of <tt>Invariant</tt>.
--   
--   Instances should satisfy the following laws:
--   
--   <pre>
--   invmap id id = id
--   invmap f2 f2' . invmap f1 f1' = invmap (f2 . f1) (f1' . f2')
--   </pre>
class Invariant (f :: Type -> TYPE LiftedRep)
invmap :: Invariant f => (a -> b) -> (b -> a) -> f a -> f b

-- | Wrap a <a>Functor</a> to be used as a member of <a>Invariant</a>.
newtype WrappedFunctor (f :: k -> Type) (a :: k)
WrapFunctor :: f a -> WrappedFunctor (f :: k -> Type) (a :: k)
[unwrapFunctor] :: WrappedFunctor (f :: k -> Type) (a :: k) -> f a

-- | Wrap a <a>Contravariant</a> functor to be used as a member of
--   <a>Invariant</a>.
newtype WrappedContravariant (f :: k -> Type) (a :: k)
WrapContravariant :: f a -> WrappedContravariant (f :: k -> Type) (a :: k)
[unwrapContravariant] :: WrappedContravariant (f :: k -> Type) (a :: k) -> f a

-- | Any <tt>* -&gt; * -&gt; *</tt> type parametric in both arguments
--   permits an instance of <tt>Invariant2</tt>.
--   
--   Instances should satisfy the following laws:
--   
--   <pre>
--   invmap2 id id id id = id
--   invmap2 f2 f2' g2 g2' . invmap2 f1 f1' g1 g1' =
--     invmap2 (f2 . f1) (f1' . f2') (g2 . g1) (g1' . g2')
--   </pre>
class Invariant2 (f :: Type -> Type -> Type)
invmap2 :: Invariant2 f => (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> f a b -> f c d

-- | Wrap a <a>Profunctor</a> to be used as a member of <a>Invariant2</a>.
newtype WrappedProfunctor (p :: k -> k1 -> Type) (a :: k) (b :: k1)
WrapProfunctor :: p a b -> WrappedProfunctor (p :: k -> k1 -> Type) (a :: k) (b :: k1)
[unwrapProfunctor] :: WrappedProfunctor (p :: k -> k1 -> Type) (a :: k) (b :: k1) -> p a b

-- | A <a>Profunctor</a> with the same input and output types can be seen
--   as an <a>Invariant</a> functor.
newtype InvariantProfunctor (p :: k -> k -> Type) (a :: k)
InvariantProfunctor :: p a a -> InvariantProfunctor (p :: k -> k -> Type) (a :: k)

-- | An <a>Arrow</a> with the same input and output types can be seen as an
--   <a>Invariant</a> functor.
newtype InvariantArrow (c :: k -> k -> Type) (a :: k)
InvariantArrow :: c a a -> InvariantArrow (c :: k -> k -> Type) (a :: k)

-- | The class of monad transformers. Instances should satisfy the
--   following laws, which state that <a>lift</a> is a monad
--   transformation:
--   
--   <ul>
--   <li><pre><a>lift</a> . <a>return</a> = <a>return</a></pre></li>
--   <li><pre><a>lift</a> (m &gt;&gt;= f) = <a>lift</a> m &gt;&gt;=
--   (<a>lift</a> . f)</pre></li>
--   </ul>
class MonadTrans (t :: Type -> Type -> Type -> Type)

-- | Lift a computation from the argument monad to the constructed monad.
lift :: (MonadTrans t, Monad m) => m a -> t m a
class (Monoid w, Monad m) => MonadWriter w (m :: Type -> Type) | m -> w

-- | <tt><a>writer</a> (a,w)</tt> embeds a simple writer action.
writer :: MonadWriter w m => (a, w) -> m a

-- | <tt><a>tell</a> w</tt> is an action that produces the output
--   <tt>w</tt>.
tell :: MonadWriter w m => w -> m ()

-- | <tt><a>listen</a> m</tt> is an action that executes the action
--   <tt>m</tt> and adds its output to the value of the computation.
listen :: MonadWriter w m => m a -> m (a, w)

-- | <tt><a>pass</a> m</tt> is an action that executes the action
--   <tt>m</tt>, which returns a value and a function, and returns the
--   value, applying the function to the output.
pass :: MonadWriter w m => m (a, w -> w) -> m a

-- | <tt><a>listens</a> f m</tt> is an action that executes the action
--   <tt>m</tt> and adds the result of applying <tt>f</tt> to the output to
--   the value of the computation.
--   
--   <ul>
--   <li><pre><a>listens</a> f m = <a>liftM</a> (id *** f) (<a>listen</a>
--   m)</pre></li>
--   </ul>
listens :: MonadWriter w m => (w -> b) -> m a -> m (a, b)

-- | <tt><a>censor</a> f m</tt> is an action that executes the action
--   <tt>m</tt> and applies the function <tt>f</tt> to its output, leaving
--   the return value unchanged.
--   
--   <ul>
--   <li><pre><a>censor</a> f m = <a>pass</a> (<a>liftM</a> (\x -&gt;
--   (x,f)) m)</pre></li>
--   </ul>
censor :: MonadWriter w m => (w -> w) -> m a -> m a

-- | A variant of <a>modify</a> in which the computation is strict in the
--   new state.
modify' :: MonadState s m => (s -> s) -> m ()

-- | Monadic state transformer.
--   
--   Maps an old state to a new state inside a state monad. The old state
--   is thrown away.
--   
--   <pre>
--   Main&gt; :t modify ((+1) :: Int -&gt; Int)
--   modify (...) :: (MonadState Int a) =&gt; a ()
--   </pre>
--   
--   This says that <tt>modify (+1)</tt> acts over any Monad that is a
--   member of the <tt>MonadState</tt> class, with an <tt>Int</tt> state.
modify :: MonadState s m => (s -> s) -> m ()

-- | Gets specific component of the state, using a projection function
--   supplied.
gets :: MonadState s m => (s -> a) -> m a

-- | Retrieves a function of the current environment.
asks :: MonadReader r m => (r -> a) -> m a

-- | The strategy of combining computations that can throw exceptions by
--   bypassing bound functions from the point an exception is thrown to the
--   point that it is handled.
--   
--   Is parameterized over the type of error information and the monad type
--   constructor. It is common to use <tt><a>Either</a> String</tt> as the
--   monad type constructor for an error monad in which error descriptions
--   take the form of strings. In that case and many other common cases the
--   resulting monad is already defined as an instance of the
--   <a>MonadError</a> class. You can also define your own error type
--   and/or use a monad type constructor other than <tt><a>Either</a>
--   <tt>String</tt></tt> or <tt><a>Either</a> <tt>IOError</tt></tt>. In
--   these cases you will have to explicitly define instances of the
--   <a>MonadError</a> class. (If you are using the deprecated
--   <a>Control.Monad.Error</a> or <a>Control.Monad.Trans.Error</a>, you
--   may also have to define an <a>Error</a> instance.)
class Monad m => MonadError e (m :: Type -> Type) | m -> e

-- | Is used within a monadic computation to begin exception processing.
throwError :: MonadError e m => e -> m a

-- | A handler function to handle previous errors and return to normal
--   execution. A common idiom is:
--   
--   <pre>
--   do { action1; action2; action3 } `catchError` handler
--   </pre>
--   
--   where the <tt>action</tt> functions can call <a>throwError</a>. Note
--   that <tt>handler</tt> and the do-block must have the same return type.
catchError :: MonadError e m => m a -> (e -> m a) -> m a

-- | Lifts an <tt><a>Either</a> e</tt> into any <tt><a>MonadError</a>
--   e</tt>.
--   
--   <pre>
--   do { val &lt;- liftEither =&lt;&lt; action1; action2 }
--   </pre>
--   
--   where <tt>action1</tt> returns an <a>Either</a> to represent errors.
liftEither :: MonadError e m => Either e a -> m a
class Monad m => MonadCont (m :: Type -> Type)

-- | <tt>callCC</tt> (call-with-current-continuation) calls a function with
--   the current continuation as its argument. Provides an escape
--   continuation mechanism for use with Continuation monads. Escape
--   continuations allow to abort the current computation and return a
--   value immediately. They achieve a similar effect to <a>throwError</a>
--   and <a>catchError</a> within an <a>Error</a> monad. Advantage of this
--   function over calling <tt>return</tt> is that it makes the
--   continuation explicit, allowing more flexibility and better control
--   (see examples in <a>Control.Monad.Cont</a>).
--   
--   The standard idiom used with <tt>callCC</tt> is to provide a
--   lambda-expression to name the continuation. Then calling the named
--   continuation anywhere within its scope will escape from the
--   computation, even if it is many layers deep within nested
--   computations.
callCC :: MonadCont m => ((a -> m b) -> m a) -> m a

-- | Construct a continuation-passing computation from a function. (The
--   inverse of <a>runCont</a>)
cont :: ((a -> r) -> r) -> Cont r a

-- | Apply a function to transform the result of a continuation-passing
--   computation.
--   
--   <ul>
--   <li><pre><a>runCont</a> (<a>mapCont</a> f m) = f . <a>runCont</a>
--   m</pre></li>
--   </ul>
mapCont :: (r -> r) -> Cont r a -> Cont r a

-- | Apply a function to transform the result of a continuation-passing
--   computation. This has a more restricted type than the <tt>map</tt>
--   operations for other monad transformers, because <a>ContT</a> does not
--   define a functor in the category of monads.
--   
--   <ul>
--   <li><pre><a>runContT</a> (<a>mapContT</a> f m) = f . <a>runContT</a>
--   m</pre></li>
--   </ul>
mapContT :: forall {k} m (r :: k) a. (m r -> m r) -> ContT r m a -> ContT r m a

-- | The result of running a CPS computation with a given final
--   continuation. (The inverse of <a>cont</a>)
runCont :: Cont r a -> (a -> r) -> r

-- | Apply a function to transform the continuation passed to a CPS
--   computation.
--   
--   <ul>
--   <li><pre><a>runCont</a> (<a>withCont</a> f m) = <a>runCont</a> m .
--   f</pre></li>
--   </ul>
withCont :: ((b -> r) -> a -> r) -> Cont r a -> Cont r b

-- | Apply a function to transform the continuation passed to a CPS
--   computation.
--   
--   <ul>
--   <li><pre><a>runContT</a> (<a>withContT</a> f m) = <a>runContT</a> m .
--   f</pre></li>
--   </ul>
withContT :: forall {k} b m (r :: k) a. ((b -> m r) -> a -> m r) -> ContT r m a -> ContT r m b

-- | Continuation monad. <tt>Cont r a</tt> is a CPS ("continuation-passing
--   style") computation that produces an intermediate result of type
--   <tt>a</tt> within a CPS computation whose final result type is
--   <tt>r</tt>.
--   
--   The <tt>return</tt> function simply creates a continuation which
--   passes the value on.
--   
--   The <tt>&gt;&gt;=</tt> operator adds the bound function into the
--   continuation chain.
type Cont r = ContT r Identity

-- | The continuation monad transformer. Can be used to add continuation
--   handling to any type constructor: the <a>Monad</a> instance and most
--   of the operations do not require <tt>m</tt> to be a monad.
--   
--   <a>ContT</a> is not a functor on the category of monads, and many
--   operations cannot be lifted through it.
newtype ContT (r :: k) (m :: k -> Type) a
ContT :: ((a -> m r) -> m r) -> ContT (r :: k) (m :: k -> Type) a
[runContT] :: ContT (r :: k) (m :: k -> Type) a -> (a -> m r) -> m r

-- | Map the unwrapped computation using the given function.
--   
--   <ul>
--   <li><pre><a>runExcept</a> (<a>mapExcept</a> f m) = f (<a>runExcept</a>
--   m)</pre></li>
--   </ul>
mapExcept :: (Either e a -> Either e' b) -> Except e a -> Except e' b

-- | Map the unwrapped computation using the given function.
--   
--   <ul>
--   <li><pre><a>runExceptT</a> (<a>mapExceptT</a> f m) = f
--   (<a>runExceptT</a> m)</pre></li>
--   </ul>
mapExceptT :: (m (Either e a) -> n (Either e' b)) -> ExceptT e m a -> ExceptT e' n b

-- | Extractor for computations in the exception monad. (The inverse of
--   <a>except</a>).
runExcept :: Except e a -> Either e a

-- | The inverse of <a>ExceptT</a>.
runExceptT :: ExceptT e m a -> m (Either e a)

-- | Transform any exceptions thrown by the computation using the given
--   function (a specialization of <a>withExceptT</a>).
withExcept :: (e -> e') -> Except e a -> Except e' a

-- | Transform any exceptions thrown by the computation using the given
--   function.
withExceptT :: forall (m :: Type -> Type) e e' a. Functor m => (e -> e') -> ExceptT e m a -> ExceptT e' m a

-- | The parameterizable exception monad.
--   
--   Computations are either exceptions or normal values.
--   
--   The <a>return</a> function returns a normal value, while
--   <tt>&gt;&gt;=</tt> exits on the first exception. For a variant that
--   continues after an error and collects all the errors, see
--   <a>Errors</a>.
type Except e = ExceptT e Identity

-- | Transform the value returned by a <tt>Reader</tt>.
--   
--   <ul>
--   <li><pre><a>runReader</a> (<a>mapReader</a> f m) = f .
--   <a>runReader</a> m</pre></li>
--   </ul>
mapReader :: (a -> b) -> Reader r a -> Reader r b

-- | Transform the computation inside a <tt>ReaderT</tt>.
--   
--   <ul>
--   <li><pre><a>runReaderT</a> (<a>mapReaderT</a> f m) = f .
--   <a>runReaderT</a> m</pre></li>
--   </ul>
mapReaderT :: (m a -> n b) -> ReaderT r m a -> ReaderT r n b

-- | Runs a <tt>Reader</tt> and extracts the final value from it. (The
--   inverse of <a>reader</a>.)
runReader :: Reader r a -> r -> a

-- | Execute a computation in a modified environment (a specialization of
--   <a>withReaderT</a>).
--   
--   <ul>
--   <li><pre><a>runReader</a> (<a>withReader</a> f m) = <a>runReader</a> m
--   . f</pre></li>
--   </ul>
withReader :: (r' -> r) -> Reader r a -> Reader r' a

-- | Execute a computation in a modified environment (a more general
--   version of <a>local</a>).
--   
--   <ul>
--   <li><pre><a>runReaderT</a> (<a>withReaderT</a> f m) =
--   <a>runReaderT</a> m . f</pre></li>
--   </ul>
withReaderT :: forall r' r (m :: Type -> Type) a. (r' -> r) -> ReaderT r m a -> ReaderT r' m a

-- | The parameterizable reader monad.
--   
--   Computations are functions of a shared environment.
--   
--   The <a>return</a> function ignores the environment, while
--   <tt>&gt;&gt;=</tt> passes the inherited environment to both
--   subcomputations.
type Reader r = ReaderT r Identity

-- | The reader monad transformer, which adds a read-only environment to
--   the given monad.
--   
--   The <a>return</a> function ignores the environment, while
--   <tt>&gt;&gt;=</tt> passes the inherited environment to both
--   subcomputations.
newtype ReaderT r (m :: Type -> Type) a
ReaderT :: (r -> m a) -> ReaderT r (m :: Type -> Type) a
[runReaderT] :: ReaderT r (m :: Type -> Type) a -> r -> m a

-- | Evaluate a state computation with the given initial state and return
--   the final value, discarding the final state.
--   
--   <ul>
--   <li><pre><a>evalState</a> m s = <a>fst</a> (<a>runState</a> m
--   s)</pre></li>
--   </ul>
evalState :: State s a -> s -> a

-- | Evaluate a state computation with the given initial state and return
--   the final value, discarding the final state.
--   
--   <ul>
--   <li><pre><a>evalStateT</a> m s = <a>liftM</a> <a>fst</a>
--   (<a>runStateT</a> m s)</pre></li>
--   </ul>
evalStateT :: Monad m => StateT s m a -> s -> m a

-- | Evaluate a state computation with the given initial state and return
--   the final state, discarding the final value.
--   
--   <ul>
--   <li><pre><a>execState</a> m s = <a>snd</a> (<a>runState</a> m
--   s)</pre></li>
--   </ul>
execState :: State s a -> s -> s

-- | Evaluate a state computation with the given initial state and return
--   the final state, discarding the final value.
--   
--   <ul>
--   <li><pre><a>execStateT</a> m s = <a>liftM</a> <a>snd</a>
--   (<a>runStateT</a> m s)</pre></li>
--   </ul>
execStateT :: Monad m => StateT s m a -> s -> m s

-- | Map both the return value and final state of a computation using the
--   given function.
--   
--   <ul>
--   <li><pre><a>runState</a> (<a>mapState</a> f m) = f . <a>runState</a>
--   m</pre></li>
--   </ul>
mapState :: ((a, s) -> (b, s)) -> State s a -> State s b

-- | Map both the return value and final state of a computation using the
--   given function.
--   
--   <ul>
--   <li><pre><a>runStateT</a> (<a>mapStateT</a> f m) = f .
--   <a>runStateT</a> m</pre></li>
--   </ul>
mapStateT :: (m (a, s) -> n (b, s)) -> StateT s m a -> StateT s n b

-- | Unwrap a state monad computation as a function. (The inverse of
--   <a>state</a>.)
runState :: State s a -> s -> (a, s)

-- | <tt><a>withState</a> f m</tt> executes action <tt>m</tt> on a state
--   modified by applying <tt>f</tt>.
--   
--   <ul>
--   <li><pre><a>withState</a> f m = <a>modify</a> f &gt;&gt; m</pre></li>
--   </ul>
withState :: (s -> s) -> State s a -> State s a

-- | <tt><a>withStateT</a> f m</tt> executes action <tt>m</tt> on a state
--   modified by applying <tt>f</tt>.
--   
--   <ul>
--   <li><pre><a>withStateT</a> f m = <a>modify</a> f &gt;&gt; m</pre></li>
--   </ul>
withStateT :: forall s (m :: Type -> Type) a. (s -> s) -> StateT s m a -> StateT s m a

-- | A state monad parameterized by the type <tt>s</tt> of the state to
--   carry.
--   
--   The <a>return</a> function leaves the state unchanged, while
--   <tt>&gt;&gt;=</tt> uses the final state of the first computation as
--   the initial state of the second.
type State s = StateT s Identity

-- | A state transformer monad parameterized by:
--   
--   <ul>
--   <li><tt>s</tt> - The state.</li>
--   <li><tt>m</tt> - The inner monad.</li>
--   </ul>
--   
--   The <a>return</a> function leaves the state unchanged, while
--   <tt>&gt;&gt;=</tt> uses the final state of the first computation as
--   the initial state of the second.
newtype StateT s (m :: Type -> Type) a
StateT :: (s -> m (a, s)) -> StateT s (m :: Type -> Type) a
[runStateT] :: StateT s (m :: Type -> Type) a -> s -> m (a, s)

-- | Extract the output from a writer computation.
--   
--   <ul>
--   <li><pre><a>execWriter</a> m = <a>snd</a> (<a>runWriter</a>
--   m)</pre></li>
--   </ul>
execWriter :: Writer w a -> w

-- | Extract the output from a writer computation.
--   
--   <ul>
--   <li><pre><a>execWriterT</a> m = <a>liftM</a> <a>snd</a>
--   (<a>runWriterT</a> m)</pre></li>
--   </ul>
execWriterT :: Monad m => WriterT w m a -> m w

-- | Map both the return value and output of a computation using the given
--   function.
--   
--   <ul>
--   <li><pre><a>runWriter</a> (<a>mapWriter</a> f m) = f (<a>runWriter</a>
--   m)</pre></li>
--   </ul>
mapWriter :: ((a, w) -> (b, w')) -> Writer w a -> Writer w' b

-- | Map both the return value and output of a computation using the given
--   function.
--   
--   <ul>
--   <li><pre><a>runWriterT</a> (<a>mapWriterT</a> f m) = f
--   (<a>runWriterT</a> m)</pre></li>
--   </ul>
mapWriterT :: (m (a, w) -> n (b, w')) -> WriterT w m a -> WriterT w' n b

-- | Unwrap a writer computation as a (result, output) pair. (The inverse
--   of <a>writer</a>.)
runWriter :: Writer w a -> (a, w)

-- | A writer monad parameterized by the type <tt>w</tt> of output to
--   accumulate.
--   
--   The <a>return</a> function produces the output <a>mempty</a>, while
--   <tt>&gt;&gt;=</tt> combines the outputs of the subcomputations using
--   <a>mappend</a>.
type Writer w = WriterT w Identity

-- | A writer monad parameterized by:
--   
--   <ul>
--   <li><tt>w</tt> - the output to accumulate.</li>
--   <li><tt>m</tt> - The inner monad.</li>
--   </ul>
--   
--   The <a>return</a> function produces the output <a>mempty</a>, while
--   <tt>&gt;&gt;=</tt> combines the outputs of the subcomputations using
--   <a>mappend</a>.
newtype WriterT w (m :: Type -> Type) a
WriterT :: m (a, w) -> WriterT w (m :: Type -> Type) a

-- | <pre>
--   <a>joinCoyoneda</a> <a>.</a> <a>produplicate</a> ≡ <a>id</a>
--   <a>produplicate</a> <a>.</a> <a>joinCoyoneda</a> ≡ <a>id</a>
--   <a>joinCoyoneda</a> ≡ <a>proextract</a>
--   </pre>
joinCoyoneda :: forall (p :: Type -> Type -> Type) a b. Coyoneda (Coyoneda p) a b -> Coyoneda p a b

-- | <pre>
--   <a>returnCoyoneda</a> <a>.</a> <a>proextract</a> ≡ <a>id</a>
--   <a>proextract</a> <a>.</a> <a>returnCoyoneda</a> ≡ <a>id</a>
--   <a>produplicate</a> ≡ <a>returnCoyoneda</a>
--   </pre>
returnCoyoneda :: p a b -> Coyoneda p a b

-- | <pre>
--   <a>projoin</a> <a>.</a> <a>duplicateYoneda</a> ≡ <a>id</a>
--   <a>duplicateYoneda</a> <a>.</a> <a>projoin</a> ≡ <a>id</a>
--   <a>duplicateYoneda</a> = <a>proreturn</a>
--   </pre>
duplicateYoneda :: forall (p :: Type -> Type -> Type) a b. Yoneda p a b -> Yoneda (Yoneda p) a b

-- | <pre>
--   <a>projoin</a> <a>.</a> <a>extractYoneda</a> ≡ <a>id</a>
--   <a>extractYoneda</a> <a>.</a> <a>projoin</a> ≡ <a>id</a>
--   <a>projoin</a> ≡ <a>extractYoneda</a>
--   </pre>
extractYoneda :: Yoneda p a b -> p a b

-- | This is the cofree profunctor given a data constructor of kind <tt>*
--   -&gt; * -&gt; *</tt>
newtype Yoneda (p :: Type -> Type -> Type) a b
Yoneda :: (forall x y. () => (x -> a) -> (b -> y) -> p x y) -> Yoneda (p :: Type -> Type -> Type) a b
[runYoneda] :: Yoneda (p :: Type -> Type -> Type) a b -> forall x y. () => (x -> a) -> (b -> y) -> p x y
data Coyoneda (p :: Type -> Type -> Type) a b
[Coyoneda] :: forall a x y b (p :: Type -> Type -> Type). (a -> x) -> (y -> b) -> p x y -> Coyoneda p a b
mapCayley :: forall {k1} {k2} {k3} f g (p :: k2 -> k3 -> k1) (x :: k2) (y :: k3). (forall (a :: k1). () => f a -> g a) -> Cayley f p x y -> Cayley g p x y

-- | Static arrows. Lifted by <a>Applicative</a>.
--   
--   <a>Cayley</a> has a polymorphic kind since <tt>5.6</tt>.
newtype Cayley (f :: k -> Type) (p :: k1 -> k2 -> k) (a :: k1) (b :: k2)
Cayley :: f (p a b) -> Cayley (f :: k -> Type) (p :: k1 -> k2 -> k) (a :: k1) (b :: k2)
[runCayley] :: Cayley (f :: k -> Type) (p :: k1 -> k2 -> k) (a :: k1) (b :: k2) -> f (p a b)
decomposeCodensity :: forall {k2} {k1} p (a :: k2) (b :: k1). Procompose (Codensity p) p a b -> p a b
uncurryRan :: forall {k1} {k2} {k3} (p :: k1 -> k2 -> Type) (q :: k3 -> k1 -> Type) (r :: k3 -> k2 -> Type). (p :-> Ran q r) -> Procompose p q :-> r
curryRan :: forall {k1} {k2} {k3} (p :: k1 -> k2 -> Type) (q :: k3 -> k1 -> Type) (r :: k3 -> k2 -> Type). (Procompose p q :-> r) -> p :-> Ran q r
precomposeRan :: forall {k} (q :: Type -> Type -> Type) (p :: TYPE LiftedRep -> k -> Type). Profunctor q => Procompose q (Ran p (->)) :-> Ran p q

-- | The 2-morphism that defines a right Kan extension.
--   
--   Note: When <tt>q</tt> is left adjoint to <tt><a>Ran</a> q (-&gt;)</tt>
--   then <a>decomposeRan</a> is the <tt>counit</tt> of the adjunction.
decomposeRan :: forall {k1} {k2} {k3} (q :: k1 -> k2 -> Type) (p :: k1 -> k3 -> Type). Procompose (Ran q p) q :-> p

-- | This represents the right Kan extension of a <a>Profunctor</a>
--   <tt>q</tt> along a <a>Profunctor</a> <tt>p</tt> in a limited version
--   of the 2-category of Profunctors where the only object is the category
--   Hask, 1-morphisms are profunctors composed and compose with Profunctor
--   composition, and 2-morphisms are just natural transformations.
--   
--   <a>Ran</a> has a polymorphic kind since <tt>5.6</tt>.
newtype Ran (p :: k -> k1 -> Type) (q :: k -> k2 -> Type) (a :: k1) (b :: k2)
Ran :: (forall (x :: k). () => p x a -> q x b) -> Ran (p :: k -> k1 -> Type) (q :: k -> k2 -> Type) (a :: k1) (b :: k2)
[runRan] :: Ran (p :: k -> k1 -> Type) (q :: k -> k2 -> Type) (a :: k1) (b :: k2) -> forall (x :: k). () => p x a -> q x b

-- | This represents the right Kan extension of a <a>Profunctor</a>
--   <tt>p</tt> along itself. This provides a generalization of the
--   "difference list" trick to profunctors.
--   
--   <a>Codensity</a> has a polymorphic kind since <tt>5.6</tt>.
newtype Codensity (p :: k -> k1 -> Type) (a :: k1) (b :: k1)
Codensity :: (forall (x :: k). () => p x a -> p x b) -> Codensity (p :: k -> k1 -> Type) (a :: k1) (b :: k1)
[runCodensity] :: Codensity (p :: k -> k1 -> Type) (a :: k1) (b :: k1) -> forall (x :: k). () => p x a -> p x b
mu :: forall {k1} (p :: k1 -> k1 -> Type). Category p => Procompose p p :-> p

-- | a <a>Category</a> that is also a <a>Profunctor</a> is a <a>Monoid</a>
--   in <tt>Prof</tt>
eta :: forall (p :: Type -> Type -> Type). (Profunctor p, Category p) => (->) :-> p

-- | The 2-morphism that defines a left Kan lift.
--   
--   Note: When <tt>p</tt> is right adjoint to <tt><a>Rift</a> p
--   (-&gt;)</tt> then <a>decomposeRift</a> is the <a>counit</a> of the
--   adjunction.
decomposeRift :: forall {k1} {k2} {k3} (p :: k1 -> k2 -> Type) (q :: k3 -> k2 -> Type). Procompose p (Rift p q) :-> q

-- | This is a variant on <a>costars</a> that uses <a>Cokleisli</a> instead
--   of <a>Costar</a>.
--   
--   <pre>
--   <a>cokleislis</a> :: <a>Functor</a> f =&gt; Iso' (<a>Procompose</a> (<a>Cokleisli</a> f) (<a>Cokleisli</a> g) d c) (<a>Cokleisli</a> (<a>Compose</a> g f) d c)
--   </pre>
cokleislis :: forall {k1} {k2} (f :: Type -> Type) (g :: k1 -> Type) (d :: k1) c (f' :: Type -> Type) (g' :: k2 -> Type) (d' :: k2) c'. Functor f => Iso (Procompose (Cokleisli f) (Cokleisli g) d c) (Procompose (Cokleisli f') (Cokleisli g') d' c') (Cokleisli (Compose f g) d c) (Cokleisli (Compose f' g') d' c')

-- | This is a variant on <a>stars</a> that uses <a>Kleisli</a> instead of
--   <a>Star</a>.
--   
--   <pre>
--   <a>kleislis</a> :: <a>Monad</a> f =&gt; Iso' (<a>Procompose</a> (<a>Kleisli</a> f) (<a>Kleisli</a> g) d c) (<a>Kleisli</a> (<a>Compose</a> f g) d c)
--   </pre>
kleislis :: forall (g :: Type -> Type) (f :: Type -> Type) d c (f' :: Type -> Type) (g' :: Type -> Type) d' c'. Monad g => Iso (Procompose (Kleisli f) (Kleisli g) d c) (Procompose (Kleisli f') (Kleisli g') d' c') (Kleisli (Compose g f) d c) (Kleisli (Compose g' f') d' c')

-- | <a>Profunctor</a> composition generalizes <a>Functor</a> composition
--   in two ways.
--   
--   This is the second, which shows that <tt>exists b. (f a -&gt; b, g b
--   -&gt; c)</tt> is isomorphic to <tt>g (f a) -&gt; c</tt>.
--   
--   <pre>
--   <a>costars</a> :: <a>Functor</a> f =&gt; Iso' (<a>Procompose</a> (<a>Costar</a> f) (<a>Costar</a> g) d c) (<a>Costar</a> (<a>Compose</a> g f) d c)
--   </pre>
costars :: forall {k1} {k2} (f :: Type -> Type) (g :: k1 -> Type) (d :: k1) c (f' :: Type -> Type) (g' :: k2 -> Type) (d' :: k2) c'. Functor f => Iso (Procompose (Costar f) (Costar g) d c) (Procompose (Costar f') (Costar g') d' c') (Costar (Compose f g) d c) (Costar (Compose f' g') d' c')

-- | <a>Profunctor</a> composition generalizes <a>Functor</a> composition
--   in two ways.
--   
--   This is the first, which shows that <tt>exists b. (a -&gt; f b, b
--   -&gt; g c)</tt> is isomorphic to <tt>a -&gt; f (g c)</tt>.
--   
--   <pre>
--   <a>stars</a> :: <a>Functor</a> f =&gt; Iso' (<a>Procompose</a> (<a>Star</a> f) (<a>Star</a> g) d c) (<a>Star</a> (<a>Compose</a> f g) d c)
--   </pre>
stars :: forall {k1} {k2} (g :: Type -> Type) (f :: k1 -> Type) d (c :: k1) (f' :: k2 -> Type) (g' :: Type -> Type) d' (c' :: k2). Functor g => Iso (Procompose (Star f) (Star g) d c) (Procompose (Star f') (Star g') d' c') (Star (Compose g f) d c) (Star (Compose g' f') d' c')

-- | The associator for <a>Profunctor</a> composition.
--   
--   This provides an <a>Iso</a> for the <tt>lens</tt> package that
--   witnesses the isomorphism between <tt><a>Procompose</a> p
--   (<a>Procompose</a> q r) a b</tt> and <tt><a>Procompose</a>
--   (<a>Procompose</a> p q) r a b</tt>, which arises because <tt>Prof</tt>
--   is only a bicategory, rather than a strict 2-category.
assoc :: forall {k1} {k2} {k3} {k4} {k5} {k6} (p :: k1 -> k2 -> Type) (q :: k3 -> k1 -> Type) (r :: k4 -> k3 -> Type) (a :: k4) (b :: k2) (x :: k5 -> k2 -> Type) (y :: k6 -> k5 -> Type) (z :: k4 -> k6 -> Type). Iso (Procompose p (Procompose q r) a b) (Procompose x (Procompose y z) a b) (Procompose (Procompose p q) r a b) (Procompose (Procompose x y) z a b)

-- | <tt>(-&gt;)</tt> functions as a lax identity for <a>Profunctor</a>
--   composition.
--   
--   This provides an <a>Iso</a> for the <tt>lens</tt> package that
--   witnesses the isomorphism between <tt><a>Procompose</a> q (-&gt;) d
--   c</tt> and <tt>q d c</tt>, which is the right identity law.
--   
--   <pre>
--   <a>idr</a> :: <a>Profunctor</a> q =&gt; Iso' (<a>Procompose</a> q (-&gt;) d c) (q d c)
--   </pre>
idr :: forall {k} (q :: Type -> Type -> Type) d c (r :: Type -> k -> Type) d' (c' :: k). Profunctor q => Iso (Procompose q (->) d c) (Procompose r (->) d' c') (q d c) (r d' c')

-- | <tt>(-&gt;)</tt> functions as a lax identity for <a>Profunctor</a>
--   composition.
--   
--   This provides an <a>Iso</a> for the <tt>lens</tt> package that
--   witnesses the isomorphism between <tt><a>Procompose</a> (-&gt;) q d
--   c</tt> and <tt>q d c</tt>, which is the left identity law.
--   
--   <pre>
--   <a>idl</a> :: <a>Profunctor</a> q =&gt; Iso' (<a>Procompose</a> (-&gt;) q d c) (q d c)
--   </pre>
idl :: forall {k} (q :: Type -> Type -> Type) d c (r :: k -> Type -> Type) (d' :: k) c'. Profunctor q => Iso (Procompose (->) q d c) (Procompose (->) r d' c') (q d c) (r d' c')
procomposed :: forall {k} p (a :: k) (b :: k). Category p => Procompose p p a b -> p a b

-- | <tt><a>Procompose</a> p q</tt> is the <a>Profunctor</a> composition of
--   the <a>Profunctor</a>s <tt>p</tt> and <tt>q</tt>.
--   
--   For a good explanation of <a>Profunctor</a> composition in Haskell see
--   Dan Piponi's article:
--   
--   <a>http://blog.sigfpe.com/2011/07/profunctors-in-haskell.html</a>
--   
--   <a>Procompose</a> has a polymorphic kind since <tt>5.6</tt>.
data Procompose (p :: k -> k1 -> Type) (q :: k2 -> k -> Type) (d :: k2) (c :: k1)
[Procompose] :: forall {k} {k1} {k2} (p :: k -> k1 -> Type) (x :: k) (c :: k1) (q :: k2 -> k -> Type) (d :: k2). p x c -> q d x -> Procompose p q d c

-- | This represents the right Kan lift of a <a>Profunctor</a> <tt>q</tt>
--   along a <a>Profunctor</a> <tt>p</tt> in a limited version of the
--   2-category of Profunctors where the only object is the category Hask,
--   1-morphisms are profunctors composed and compose with Profunctor
--   composition, and 2-morphisms are just natural transformations.
--   
--   <a>Rift</a> has a polymorphic kind since <tt>5.6</tt>.
newtype Rift (p :: k -> k1 -> Type) (q :: k2 -> k1 -> Type) (a :: k2) (b :: k)
Rift :: (forall (x :: k1). () => p b x -> q a x) -> Rift (p :: k -> k1 -> Type) (q :: k2 -> k1 -> Type) (a :: k2) (b :: k)
[runRift] :: Rift (p :: k -> k1 -> Type) (q :: k2 -> k1 -> Type) (a :: k2) (b :: k) -> forall (x :: k1). () => p b x -> q a x
coprepCounit :: forall {k} f (a :: k). f a -> Coprep (Costar f) a
coprepUnit :: forall {k} (p :: k -> Type -> Type). p :-> Costar (Coprep p)
uncoprepAdj :: forall {k} (p :: k -> Type -> Type) f (a :: k). (p :-> Costar f) -> f a -> Coprep p a

-- | <pre>
--   <a>Coprep</a> -| <a>Costar</a> :: [Hask, Hask]^op -&gt; Prof
--   </pre>
--   
--   Like all adjunctions this gives rise to a monad and a comonad.
--   
--   This gives rise to a monad on Prof
--   <tt>(<a>Costar</a>.<a>Coprep</a>)</tt> and a comonad on <tt>[Hask,
--   Hask]^op</tt> given by <tt>(<a>Coprep</a>.<a>Costar</a>)</tt> which is
--   a monad in <tt>[Hask,Hask]</tt>
coprepAdj :: forall {k} f (p :: k -> Type -> Type). (forall (a :: k). () => f a -> Coprep p a) -> p :-> Costar f
prepCounit :: forall {k} f (a :: k). Prep (Star f) a -> f a
prepUnit :: forall {k} (p :: Type -> k -> Type). p :-> Star (Prep p)
unprepAdj :: forall {k} (p :: Type -> k -> Type) g (a :: k). (p :-> Star g) -> Prep p a -> g a
prepAdj :: forall {k1} (p :: Type -> k1 -> Type) g. (forall (a :: k1). () => Prep p a -> g a) -> p :-> Star g

-- | <a>cotabulate</a> and <a>cosieve</a> form two halves of an
--   isomorphism.
--   
--   This can be used with the combinators from the <tt>lens</tt> package.
--   
--   <pre>
--   <a>cotabulated</a> :: <a>Corep</a> f p =&gt; <tt>Iso'</tt> (f d -&gt; c) (p d c)
--   </pre>
cotabulated :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type) d c d' c'. (Corepresentable p, Corepresentable q) => Iso (Corep p d -> c) (Corep q d' -> c') (p d c) (q d' c')

-- | Default definition for <a>closed</a> given that <tt>p</tt> is
--   <a>Corepresentable</a>
closedCorep :: Corepresentable p => p a b -> p (x -> a) (x -> b)

-- | Default definition for <a>unsecond</a> given that <tt>p</tt> is
--   <a>Corepresentable</a>.
unsecondCorep :: Corepresentable p => p (d, a) (d, b) -> p a b

-- | Default definition for <a>unfirst</a> given that <tt>p</tt> is
--   <a>Corepresentable</a>.
unfirstCorep :: Corepresentable p => p (a, d) (b, d) -> p a b

-- | <a>tabulate</a> and <a>sieve</a> form two halves of an isomorphism.
--   
--   This can be used with the combinators from the <tt>lens</tt> package.
--   
--   <pre>
--   <a>tabulated</a> :: <a>Representable</a> p =&gt; <tt>Iso'</tt> (d -&gt; <a>Rep</a> p c) (p d c)
--   </pre>
tabulated :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type) d c d' c'. (Representable p, Representable q) => Iso (d -> Rep p c) (d' -> Rep q c') (p d c) (q d' c')

-- | Default definition for <a>second'</a> given that p is
--   <a>Representable</a>.
secondRep :: Representable p => p a b -> p (c, a) (c, b)

-- | Default definition for <a>first'</a> given that p is
--   <a>Representable</a>.
firstRep :: Representable p => p a b -> p (a, c) (b, c)
type family Rep (p :: Type -> Type -> Type) :: Type -> Type

-- | A <a>Profunctor</a> <tt>p</tt> is <a>Representable</a> if there exists
--   a <a>Functor</a> <tt>f</tt> such that <tt>p d c</tt> is isomorphic to
--   <tt>d -&gt; f c</tt>.
class (Sieve p Rep p, Strong p) => Representable (p :: Type -> Type -> Type) where {
    type family Rep (p :: Type -> Type -> Type) :: Type -> Type;
}

-- | Laws:
--   
--   <pre>
--   <a>tabulate</a> <a>.</a> <a>sieve</a> ≡ <a>id</a>
--   <a>sieve</a> <a>.</a> <a>tabulate</a> ≡ <a>id</a>
--   </pre>
tabulate :: Representable p => (d -> Rep p c) -> p d c
type family Corep (p :: Type -> Type -> Type) :: Type -> Type

-- | A <a>Profunctor</a> <tt>p</tt> is <a>Corepresentable</a> if there
--   exists a <a>Functor</a> <tt>f</tt> such that <tt>p d c</tt> is
--   isomorphic to <tt>f d -&gt; c</tt>.
class (Cosieve p Corep p, Costrong p) => Corepresentable (p :: Type -> Type -> Type) where {
    type family Corep (p :: Type -> Type -> Type) :: Type -> Type;
}

-- | Laws:
--   
--   <pre>
--   <a>cotabulate</a> <a>.</a> <a>cosieve</a> ≡ <a>id</a>
--   <a>cosieve</a> <a>.</a> <a>cotabulate</a> ≡ <a>id</a>
--   </pre>
cotabulate :: Corepresentable p => (Corep p d -> c) -> p d c

-- | <pre>
--   <a>Prep</a> -| <a>Star</a> :: [Hask, Hask] -&gt; Prof
--   </pre>
--   
--   This gives rise to a monad in <tt>Prof</tt>,
--   <tt>(<a>Star</a>.<a>Prep</a>)</tt>, and a comonad in
--   <tt>[Hask,Hask]</tt> <tt>(<a>Prep</a>.<a>Star</a>)</tt>
--   
--   <a>Prep</a> has a polymorphic kind since <tt>5.6</tt>.
data Prep (p :: Type -> k -> Type) (a :: k)
[Prep] :: forall {k} x (p :: Type -> k -> Type) (a :: k). x -> p x a -> Prep p a

-- | <a>Prep</a> has a polymorphic kind since <tt>5.6</tt>.
newtype Coprep (p :: k -> Type -> Type) (a :: k)
Coprep :: (forall r. () => p a r -> r) -> Coprep (p :: k -> Type -> Type) (a :: k)
[runCoprep] :: Coprep (p :: k -> Type -> Type) (a :: k) -> forall r. () => p a r -> r

-- | A <a>Profunctor</a> <tt>p</tt> is a <a>Sieve</a> <b>on</b> <tt>f</tt>
--   if it is a subprofunctor of <tt><a>Star</a> f</tt>.
--   
--   That is to say it is a subset of <tt>Hom(-,f=)</tt> closed under
--   <a>lmap</a> and <a>rmap</a>.
--   
--   Alternately, you can view it as a sieve <b>in</b> the comma category
--   <tt>Hask/f</tt>.
class (Profunctor p, Functor f) => Sieve (p :: Type -> Type -> Type) (f :: Type -> Type) | p -> f
sieve :: Sieve p f => p a b -> a -> f b

-- | A <a>Profunctor</a> <tt>p</tt> is a <a>Cosieve</a> <b>on</b>
--   <tt>f</tt> if it is a subprofunctor of <tt><a>Costar</a> f</tt>.
--   
--   That is to say it is a subset of <tt>Hom(f-,=)</tt> closed under
--   <a>lmap</a> and <a>rmap</a>.
--   
--   Alternately, you can view it as a cosieve <b>in</b> the comma category
--   <tt>f/Hask</tt>.
class (Profunctor p, Functor f) => Cosieve (p :: Type -> Type -> Type) (f :: Type -> Type) | p -> f
cosieve :: Cosieve p f => p a b -> f a -> b
closedMapping :: Mapping p => p a b -> p (x -> a) (x -> b)
traverseMapping :: (Mapping p, Functor f) => p a b -> p (f a) (f b)
wanderMapping :: Mapping p => (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> p a b -> p s t
class (Traversing p, Closed p) => Mapping (p :: Type -> Type -> Type)

-- | Laws:
--   
--   <pre>
--   <a>map'</a> <a>.</a> <a>rmap</a> f ≡ <a>rmap</a> (<a>fmap</a> f) <a>.</a> <a>map'</a>
--   <a>map'</a> <a>.</a> <a>map'</a> ≡ <a>dimap</a> <a>Compose</a> <a>getCompose</a> <a>.</a> <a>map'</a>
--   <a>dimap</a> <a>Identity</a> <a>runIdentity</a> <a>.</a> <a>map'</a> ≡ <a>id</a>
--   </pre>
map' :: (Mapping p, Functor f) => p a b -> p (f a) (f b)
roam :: Mapping p => ((a -> b) -> s -> t) -> p a b -> p s t
newtype CofreeMapping (p :: Type -> Type -> Type) a b
CofreeMapping :: (forall (f :: Type -> Type). Functor f => p (f a) (f b)) -> CofreeMapping (p :: Type -> Type -> Type) a b
[runCofreeMapping] :: CofreeMapping (p :: Type -> Type -> Type) a b -> forall (f :: Type -> Type). Functor f => p (f a) (f b)

-- | <pre>
--   FreeMapping -| CofreeMapping
--   </pre>
data FreeMapping (p :: Type -> Type -> Type) a b
[FreeMapping] :: forall (f :: Type -> Type) y b (p :: Type -> Type -> Type) x a. Functor f => (f y -> b) -> p x y -> (a -> f x) -> FreeMapping p a b
rightTraversing :: Traversing p => p a b -> p (Either c a) (Either c b)
leftTraversing :: Traversing p => p a b -> p (Either a c) (Either b c)

-- | <a>rmapWandering</a> is the same as the default produced from
--   <a>dimapWandering</a>.
rmapWandering :: Traversing p => (b -> c) -> p a b -> p a c

-- | <a>lmapWandering</a> may be a more efficient implementation of
--   <a>lmap</a> than the default produced from <a>dimapWandering</a>.
lmapWandering :: Traversing p => (a -> b) -> p b c -> p a c

-- | A definition of <a>dimap</a> for <a>Traversing</a> instances that
--   define an explicit <a>wander</a>.
dimapWandering :: Traversing p => (a' -> a) -> (b -> b') -> p a b -> p a' b'
secondTraversing :: Traversing p => p a b -> p (c, a) (c, b)
firstTraversing :: Traversing p => p a b -> p (a, c) (b, c)

-- | Note: Definitions in terms of <a>wander</a> are much more efficient!
class (Choice p, Strong p) => Traversing (p :: Type -> Type -> Type)

-- | Laws:
--   
--   <pre>
--   <a>traverse'</a> ≡ <a>wander</a> <a>traverse</a>
--   <a>traverse'</a> <a>.</a> <a>rmap</a> f ≡ <a>rmap</a> (<a>fmap</a> f) <a>.</a> <a>traverse'</a>
--   <a>traverse'</a> <a>.</a> <a>traverse'</a> ≡ <a>dimap</a> <a>Compose</a> <a>getCompose</a> <a>.</a> <a>traverse'</a>
--   <a>dimap</a> <a>Identity</a> <a>runIdentity</a> <a>.</a> <a>traverse'</a> ≡ <a>id</a>
--   </pre>
traverse' :: (Traversing p, Traversable f) => p a b -> p (f a) (f b)

-- | This combinator is mutually defined in terms of <a>traverse'</a>
wander :: Traversing p => (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> p a b -> p s t
newtype CofreeTraversing (p :: Type -> Type -> Type) a b
CofreeTraversing :: (forall (f :: Type -> Type). Traversable f => p (f a) (f b)) -> CofreeTraversing (p :: Type -> Type -> Type) a b
[runCofreeTraversing] :: CofreeTraversing (p :: Type -> Type -> Type) a b -> forall (f :: Type -> Type). Traversable f => p (f a) (f b)

-- | <pre>
--   FreeTraversing -| CofreeTraversing
--   </pre>
data FreeTraversing (p :: Type -> Type -> Type) a b
[FreeTraversing] :: forall (f :: Type -> Type) y b (p :: Type -> Type -> Type) x a. Traversable f => (f y -> b) -> p x y -> (a -> f x) -> FreeTraversing p a b

-- | <pre>
--   <a>cotambaraSum</a> <a>.</a> <a>uncotambaraSum</a> ≡ <a>id</a>
--   <a>uncotambaraSum</a> <a>.</a> <a>cotambaraSum</a> ≡ <a>id</a>
--   </pre>
uncotambaraSum :: forall (q :: Type -> Type -> Type) (p :: Type -> Type -> Type). Profunctor q => (p :-> CotambaraSum q) -> p :-> q

-- | <pre>
--   <a>cotambaraSum</a> <a>.</a> <a>uncotambaraSum</a> ≡ <a>id</a>
--   <a>uncotambaraSum</a> <a>.</a> <a>cotambaraSum</a> ≡ <a>id</a>
--   </pre>
cotambaraSum :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Cochoice p => (p :-> q) -> p :-> CotambaraSum q

-- | <pre>
--   <a>tambaraSum</a> <a>.</a> <a>untambaraSum</a> ≡ <a>id</a>
--   <a>untambaraSum</a> <a>.</a> <a>tambaraSum</a> ≡ <a>id</a>
--   </pre>
untambaraSum :: forall (q :: Type -> Type -> Type) (p :: Type -> Type -> Type). Profunctor q => (p :-> TambaraSum q) -> p :-> q

-- | <pre>
--   <a>tambaraSum</a> <a>.</a> <a>untambaraSum</a> ≡ <a>id</a>
--   <a>untambaraSum</a> <a>.</a> <a>tambaraSum</a> ≡ <a>id</a>
--   </pre>
tambaraSum :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Choice p => (p :-> q) -> p :-> TambaraSum q

-- | The generalization of <a>Costar</a> of <a>Functor</a> that is strong
--   with respect to <a>Either</a>.
--   
--   Note: This is also a notion of strength, except with regards to
--   another monoidal structure that we can choose to equip Hask with: the
--   cocartesian coproduct.
class Profunctor p => Choice (p :: Type -> Type -> Type)

-- | Laws:
--   
--   <pre>
--   <a>left'</a> ≡ <a>dimap</a> swapE swapE <a>.</a> <a>right'</a> where
--     swapE :: <a>Either</a> a b -&gt; <a>Either</a> b a
--     swapE = <a>either</a> <a>Right</a> <a>Left</a>
--   <a>rmap</a> <a>Left</a> ≡ <a>lmap</a> <a>Left</a> <a>.</a> <a>left'</a>
--   <a>lmap</a> (<a>right</a> f) <a>.</a> <a>left'</a> ≡ <a>rmap</a> (<a>right</a> f) <a>.</a> <a>left'</a>
--   <a>left'</a> <a>.</a> <a>left'</a> ≡ <a>dimap</a> assocE unassocE <a>.</a> <a>left'</a> where
--     assocE :: <a>Either</a> (<a>Either</a> a b) c -&gt; <a>Either</a> a (<a>Either</a> b c)
--     assocE (<a>Left</a> (<a>Left</a> a)) = <a>Left</a> a
--     assocE (<a>Left</a> (<a>Right</a> b)) = <a>Right</a> (<a>Left</a> b)
--     assocE (<a>Right</a> c) = <a>Right</a> (<a>Right</a> c)
--     unassocE :: <a>Either</a> a (<a>Either</a> b c) -&gt; <a>Either</a> (<a>Either</a> a b) c
--     unassocE (<a>Left</a> a) = <a>Left</a> (<a>Left</a> a)
--     unassocE (<a>Right</a> (<a>Left</a> b)) = <a>Left</a> (<a>Right</a> b)
--     unassocE (<a>Right</a> (<a>Right</a> c)) = <a>Right</a> c
--   </pre>
left' :: Choice p => p a b -> p (Either a c) (Either b c)

-- | Laws:
--   
--   <pre>
--   <a>right'</a> ≡ <a>dimap</a> swapE swapE <a>.</a> <a>left'</a> where
--     swapE :: <a>Either</a> a b -&gt; <a>Either</a> b a
--     swapE = <a>either</a> <a>Right</a> <a>Left</a>
--   <a>rmap</a> <a>Right</a> ≡ <a>lmap</a> <a>Right</a> <a>.</a> <a>right'</a>
--   <a>lmap</a> (<a>left</a> f) <a>.</a> <a>right'</a> ≡ <a>rmap</a> (<a>left</a> f) <a>.</a> <a>right'</a>
--   <a>right'</a> <a>.</a> <a>right'</a> ≡ <a>dimap</a> unassocE assocE <a>.</a> <a>right'</a> where
--     assocE :: <a>Either</a> (<a>Either</a> a b) c -&gt; <a>Either</a> a (<a>Either</a> b c)
--     assocE (<a>Left</a> (<a>Left</a> a)) = <a>Left</a> a
--     assocE (<a>Left</a> (<a>Right</a> b)) = <a>Right</a> (<a>Left</a> b)
--     assocE (<a>Right</a> c) = <a>Right</a> (<a>Right</a> c)
--     unassocE :: <a>Either</a> a (<a>Either</a> b c) -&gt; <a>Either</a> (<a>Either</a> a b) c
--     unassocE (<a>Left</a> a) = <a>Left</a> (<a>Left</a> a)
--     unassocE (<a>Right</a> (<a>Left</a> b)) = <a>Left</a> (<a>Right</a> b)
--     unassocE (<a>Right</a> (<a>Right</a> c)) = <a>Right</a> c
--   </pre>
right' :: Choice p => p a b -> p (Either c a) (Either c b)

-- | TambaraSum is cofreely adjoins strength with respect to Either.
--   
--   Note: this is not dual to <a>Tambara</a>. It is <a>Tambara</a> with
--   respect to a different tensor.
newtype TambaraSum (p :: Type -> Type -> Type) a b
TambaraSum :: (forall c. () => p (Either a c) (Either b c)) -> TambaraSum (p :: Type -> Type -> Type) a b
[runTambaraSum] :: TambaraSum (p :: Type -> Type -> Type) a b -> forall c. () => p (Either a c) (Either b c)

-- | PastroSum -| TambaraSum
--   
--   PastroSum freely constructs strength with respect to Either.
data PastroSum (p :: Type -> Type -> Type) a b
[PastroSum] :: forall y z b (p :: Type -> Type -> Type) x a. (Either y z -> b) -> p x y -> (a -> Either x z) -> PastroSum p a b
class Profunctor p => Cochoice (p :: Type -> Type -> Type)

-- | Laws:
--   
--   <pre>
--   <a>unleft</a> ≡ <a>unright</a> <a>.</a> <a>dimap</a> swapE swapE where
--     swapE :: <a>Either</a> a b -&gt; <a>Either</a> b a
--     swapE = <a>either</a> <a>Right</a> <a>Left</a>
--   <a>rmap</a> (<a>either</a> <a>id</a> <tt>absurd</tt>) ≡ <a>unleft</a> <a>.</a> <a>lmap</a> (<a>either</a> <a>id</a> <tt>absurd</tt>)
--   <a>unfirst</a> <a>.</a> <a>rmap</a> (<a>second</a> f) ≡ <a>unfirst</a> <a>.</a> <a>lmap</a> (<a>second</a> f)
--   <a>unleft</a> <a>.</a> <a>unleft</a> ≡ <a>unleft</a> <a>.</a> <a>dimap</a> assocE unassocE where
--     assocE :: <a>Either</a> (<a>Either</a> a b) c -&gt; <a>Either</a> a (<a>Either</a> b c)
--     assocE (<a>Left</a> (<a>Left</a> a)) = <a>Left</a> a
--     assocE (<a>Left</a> (<a>Right</a> b)) = <a>Right</a> (<a>Left</a> b)
--     assocE (<a>Right</a> c) = <a>Right</a> (<a>Right</a> c)
--     unassocE :: <a>Either</a> a (<a>Either</a> b c) -&gt; <a>Either</a> (<a>Either</a> a b) c
--     unassocE (<a>Left</a> a) = <a>Left</a> (<a>Left</a> a)
--     unassocE (<a>Right</a> (<a>Left</a> b)) = <a>Left</a> (<a>Right</a> b)
--     unassocE (<a>Right</a> (<a>Right</a> c)) = <a>Right</a> c
--   </pre>
unleft :: Cochoice p => p (Either a d) (Either b d) -> p a b

-- | Laws:
--   
--   <pre>
--   <a>unright</a> ≡ <a>unleft</a> <a>.</a> <a>dimap</a> swapE swapE where
--     swapE :: <a>Either</a> a b -&gt; <a>Either</a> b a
--     swapE = <a>either</a> <a>Right</a> <a>Left</a>
--   <a>rmap</a> (<a>either</a> <tt>absurd</tt> <a>id</a>) ≡ <a>unright</a> <a>.</a> <a>lmap</a> (<a>either</a> <tt>absurd</tt> <a>id</a>)
--   <a>unsecond</a> <a>.</a> <a>rmap</a> (<a>first</a> f) ≡ <a>unsecond</a> <a>.</a> <a>lmap</a> (<a>first</a> f)
--   <a>unright</a> <a>.</a> <a>unright</a> ≡ <a>unright</a> <a>.</a> <a>dimap</a> unassocE assocE where
--     assocE :: <a>Either</a> (<a>Either</a> a b) c -&gt; <a>Either</a> a (<a>Either</a> b c)
--     assocE (<a>Left</a> (<a>Left</a> a)) = <a>Left</a> a
--     assocE (<a>Left</a> (<a>Right</a> b)) = <a>Right</a> (<a>Left</a> b)
--     assocE (<a>Right</a> c) = <a>Right</a> (<a>Right</a> c)
--     unassocE :: <a>Either</a> a (<a>Either</a> b c) -&gt; <a>Either</a> (<a>Either</a> a b) c
--     unassocE (<a>Left</a> a) = <a>Left</a> (<a>Left</a> a)
--     unassocE (<a>Right</a> (<a>Left</a> b)) = <a>Left</a> (<a>Right</a> b)
--     unassocE (<a>Right</a> (<a>Right</a> c)) = <a>Right</a> c
--   </pre>
unright :: Cochoice p => p (Either d a) (Either d b) -> p a b

-- | <a>CotambaraSum</a> cofreely constructs costrength with respect to
--   <a>Either</a> (aka <a>Choice</a>)
data CotambaraSum (q :: Type -> Type -> Type) a b
[CotambaraSum] :: forall (r :: Type -> Type -> Type) (q :: Type -> Type -> Type) a b. Cochoice r => (r :-> q) -> r a b -> CotambaraSum q a b

-- | CopastroSum -| CotambaraSum
--   
--   <a>CopastroSum</a> freely constructs costrength with respect to
--   <a>Either</a> (aka <a>Choice</a>)
newtype CopastroSum (p :: Type -> Type -> Type) a b
CopastroSum :: (forall (r :: Type -> Type -> Type). Cochoice r => (forall x y. () => p x y -> r x y) -> r a b) -> CopastroSum (p :: Type -> Type -> Type) a b
[runCopastroSum] :: CopastroSum (p :: Type -> Type -> Type) a b -> forall (r :: Type -> Type -> Type). Cochoice r => (forall x y. () => p x y -> r x y) -> r a b

-- | <pre>
--   <a>close</a> <a>.</a> <a>unclose</a> ≡ <a>id</a>
--   <a>unclose</a> <a>.</a> <a>close</a> ≡ <a>id</a>
--   </pre>
unclose :: forall (q :: Type -> Type -> Type) (p :: Type -> Type -> Type). Profunctor q => (p :-> Closure q) -> p :-> q

-- | <pre>
--   <a>close</a> <a>.</a> <a>unclose</a> ≡ <a>id</a>
--   <a>unclose</a> <a>.</a> <a>close</a> ≡ <a>id</a>
--   </pre>
close :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Closed p => (p :-> q) -> p :-> Closure q
curry' :: Closed p => p (a, b) c -> p a (b -> c)

-- | A strong profunctor allows the monoidal structure to pass through.
--   
--   A closed profunctor allows the closed structure to pass through.
class Profunctor p => Closed (p :: Type -> Type -> Type)

-- | Laws:
--   
--   <pre>
--   <a>lmap</a> (<a>.</a> f) <a>.</a> <a>closed</a> ≡ <a>rmap</a> (<a>.</a> f) <a>.</a> <a>closed</a>
--   <a>closed</a> <a>.</a> <a>closed</a> ≡ <a>dimap</a> <a>uncurry</a> <a>curry</a> <a>.</a> <a>closed</a>
--   <a>dimap</a> <a>const</a> (<a>$</a>()) <a>.</a> <a>closed</a> ≡ <a>id</a>
--   </pre>
closed :: Closed p => p a b -> p (x -> a) (x -> b)

-- | <a>Closure</a> adjoins a <a>Closed</a> structure to any
--   <a>Profunctor</a>.
--   
--   Analogous to <a>Tambara</a> for <a>Strong</a>.
newtype Closure (p :: Type -> Type -> Type) a b
Closure :: (forall x. () => p (x -> a) (x -> b)) -> Closure (p :: Type -> Type -> Type) a b
[runClosure] :: Closure (p :: Type -> Type -> Type) a b -> forall x. () => p (x -> a) (x -> b)
data Environment (p :: Type -> Type -> Type) a b
[Environment] :: forall z y b (p :: Type -> Type -> Type) x a. ((z -> y) -> b) -> p x y -> (a -> z -> x) -> Environment p a b

-- | <pre>
--   <a>cotambara</a> <a>.</a> <a>uncotambara</a> ≡ <a>id</a>
--   <a>uncotambara</a> <a>.</a> <a>cotambara</a> ≡ <a>id</a>
--   </pre>
uncotambara :: forall (q :: Type -> Type -> Type) (p :: Type -> Type -> Type). Profunctor q => (p :-> Cotambara q) -> p :-> q

-- | <pre>
--   <a>cotambara</a> <a>.</a> <a>uncotambara</a> ≡ <a>id</a>
--   <a>uncotambara</a> <a>.</a> <a>cotambara</a> ≡ <a>id</a>
--   </pre>
cotambara :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Costrong p => (p :-> q) -> p :-> Cotambara q

-- | <pre>
--   <a>pastro</a> (<a>unpastro</a> f) ≡ f
--   <a>unpastro</a> (<a>pastro</a> f) ≡ f
--   </pre>
unpastro :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). (Pastro p :-> q) -> p :-> q

-- | <pre>
--   <a>pastro</a> (<a>unpastro</a> f) ≡ f
--   <a>unpastro</a> (<a>pastro</a> f) ≡ f
--   </pre>
pastro :: forall (q :: Type -> Type -> Type) (p :: Type -> Type -> Type). Strong q => (p :-> q) -> Pastro p :-> q

-- | <pre>
--   <a>tambara</a> (<a>untambara</a> f) ≡ f
--   <a>untambara</a> (<a>tambara</a> f) ≡ f
--   </pre>
untambara :: forall (q :: Type -> Type -> Type) (p :: Type -> Type -> Type). Profunctor q => (p :-> Tambara q) -> p :-> q

-- | <pre>
--   <a>tambara</a> (<a>untambara</a> f) ≡ f
--   <a>untambara</a> (<a>tambara</a> f) ≡ f
--   </pre>
tambara :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Strong p => (p :-> q) -> p :-> Tambara q
strong :: Strong p => (a -> b -> c) -> p a b -> p a c
uncurry' :: Strong p => p a (b -> c) -> p (a, b) c

-- | Generalizing <a>Star</a> of a strong <a>Functor</a>
--   
--   <i>Note:</i> Every <a>Functor</a> in Haskell is strong with respect to
--   <tt>(,)</tt>.
--   
--   This describes profunctor strength with respect to the product
--   structure of Hask.
--   
--   <a>http://www.riec.tohoku.ac.jp/~asada/papers/arrStrMnd.pdf</a>
class Profunctor p => Strong (p :: Type -> Type -> Type)

-- | Laws:
--   
--   <pre>
--   <a>first'</a> ≡ <a>dimap</a> <a>swap</a> <a>swap</a> <a>.</a> <a>second'</a>
--   <a>lmap</a> <a>fst</a> ≡ <a>rmap</a> <a>fst</a> <a>.</a> <a>first'</a>
--   <a>lmap</a> (<a>second'</a> f) <a>.</a> <a>first'</a> ≡ <a>rmap</a> (<a>second'</a> f) <a>.</a> <a>first'</a>
--   <a>first'</a> <a>.</a> <a>first'</a> ≡ <a>dimap</a> assoc unassoc <a>.</a> <a>first'</a> where
--     assoc ((a,b),c) = (a,(b,c))
--     unassoc (a,(b,c)) = ((a,b),c)
--   </pre>
first' :: Strong p => p a b -> p (a, c) (b, c)

-- | Laws:
--   
--   <pre>
--   <a>second'</a> ≡ <a>dimap</a> <a>swap</a> <a>swap</a> <a>.</a> <a>first'</a>
--   <a>lmap</a> <a>snd</a> ≡ <a>rmap</a> <a>snd</a> <a>.</a> <a>second'</a>
--   <a>lmap</a> (<a>first'</a> f) <a>.</a> <a>second'</a> ≡ <a>rmap</a> (<a>first'</a> f) <a>.</a> <a>second'</a>
--   <a>second'</a> <a>.</a> <a>second'</a> ≡ <a>dimap</a> unassoc assoc <a>.</a> <a>second'</a> where
--     assoc ((a,b),c) = (a,(b,c))
--     unassoc (a,(b,c)) = ((a,b),c)
--   </pre>
second' :: Strong p => p a b -> p (c, a) (c, b)

-- | <a>Tambara</a> cofreely makes any <a>Profunctor</a> <a>Strong</a>.
newtype Tambara (p :: Type -> Type -> Type) a b
Tambara :: (forall c. () => p (a, c) (b, c)) -> Tambara (p :: Type -> Type -> Type) a b
[runTambara] :: Tambara (p :: Type -> Type -> Type) a b -> forall c. () => p (a, c) (b, c)

-- | Pastro -| Tambara
--   
--   <pre>
--   Pastro p ~ exists z. Costar ((,)z) <tt>Procompose</tt> p <tt>Procompose</tt> Star ((,)z)
--   </pre>
--   
--   <a>Pastro</a> freely makes any <a>Profunctor</a> <a>Strong</a>.
data Pastro (p :: Type -> Type -> Type) a b
[Pastro] :: forall y z b (p :: Type -> Type -> Type) x a. ((y, z) -> b) -> p x y -> (a -> (x, z)) -> Pastro p a b

-- | Analogous to <a>ArrowLoop</a>, <a>loop</a> = <a>unfirst</a>
class Profunctor p => Costrong (p :: Type -> Type -> Type)

-- | Laws:
--   
--   <pre>
--   <a>unfirst</a> ≡ <a>unsecond</a> <a>.</a> <a>dimap</a> <a>swap</a> <a>swap</a>
--   <a>lmap</a> (,()) ≡ <a>unfirst</a> <a>.</a> <a>rmap</a> (,())
--   <a>unfirst</a> <a>.</a> <a>lmap</a> (<a>second</a> f) ≡ <a>unfirst</a> <a>.</a> <a>rmap</a> (<a>second</a> f)
--   <a>unfirst</a> <a>.</a> <a>unfirst</a> = <a>unfirst</a> <a>.</a> <a>dimap</a> assoc unassoc where
--     assoc ((a,b),c) = (a,(b,c))
--     unassoc (a,(b,c)) = ((a,b),c)
--   </pre>
unfirst :: Costrong p => p (a, d) (b, d) -> p a b

-- | Laws:
--   
--   <pre>
--   <a>unsecond</a> ≡ <a>unfirst</a> <a>.</a> <a>dimap</a> <a>swap</a> <a>swap</a>
--   <a>lmap</a> ((),) ≡ <a>unsecond</a> <a>.</a> <a>rmap</a> ((),)
--   <a>unsecond</a> <a>.</a> <a>lmap</a> (<a>first</a> f) ≡ <a>unsecond</a> <a>.</a> <a>rmap</a> (<a>first</a> f)
--   <a>unsecond</a> <a>.</a> <a>unsecond</a> = <a>unsecond</a> <a>.</a> <a>dimap</a> unassoc assoc where
--     assoc ((a,b),c) = (a,(b,c))
--     unassoc (a,(b,c)) = ((a,b),c)
--   </pre>
unsecond :: Costrong p => p (d, a) (d, b) -> p a b

-- | Cotambara cofreely constructs costrength
data Cotambara (q :: Type -> Type -> Type) a b
[Cotambara] :: forall (r :: Type -> Type -> Type) (q :: Type -> Type -> Type) a b. Costrong r => (r :-> q) -> r a b -> Cotambara q a b

-- | Copastro -| Cotambara
--   
--   Copastro freely constructs costrength
newtype Copastro (p :: Type -> Type -> Type) a b
Copastro :: (forall (r :: Type -> Type -> Type). Costrong r => (forall x y. () => p x y -> r x y) -> r a b) -> Copastro (p :: Type -> Type -> Type) a b
[runCopastro] :: Copastro (p :: Type -> Type -> Type) a b -> forall (r :: Type -> Type -> Type). Costrong r => (forall x y. () => p x y -> r x y) -> r a b

-- | Laws:
--   
--   <pre>
--   <a>unit</a> <a>.</a> <a>counit</a> ≡ <a>id</a>
--   <a>counit</a> <a>.</a> <a>unit</a> ≡ <a>id</a>
--   </pre>
class (ProfunctorFunctor f, ProfunctorFunctor u) => ProfunctorAdjunction (f :: Type -> Type -> Type -> Type -> Type -> Type) (u :: Type -> Type -> Type -> Type -> Type -> Type) | f -> u, u -> f
unit :: forall (p :: Type -> Type -> Type). (ProfunctorAdjunction f u, Profunctor p) => p :-> u (f p)
counit :: forall (p :: Type -> Type -> Type). (ProfunctorAdjunction f u, Profunctor p) => f (u p) :-> p

-- | <a>ProfunctorFunctor</a> has a polymorphic kind since <tt>5.6</tt>.
class ProfunctorFunctor (t :: Type -> Type -> Type -> k -> k1 -> Type)

-- | Laws:
--   
--   <pre>
--   <a>promap</a> f <a>.</a> <a>promap</a> g ≡ <a>promap</a> (f <a>.</a> g)
--   <a>promap</a> <a>id</a> ≡ <a>id</a>
--   </pre>
promap :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). (ProfunctorFunctor t, Profunctor p) => (p :-> q) -> t p :-> t q

-- | Laws:
--   
--   <pre>
--   <a>promap</a> f <a>.</a> <a>proreturn</a> ≡ <a>proreturn</a> <a>.</a> f
--   <a>projoin</a> <a>.</a> <a>proreturn</a> ≡ <a>id</a>
--   <a>projoin</a> <a>.</a> <a>promap</a> <a>proreturn</a> ≡ <a>id</a>
--   <a>projoin</a> <a>.</a> <a>projoin</a> ≡ <a>projoin</a> <a>.</a> <a>promap</a> <a>projoin</a>
--   </pre>
class ProfunctorFunctor t => ProfunctorMonad (t :: Type -> Type -> Type -> Type -> Type -> Type)
proreturn :: forall (p :: Type -> Type -> Type). (ProfunctorMonad t, Profunctor p) => p :-> t p
projoin :: forall (p :: Type -> Type -> Type). (ProfunctorMonad t, Profunctor p) => t (t p) :-> t p

-- | Laws:
--   
--   <pre>
--   <a>proextract</a> <a>.</a> <a>promap</a> f ≡ f <a>.</a> <a>proextract</a>
--   <a>proextract</a> <a>.</a> <a>produplicate</a> ≡ <a>id</a>
--   <a>promap</a> <a>proextract</a> <a>.</a> <a>produplicate</a> ≡ <a>id</a>
--   <a>produplicate</a> <a>.</a> <a>produplicate</a> ≡ <a>promap</a> <a>produplicate</a> <a>.</a> <a>produplicate</a>
--   </pre>
class ProfunctorFunctor t => ProfunctorComonad (t :: Type -> Type -> Type -> Type -> Type -> Type)
proextract :: forall (p :: Type -> Type -> Type). (ProfunctorComonad t, Profunctor p) => t p :-> p
produplicate :: forall (p :: Type -> Type -> Type). (ProfunctorComonad t, Profunctor p) => t p :-> t (t p)

-- | (<a>:-&gt;</a>) has a polymorphic kind since <tt>5.6</tt>.
type (p :: k -> k1 -> Type) :-> (q :: k -> k1 -> Type) = forall (a :: k) (b :: k1). () => p a b -> q a b
infixr 0 :->

-- | Lift a <a>Functor</a> into a <a>Profunctor</a> (forwards).
--   
--   <a>Star</a> has a polymorphic kind since <tt>5.6</tt>.
newtype Star (f :: k -> Type) d (c :: k)
Star :: (d -> f c) -> Star (f :: k -> Type) d (c :: k)
[runStar] :: Star (f :: k -> Type) d (c :: k) -> d -> f c

-- | Lift a <a>Functor</a> into a <a>Profunctor</a> (backwards).
--   
--   <a>Costar</a> has a polymorphic kind since <tt>5.6</tt>.
newtype Costar (f :: k -> Type) (d :: k) c
Costar :: (f d -> c) -> Costar (f :: k -> Type) (d :: k) c
[runCostar] :: Costar (f :: k -> Type) (d :: k) c -> f d -> c

-- | <a>Forget</a> has a polymorphic kind since <tt>5.6</tt>.
newtype Forget r a (b :: k)
Forget :: (a -> r) -> Forget r a (b :: k)
[runForget] :: Forget r a (b :: k) -> a -> r

-- | An arbitrary-precision number represented using <a>scientific
--   notation</a>.
--   
--   This type describes the set of all <tt><a>Real</a>s</tt> which have a
--   finite decimal expansion.
--   
--   A scientific number with <a>coefficient</a> <tt>c</tt> and
--   <a>base10Exponent</a> <tt>e</tt> corresponds to the <a>Fractional</a>
--   number: <tt><a>fromInteger</a> c * 10 <a>^^</a> e</tt>
data Scientific

-- | Generalised folding with the short-circuiting behaviour.
foldS :: (Selective f, Foldable t, Monoid a) => t (f (Either e a)) -> f (Either e a)

-- | A lifted version of <a>all</a>. Retains the short-circuiting
--   behaviour.
allS :: Selective f => (a -> f Bool) -> [a] -> f Bool

-- | A lifted version of <a>any</a>. Retains the short-circuiting
--   behaviour.
anyS :: Selective f => (a -> f Bool) -> [a] -> f Bool

-- | A lifted version of lazy Boolean AND.
(<&&>) :: Selective f => f Bool -> f Bool -> f Bool

-- | A lifted version of lazy Boolean OR.
(<||>) :: Selective f => f Bool -> f Bool -> f Bool

-- | Keep running an effectful computation until it returns a
--   <tt>Right</tt> value, collecting the <tt>Left</tt>'s using a supplied
--   <tt>Monoid</tt> instance.
untilRight :: (Monoid a, Selective f) => f (Either a b) -> f (a, b)

-- | Keep checking an effectful condition while it holds.
whileS :: Selective f => f Bool -> f ()

-- | Accumulate the <tt>Right</tt> values, or return the first
--   <tt>Left</tt>.
andAlso :: (Selective f, Semigroup a) => f (Either e a) -> f (Either e a) -> f (Either e a)

-- | Return the first <tt>Right</tt> value. If both are <tt>Left</tt>'s,
--   accumulate errors.
orElse :: (Selective f, Semigroup e) => f (Either e a) -> f (Either e a) -> f (Either e a)

-- | A lifted version of <a>fromMaybe</a>.
fromMaybeS :: Selective f => f a -> f (Maybe a) -> f a

-- | Conditionally perform an effect.
whenS :: Selective f => f Bool -> f () -> f ()

-- | A restricted version of monadic bind. Fails with an error if the
--   <a>Bounded</a> and <a>Enum</a> instances for <tt>a</tt> do not cover
--   all values of <tt>a</tt>.
bindS :: (Bounded a, Enum a, Eq a, Selective f) => f a -> (a -> f b) -> f b

-- | Eliminate all specified values <tt>a</tt> from <tt>f (Either a b)</tt>
--   by replacing each of them with a given <tt>f a</tt>.
matchM :: Monad m => Cases a -> m a -> (a -> m b) -> m (Either a b)

-- | Eliminate all specified values <tt>a</tt> from <tt>f (Either a b)</tt>
--   by replacing each of them with a given <tt>f a</tt>.
matchS :: (Eq a, Selective f) => Cases a -> f a -> (a -> f b) -> f (Either a b)

-- | Embed a list of values into <a>Cases</a> using the trivial but slow
--   membership test based on <a>elem</a>.
cases :: Eq a => [a] -> Cases a

-- | The list of all possible values of an enumerable data type.
casesEnum :: (Bounded a, Enum a) => Cases a

-- | Branch on a Boolean value, skipping unnecessary effects.
ifS :: Selective f => f Bool -> f a -> f a -> f a

-- | One can easily implement a monadic <a>selectM</a> that satisfies the
--   laws, hence any <a>Monad</a> is <a>Selective</a>.
selectM :: Monad f => f (Either a b) -> f (a -> b) -> f b

-- | Recover the application operator <a>&lt;*&gt;</a> from <a>select</a>.
--   <i>Rigid</i> selective functors satisfy the law <a>&lt;*&gt;</a>
--   <tt>=</tt> <a>apS</a> and furthermore, the resulting applicative
--   functor satisfies all laws of <a>Applicative</a>:
--   
--   <ul>
--   <li>Identity:<pre>pure id &lt;*&gt; v = v</pre></li>
--   <li>Homomorphism:<pre>pure f &lt;*&gt; pure x = pure (f x)</pre></li>
--   <li>Interchange:<pre>u &lt;*&gt; pure y = pure ($y) &lt;*&gt;
--   u</pre></li>
--   <li>Composition:<pre>(.) &lt;$&gt; u &lt;*&gt; v &lt;*&gt; w = u
--   &lt;*&gt; (v &lt;*&gt; w)</pre></li>
--   </ul>
apS :: Selective f => f (a -> b) -> f a -> f b

-- | For traversable functors, we can implement <a>select</a> in another
--   interesting way: the effects associated with the second argument can
--   be skipped as long as the first argument contains only <a>Right</a>
--   values.
selectT :: Traversable f => f (Either a b) -> f (a -> b) -> f b

-- | We can write a function with the type signature of <a>select</a> using
--   the <a>Applicative</a> type class, but it will always execute the
--   effects associated with the second argument, hence being potentially
--   less efficient.
selectA :: Applicative f => f (Either a b) -> f (a -> b) -> f b

-- | The <a>branch</a> function is a natural generalisation of
--   <a>select</a>: instead of skipping an unnecessary effect, it chooses
--   which of the two given effectful functions to apply to a given
--   argument; the other effect is unnecessary. It is possible to implement
--   <a>branch</a> in terms of <a>select</a>, which is a good puzzle (give
--   it a try!).
--   
--   We can also implement <a>select</a> via <a>branch</a>:
--   
--   <pre>
--   selectB :: Selective f =&gt; f (Either a b) -&gt; f (a -&gt; b) -&gt; f b
--   selectB x y = branch x y (pure id)
--   </pre>
branch :: Selective f => f (Either a b) -> f (a -> c) -> f (b -> c) -> f c

-- | An operator alias for <a>select</a>, which is sometimes convenient. It
--   tries to follow the notational convention for <a>Applicative</a>
--   operators. The angle bracket pointing to the left means we always use
--   the corresponding value. The value on the right, however, may be
--   skipped, hence the question mark.
(<*?) :: Selective f => f (Either a b) -> f (a -> b) -> f b
infixl 4 <*?

-- | Selective applicative functors. You can think of <a>select</a> as a
--   selective function application: when given a value of type <a>Left</a>
--   <tt>a</tt>, you <b>must apply</b> the given function, but when given a
--   <a>Right</a> <tt>b</tt>, you <b>may skip</b> the function and
--   associated effects, and simply return the <tt>b</tt>.
--   
--   Note that it is not a requirement for selective functors to skip
--   unnecessary effects. It may be counterintuitive, but this makes them
--   more useful. Why? Typically, when executing a selective computation,
--   you would want to skip the effects (saving work); but on the other
--   hand, if your goal is to statically analyse a given selective
--   computation and extract the set of all possible effects (without
--   actually executing them), then you do not want to skip any effects,
--   because that defeats the purpose of static analysis.
--   
--   The type signature of <a>select</a> is reminiscent of both
--   <a>&lt;*&gt;</a> and <a>&gt;&gt;=</a>, and indeed a selective functor
--   is in some sense a composition of an applicative functor and the
--   <a>Either</a> monad.
--   
--   Laws:
--   
--   <ul>
--   <li>Identity:</li>
--   </ul>
--   
--   <pre>
--   x &lt;*? pure id = either id id &lt;$&gt; x
--   </pre>
--   
--   <ul>
--   <li>Distributivity; note that <tt>y</tt> and <tt>z</tt> have the same
--   type <tt>f (a -&gt; b)</tt>:</li>
--   </ul>
--   
--   <pre>
--   pure x &lt;*? (y *&gt; z) = (pure x &lt;*? y) *&gt; (pure x &lt;*? z)
--   </pre>
--   
--   <ul>
--   <li>Associativity:</li>
--   </ul>
--   
--   <pre>
--   x &lt;*? (y &lt;*? z) = (f &lt;$&gt; x) &lt;*? (g &lt;$&gt; y) &lt;*? (h &lt;$&gt; z)
--     where
--       f x = Right &lt;$&gt; x
--       g y = a -&gt; bimap (,a) ($a) y
--       h z = uncurry z
--   </pre>
--   
--   <ul>
--   <li>Monadic <a>select</a> (for selective functors that are also
--   monads):</li>
--   </ul>
--   
--   <pre>
--   select = selectM
--   </pre>
--   
--   There are also a few useful theorems:
--   
--   <ul>
--   <li>Apply a pure function to the result:</li>
--   </ul>
--   
--   <pre>
--   f &lt;$&gt; select x y = select (fmap f &lt;$&gt; x) (fmap f &lt;$&gt; y)
--   </pre>
--   
--   <ul>
--   <li>Apply a pure function to the <tt>Left</tt> case of the first
--   argument:</li>
--   </ul>
--   
--   <pre>
--   select (first f &lt;$&gt; x) y = select x ((. f) &lt;$&gt; y)
--   </pre>
--   
--   <ul>
--   <li>Apply a pure function to the second argument:</li>
--   </ul>
--   
--   <pre>
--   select x (f &lt;$&gt; y) = select (first (flip f) &lt;$&gt; x) ((&amp;) &lt;$&gt; y)
--   </pre>
--   
--   <ul>
--   <li>Generalised identity:</li>
--   </ul>
--   
--   <pre>
--   x &lt;*? pure y = either y id &lt;$&gt; x
--   </pre>
--   
--   <ul>
--   <li>A selective functor is <i>rigid</i> if it satisfies
--   <a>&lt;*&gt;</a> <tt>=</tt> <a>apS</a>. The following
--   <i>interchange</i> law holds for rigid selective functors:</li>
--   </ul>
--   
--   <pre>
--   x *&gt; (y &lt;*? z) = (x *&gt; y) &lt;*? z
--   </pre>
--   
--   If f is also a <a>Monad</a>, we require that <a>select</a> =
--   <a>selectM</a>, from which one can prove <a>&lt;*&gt;</a> <tt>=</tt>
--   <a>apS</a>.
class Applicative f => Selective (f :: Type -> Type)
select :: Selective f => f (Either a b) -> f (a -> b) -> f b

-- | A list of values, equipped with a fast membership test.
data Cases a

-- | Any applicative functor can be given a <a>Selective</a> instance by
--   defining <a>select</a> <tt>=</tt> <a>selectA</a>. This data type
--   captures this pattern, so you can use it in combination with the
--   <tt>DerivingVia</tt> extension as follows:
--   
--   <pre>
--   newtype Over m a = Over m
--       deriving (Functor, Applicative, Selective) via SelectA (Const m)
--   </pre>
newtype SelectA (f :: Type -> Type) a
SelectA :: f a -> SelectA (f :: Type -> Type) a
[getSelectA] :: SelectA (f :: Type -> Type) a -> f a

-- | Any monad can be given a <a>Selective</a> instance by defining
--   <a>select</a> <tt>=</tt> <a>selectM</a>. This data type captures this
--   pattern, so you can use it in combination with the
--   <tt>DerivingVia</tt> extension as follows:
--   
--   <pre>
--   newtype V1 a = V1 a
--       deriving (Functor, Applicative, Selective, Monad) via SelectM Identity
--   </pre>
newtype SelectM (f :: Type -> Type) a
SelectM :: f a -> SelectM (f :: Type -> Type) a
[getSelectM] :: SelectM (f :: Type -> Type) a -> f a

-- | Static analysis of selective functors with over-approximation.
newtype Over m a
Over :: m -> Over m a
[getOver] :: Over m a -> m

-- | Static analysis of selective functors with under-approximation.
newtype Under m a
Under :: m -> Under m a
[getUnder] :: Under m a -> m

-- | Selective instance for the standard applicative functor Validation.
--   This is a good example of a non-trivial selective functor which is not
--   a monad.
data Validation e a
Failure :: e -> Validation e a
Success :: a -> Validation e a

-- | Composition of a selective functor <tt>f</tt> and an applicative
--   traversable functor <tt>g</tt>.
newtype ComposeTraversable (f :: Type -> Type) (g :: Type -> Type) a
ComposeTraversable :: f (g a) -> ComposeTraversable (f :: Type -> Type) (g :: Type -> Type) a

-- | Composition of a selective functor <tt>f</tt> with the <a>Either</a>
--   monad.
newtype ComposeEither (f :: Type -> Type) e a
ComposeEither :: f (Either e a) -> ComposeEither (f :: Type -> Type) e a

-- | The sum of a collection of actions, generalizing <a>concat</a>.
--   
--   <pre>
--   &gt;&gt;&gt; psum [Just "Hello", Nothing, Just "World"]
--   Just "Hello"
--   </pre>
psum :: (Foldable t, Plus f) => t (f a) -> f a

-- | Laws:
--   
--   <pre>
--   zero &lt;!&gt; m = m
--   m &lt;!&gt; zero = m
--   </pre>
--   
--   If extended to an <a>Alternative</a> then <a>zero</a> should equal
--   <a>empty</a>.
class Alt f => Plus (f :: Type -> Type)
zero :: Plus f => f a
bifoldMap1Default :: (Bitraversable1 t, Semigroup m) => (a -> m) -> (b -> m) -> t a b -> m

-- | Default implementation of <tt>foldMap1</tt> given an implementation of
--   <a>Traversable1</a>.
foldMap1Default :: (Traversable1 f, Semigroup m) => (a -> m) -> f a -> m
class (Bifoldable1 t, Bitraversable t) => Bitraversable1 (t :: TYPE LiftedRep -> TYPE LiftedRep -> Type)
bitraverse1 :: (Bitraversable1 t, Apply f) => (a -> f b) -> (c -> f d) -> t a c -> f (t b d)
bisequence1 :: (Bitraversable1 t, Apply f) => t (f a) (f b) -> f (t a b)
class (Foldable1 t, Traversable t) => Traversable1 (t :: TYPE LiftedRep -> Type)
traverse1 :: (Traversable1 t, Apply f) => (a -> f b) -> t a -> f (t b)
sequence1 :: (Traversable1 t, Apply f) => t (f b) -> f (t b)

-- | Monadic fold over the elements of a non-empty structure, associating
--   to the left, i.e. from left to right.
--   
--   <pre>
--   let g = flip $ (=&lt;&lt;) . f
--   in foldlM1 f (x1 :| [x2, ..., xn]) == (...((x1 `f` x2) `g` x2) `g`...) `g` xn
--   </pre>
foldlM1 :: (Foldable1 t, Monad m) => (a -> a -> m a) -> t a -> m a

-- | Monadic fold over the elements of a non-empty structure, associating
--   to the right, i.e. from right to left.
--   
--   <pre>
--   let g = (=&lt;&lt;) . f
--   in foldrM1 f (x1 :| [x2, ..., xn]) == x1 `g` (x2 `g` ... (xn-1 `f` xn)...)
--   </pre>
foldrM1 :: (Foldable1 t, Monad m) => (a -> a -> m a) -> t a -> m a
asum1 :: (Foldable1 t, Alt m) => t (m a) -> m a

-- | Usable default for foldMap, but only if you define foldMap1 yourself
foldMapDefault1 :: (Foldable1 t, Monoid m) => (a -> m) -> t a -> m
sequenceA1_ :: (Foldable1 t, Apply f) => t (f a) -> f ()
for1_ :: (Foldable1 t, Apply f) => t a -> (a -> f b) -> f ()
traverse1_ :: (Foldable1 t, Apply f) => (a -> f b) -> t a -> f ()

-- | Insert <tt>m</tt> between each pair of <tt>m</tt> derived from
--   <tt>a</tt>.
--   
--   <pre>
--   &gt;&gt;&gt; intercalateMap1 " " show $ True :| [False, True]
--   "True False True"
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; intercalateMap1 " " show $ True :| []
--   "True"
--   </pre>
intercalateMap1 :: (Foldable1 t, Semigroup m) => m -> (a -> m) -> t a -> m

-- | Insert an <tt>m</tt> between each pair of <tt>t m</tt>. Equivalent to
--   <a>intercalateMap1</a> with <a>id</a> as the second argument.
--   
--   <pre>
--   &gt;&gt;&gt; intercalate1 ", " $ "hello" :| ["how", "are", "you"]
--   "hello, how, are, you"
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; intercalate1 ", " $ "hello" :| []
--   "hello"
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; intercalate1 mempty $ "I" :| ["Am", "Fine", "You?"]
--   "IAmFineYou?"
--   </pre>
intercalate1 :: (Foldable1 t, Semigroup m) => m -> t m -> m

-- | Laws:
--   
--   <pre>
--   &lt;!&gt; is associative:             (a &lt;!&gt; b) &lt;!&gt; c = a &lt;!&gt; (b &lt;!&gt; c)
--   &lt;$&gt; left-distributes over &lt;!&gt;:  f &lt;$&gt; (a &lt;!&gt; b) = (f &lt;$&gt; a) &lt;!&gt; (f &lt;$&gt; b)
--   </pre>
--   
--   If extended to an <a>Alternative</a> then <a>&lt;!&gt;</a> should
--   equal <a>&lt;|&gt;</a>.
--   
--   Ideally, an instance of <a>Alt</a> also satisfies the "left
--   distribution" law of MonadPlus with respect to <a>&lt;.&gt;</a>:
--   
--   <pre>
--   &lt;.&gt; right-distributes over &lt;!&gt;: (a &lt;!&gt; b) &lt;.&gt; c = (a &lt;.&gt; c) &lt;!&gt; (b &lt;.&gt; c)
--   </pre>
--   
--   <a>IO</a>, <tt><a>Either</a> a</tt>, <tt><a>ExceptT</a> e m</tt> and
--   <a>STM</a> instead satisfy the "left catch" law:
--   
--   <pre>
--   pure a &lt;!&gt; b = pure a
--   </pre>
--   
--   <a>Maybe</a> and <a>Identity</a> satisfy both "left distribution" and
--   "left catch".
--   
--   These variations cannot be stated purely in terms of the dependencies
--   of <a>Alt</a>.
--   
--   When and if MonadPlus is successfully refactored, this class should
--   also be refactored to remove these instances.
--   
--   The right distributive law should extend in the cases where the a
--   <tt>Bind</tt> or <a>Monad</a> is provided to yield variations of the
--   right distributive law:
--   
--   <pre>
--   (m &lt;!&gt; n) &gt;&gt;- f = (m &gt;&gt;- f) &lt;!&gt; (m &gt;&gt;- f)
--   (m &lt;!&gt; n) &gt;&gt;= f = (m &gt;&gt;= f) &lt;!&gt; (m &gt;&gt;= f)
--   </pre>
class Functor f => Alt (f :: Type -> Type)

-- | <a>&lt;|&gt;</a> without a required <tt>empty</tt>
(<!>) :: Alt f => f a -> f a -> f a
infixl 3 <!>

-- | Lift ternary functions
bilift3 :: Biapply w => (a -> b -> c -> d) -> (e -> f -> g -> h) -> w a e -> w b f -> w c g -> w d h

-- | Lift binary functions
bilift2 :: Biapply w => (a -> b -> c) -> (d -> e -> f) -> w a d -> w b e -> w c f
(<<..>>) :: Biapply p => p a c -> p (a -> b) (c -> d) -> p b d
infixl 4 <<..>>

-- | semigroupoid with inverses. This technically should be a category with
--   inverses, except we need to use Ob to define the valid objects for the
--   category
class Semigroupoid k1 => Groupoid (k1 :: k -> k -> Type)
inv :: forall (a :: k) (b :: k). Groupoid k1 => k1 a b -> k1 b a

-- | <a>Category</a> sans <a>id</a>
class Semigroupoid (c :: k -> k -> Type)
o :: forall (j :: k) (k1 :: k) (i :: k). Semigroupoid c => c j k1 -> c i j -> c i k1
newtype WrappedCategory (k2 :: k -> k1 -> Type) (a :: k) (b :: k1)
WrapCategory :: k2 a b -> WrappedCategory (k2 :: k -> k1 -> Type) (a :: k) (b :: k1)
[unwrapCategory] :: WrappedCategory (k2 :: k -> k1 -> Type) (a :: k) (b :: k1) -> k2 a b
newtype Semi m (a :: k) (b :: k1)
Semi :: m -> Semi m (a :: k) (b :: k1)
[getSemi] :: Semi m (a :: k) (b :: k1) -> m
(-<-) :: Bind m => (b -> m c) -> (a -> m b) -> a -> m c
infixr 1 -<-
(->-) :: Bind m => (a -> m b) -> (b -> m c) -> a -> m c
infixr 1 ->-
(-<<) :: Bind m => (a -> m b) -> m a -> m b
infixr 1 -<<

-- | Usable default for foldMap, but only if you define bifoldMap1 yourself
bifoldMapDefault1 :: (Bifoldable1 t, Monoid m) => (a -> m) -> (b -> m) -> t a b -> m
bisequenceA1_ :: (Bifoldable1 t, Apply f) => t (f a) (f b) -> f ()
bifor1_ :: (Bifoldable1 t, Apply f) => t a c -> (a -> f b) -> (c -> f d) -> f ()
bitraverse1_ :: (Bifoldable1 t, Apply f) => (a -> f b) -> (c -> f d) -> t a c -> f ()

-- | Lift a ternary function into a comonad with zipping
liftF3 :: Apply w => (a -> b -> c -> d) -> w a -> w b -> w c -> w d

-- | A variant of <a>&lt;.&gt;</a> with the arguments reversed.
(<..>) :: Apply w => w a -> w (a -> b) -> w b
infixl 4 <..>
apDefault :: Bind f => f (a -> b) -> f a -> f b
returning :: Functor f => f a -> (a -> b) -> f b

-- | Traverse a <a>Traversable</a> using <a>Apply</a>, getting the results
--   back in a <a>MaybeApply</a>.
traverse1Maybe :: (Traversable t, Apply f) => (a -> f b) -> t a -> MaybeApply f (t b)

-- | Apply a possibly-empty-with-unit container of functions to a non-empty
--   container of values.
(<*.>) :: Apply f => MaybeApply f (a -> b) -> f a -> f b
infixl 4 <*.>

-- | Apply a non-empty container of functions to a possibly-empty-with-unit
--   container of values.
(<.*>) :: Apply f => f (a -> b) -> MaybeApply f a -> f b
infixl 4 <.*>

-- | A strong lax semi-monoidal endofunctor. This is equivalent to an
--   <a>Applicative</a> without <a>pure</a>.
--   
--   Laws:
--   
--   <pre>
--   (<a>.</a>) <a>&lt;$&gt;</a> u <a>&lt;.&gt;</a> v <a>&lt;.&gt;</a> w = u <a>&lt;.&gt;</a> (v <a>&lt;.&gt;</a> w)
--   x <a>&lt;.&gt;</a> (f <a>&lt;$&gt;</a> y) = (<a>.</a> f) <a>&lt;$&gt;</a> x <a>&lt;.&gt;</a> y
--   f <a>&lt;$&gt;</a> (x <a>&lt;.&gt;</a> y) = (f <a>.</a>) <a>&lt;$&gt;</a> x <a>&lt;.&gt;</a> y
--   </pre>
--   
--   The laws imply that <a>.&gt;</a> and <a>&lt;.</a> really ignore their
--   left and right results, respectively, and really return their right
--   and left results, respectively. Specifically,
--   
--   <pre>
--   (mf <a>&lt;$&gt;</a> m) <a>.&gt;</a> (nf <a>&lt;$&gt;</a> n) = nf <a>&lt;$&gt;</a> (m <a>.&gt;</a> n)
--   (mf <a>&lt;$&gt;</a> m) <a>&lt;.</a> (nf <a>&lt;$&gt;</a> n) = mf <a>&lt;$&gt;</a> (m <a>&lt;.</a> n)
--   </pre>
class Functor f => Apply (f :: Type -> Type)
(<.>) :: Apply f => f (a -> b) -> f a -> f b

-- | <pre>
--   a <a>.&gt;</a> b = <a>const</a> <a>id</a> <a>&lt;$&gt;</a> a <a>&lt;.&gt;</a> b
--   </pre>
(.>) :: Apply f => f a -> f b -> f b

-- | <pre>
--   a <a>&lt;.</a> b = <a>const</a> <a>&lt;$&gt;</a> a <a>&lt;.&gt;</a> b
--   </pre>
(<.) :: Apply f => f a -> f b -> f a

-- | Lift a binary function into a comonad with zipping
liftF2 :: Apply f => (a -> b -> c) -> f a -> f b -> f c
infixl 4 <.
infixl 4 <.>
infixl 4 .>

-- | Wrap an <a>Applicative</a> to be used as a member of <a>Apply</a>
newtype WrappedApplicative (f :: Type -> Type) a
WrapApplicative :: f a -> WrappedApplicative (f :: Type -> Type) a
[unwrapApplicative] :: WrappedApplicative (f :: Type -> Type) a -> f a

-- | Transform an Apply into an Applicative by adding a unit.
newtype MaybeApply (f :: Type -> Type) a
MaybeApply :: Either (f a) a -> MaybeApply (f :: Type -> Type) a
[runMaybeApply] :: MaybeApply (f :: Type -> Type) a -> Either (f a) a

-- | A <a>Monad</a> sans <a>return</a>.
--   
--   Minimal definition: Either <a>join</a> or <a>&gt;&gt;-</a>
--   
--   If defining both, then the following laws (the default definitions)
--   must hold:
--   
--   <pre>
--   join = (&gt;&gt;- id)
--   m &gt;&gt;- f = join (fmap f m)
--   </pre>
--   
--   Laws:
--   
--   <pre>
--   induced definition of &lt;.&gt;: f &lt;.&gt; x = f &gt;&gt;- (&lt;$&gt; x)
--   </pre>
--   
--   Finally, there are two associativity conditions:
--   
--   <pre>
--   associativity of (&gt;&gt;-):    (m &gt;&gt;- f) &gt;&gt;- g == m &gt;&gt;- (\x -&gt; f x &gt;&gt;- g)
--   associativity of join:     join . join = join . fmap join
--   </pre>
--   
--   These can both be seen as special cases of the constraint that
--   
--   <pre>
--   associativity of (-&gt;-): (f -&gt;- g) -&gt;- h = f -&gt;- (g -&gt;- h)
--   </pre>
class Apply m => Bind (m :: Type -> Type)
(>>-) :: Bind m => m a -> (a -> m b) -> m b
infixl 1 >>-
class Bifunctor p => Biapply (p :: Type -> Type -> Type)
(<<.>>) :: Biapply p => p (a -> b) (c -> d) -> p a c -> p b d

-- | <pre>
--   a <a>.&gt;</a> b ≡ <a>const</a> <a>id</a> <a>&lt;$&gt;</a> a <a>&lt;.&gt;</a> b
--   </pre>
(.>>) :: Biapply p => p a b -> p c d -> p c d

-- | <pre>
--   a <a>&lt;.</a> b ≡ <a>const</a> <a>&lt;$&gt;</a> a <a>&lt;.&gt;</a> b
--   </pre>
(<<.) :: Biapply p => p a b -> p c d -> p a b
infixl 4 <<.
infixl 4 <<.>>
infixl 4 .>>
class Foldable t => Foldable1 (t :: TYPE LiftedRep -> Type)
fold1 :: (Foldable1 t, Semigroup m) => t m -> m
foldMap1 :: (Foldable1 t, Semigroup m) => (a -> m) -> t a -> m
toNonEmpty :: Foldable1 t => t a -> NonEmpty a
class Bifoldable t => Bifoldable1 (t :: TYPE LiftedRep -> TYPE LiftedRep -> Type)
bifold1 :: (Bifoldable1 t, Semigroup m) => t m m -> m
bifoldMap1 :: (Bifoldable1 t, Semigroup m) => (a -> m) -> (b -> m) -> t a b -> m
class Functor w => Extend (w :: Type -> Type)

-- | <pre>
--   duplicated = extended id
--   fmap (fmap f) . duplicated = duplicated . fmap f
--   </pre>
duplicated :: Extend w => w a -> w (w a)

-- | <pre>
--   extended f  = fmap f . duplicated
--   </pre>
extended :: Extend w => (w a -> b) -> w a -> w b

-- | Check that the boolean condition is true and, if not, <a>retry</a>.
--   
--   In other words, <tt>check b = unless b retry</tt>.
check :: Bool -> STM ()

-- | TArray is a transactional array, supporting the usual <a>MArray</a>
--   interface for mutable arrays.
--   
--   It is currently implemented as <tt>Array ix (TVar e)</tt>, but it may
--   be replaced by a more efficient implementation in the future (the
--   interface will remain the same, however).
data TArray i e

-- | Swap the contents of a <a>TVar</a> for a new value.
swapTVar :: TVar a -> a -> STM a

-- | Like <a>modifyTVar'</a> but the function is a simple state transition
--   that can return a side value which is passed on as the result of the
--   <a>STM</a>.
stateTVar :: TVar s -> (s -> (a, s)) -> STM a

-- | Strict version of <a>modifyTVar</a>.
modifyTVar' :: TVar a -> (a -> a) -> STM ()

-- | Mutate the contents of a <a>TVar</a>. <i>N.B.</i>, this version is
--   non-strict.
modifyTVar :: TVar a -> (a -> a) -> STM ()

-- | Make a <a>Weak</a> pointer to a <a>TVar</a>, using the second argument
--   as a finalizer to run when <a>TVar</a> is garbage-collected
mkWeakTVar :: TVar a -> IO () -> IO (Weak (TVar a))

-- | <a>TQueue</a> is an abstract type representing an unbounded FIFO
--   channel.
data TQueue a

-- | Write a value to a <a>TQueue</a>.
writeTQueue :: TQueue a -> a -> STM ()

-- | Put a data item back onto a channel, where it will be the next item
--   read.
unGetTQueue :: TQueue a -> a -> STM ()

-- | A version of <a>readTQueue</a> which does not retry. Instead it
--   returns <tt>Nothing</tt> if no value is available.
tryReadTQueue :: TQueue a -> STM (Maybe a)

-- | A version of <a>peekTQueue</a> which does not retry. Instead it
--   returns <tt>Nothing</tt> if no value is available.
tryPeekTQueue :: TQueue a -> STM (Maybe a)

-- | Read the next value from the <a>TQueue</a>.
readTQueue :: TQueue a -> STM a

-- | Get the next value from the <tt>TQueue</tt> without removing it,
--   retrying if the channel is empty.
peekTQueue :: TQueue a -> STM a

-- | <tt>IO</tt> version of <a>newTQueue</a>. This is useful for creating
--   top-level <a>TQueue</a>s using <a>unsafePerformIO</a>, because using
--   <a>atomically</a> inside <a>unsafePerformIO</a> isn't possible.
newTQueueIO :: IO (TQueue a)

-- | Build and returns a new instance of <a>TQueue</a>
newTQueue :: STM (TQueue a)

-- | Returns <a>True</a> if the supplied <a>TQueue</a> is empty.
isEmptyTQueue :: TQueue a -> STM Bool

-- | Efficiently read the entire contents of a <a>TQueue</a> into a list.
--   This function never retries.
flushTQueue :: TQueue a -> STM [a]

-- | A <a>TMVar</a> is a synchronising variable, used for communication
--   between concurrent threads. It can be thought of as a box, which may
--   be empty or full.
data TMVar a

-- | A version of <a>takeTMVar</a> that does not <a>retry</a>. The
--   <a>tryTakeTMVar</a> function returns <a>Nothing</a> if the
--   <a>TMVar</a> was empty, or <tt><a>Just</a> a</tt> if the <a>TMVar</a>
--   was full with contents <tt>a</tt>. After <a>tryTakeTMVar</a>, the
--   <a>TMVar</a> is left empty.
tryTakeTMVar :: TMVar a -> STM (Maybe a)

-- | A version of <a>readTMVar</a> which does not retry. Instead it returns
--   <tt>Nothing</tt> if no value is available.
tryReadTMVar :: TMVar a -> STM (Maybe a)

-- | A version of <a>putTMVar</a> that does not <a>retry</a>. The
--   <a>tryPutTMVar</a> function attempts to put the value <tt>a</tt> into
--   the <a>TMVar</a>, returning <a>True</a> if it was successful, or
--   <a>False</a> otherwise.
tryPutTMVar :: TMVar a -> a -> STM Bool

-- | Return the contents of the <a>TMVar</a>. If the <a>TMVar</a> is
--   currently empty, the transaction will <a>retry</a>. After a
--   <a>takeTMVar</a>, the <a>TMVar</a> is left empty.
takeTMVar :: TMVar a -> STM a

-- | Swap the contents of a <a>TMVar</a> for a new value.
swapTMVar :: TMVar a -> a -> STM a

-- | This is a combination of <a>takeTMVar</a> and <a>putTMVar</a>; ie. it
--   takes the value from the <a>TMVar</a>, puts it back, and also returns
--   it.
readTMVar :: TMVar a -> STM a

-- | Put a value into a <a>TMVar</a>. If the <a>TMVar</a> is currently
--   full, <a>putTMVar</a> will <a>retry</a>.
putTMVar :: TMVar a -> a -> STM ()

-- | <tt>IO</tt> version of <a>newTMVar</a>. This is useful for creating
--   top-level <a>TMVar</a>s using <a>unsafePerformIO</a>, because using
--   <a>atomically</a> inside <a>unsafePerformIO</a> isn't possible.
newTMVarIO :: a -> IO (TMVar a)

-- | Create a <a>TMVar</a> which contains the supplied value.
newTMVar :: a -> STM (TMVar a)

-- | <tt>IO</tt> version of <a>newEmptyTMVar</a>. This is useful for
--   creating top-level <a>TMVar</a>s using <a>unsafePerformIO</a>, because
--   using <a>atomically</a> inside <a>unsafePerformIO</a> isn't possible.
newEmptyTMVarIO :: IO (TMVar a)

-- | Create a <a>TMVar</a> which is initially empty.
newEmptyTMVar :: STM (TMVar a)

-- | Make a <a>Weak</a> pointer to a <a>TMVar</a>, using the second
--   argument as a finalizer to run when the <a>TMVar</a> is
--   garbage-collected.
mkWeakTMVar :: TMVar a -> IO () -> IO (Weak (TMVar a))

-- | Check whether a given <a>TMVar</a> is empty.
isEmptyTMVar :: TMVar a -> STM Bool

-- | <a>TChan</a> is an abstract type representing an unbounded FIFO
--   channel.
data TChan a

-- | Write a value to a <a>TChan</a>.
writeTChan :: TChan a -> a -> STM ()

-- | Put a data item back onto a channel, where it will be the next item
--   read.
unGetTChan :: TChan a -> a -> STM ()

-- | A version of <a>readTChan</a> which does not retry. Instead it returns
--   <tt>Nothing</tt> if no value is available.
tryReadTChan :: TChan a -> STM (Maybe a)

-- | A version of <a>peekTChan</a> which does not retry. Instead it returns
--   <tt>Nothing</tt> if no value is available.
tryPeekTChan :: TChan a -> STM (Maybe a)

-- | Read the next value from the <a>TChan</a>.
readTChan :: TChan a -> STM a

-- | Get the next value from the <tt>TChan</tt> without removing it,
--   retrying if the channel is empty.
peekTChan :: TChan a -> STM a

-- | <tt>IO</tt> version of <a>newTChan</a>. This is useful for creating
--   top-level <a>TChan</a>s using <a>unsafePerformIO</a>, because using
--   <a>atomically</a> inside <a>unsafePerformIO</a> isn't possible.
newTChanIO :: IO (TChan a)

-- | Build and return a new instance of <a>TChan</a>
newTChan :: STM (TChan a)

-- | <tt>IO</tt> version of <a>newBroadcastTChan</a>.
newBroadcastTChanIO :: IO (TChan a)

-- | Create a write-only <a>TChan</a>. More precisely, <a>readTChan</a>
--   will <a>retry</a> even after items have been written to the channel.
--   The only way to read a broadcast channel is to duplicate it with
--   <a>dupTChan</a>.
--   
--   Consider a server that broadcasts messages to clients:
--   
--   <pre>
--   serve :: TChan Message -&gt; Client -&gt; IO loop
--   serve broadcastChan client = do
--       myChan &lt;- dupTChan broadcastChan
--       forever $ do
--           message &lt;- readTChan myChan
--           send client message
--   </pre>
--   
--   The problem with using <a>newTChan</a> to create the broadcast channel
--   is that if it is only written to and never read, items will pile up in
--   memory. By using <a>newBroadcastTChan</a> to create the broadcast
--   channel, items can be garbage collected after clients have seen them.
newBroadcastTChan :: STM (TChan a)

-- | Returns <a>True</a> if the supplied <a>TChan</a> is empty.
isEmptyTChan :: TChan a -> STM Bool

-- | Duplicate a <a>TChan</a>: the duplicate channel begins empty, but data
--   written to either channel from then on will be available from both.
--   Hence this creates a kind of broadcast channel, where data written by
--   anyone is seen by everyone else.
dupTChan :: TChan a -> STM (TChan a)

-- | Clone a <a>TChan</a>: similar to dupTChan, but the cloned channel
--   starts with the same content available as the original channel.
cloneTChan :: TChan a -> STM (TChan a)

-- | <a>TBQueue</a> is an abstract type representing a bounded FIFO
--   channel.
data TBQueue a

-- | Write a value to a <a>TBQueue</a>; blocks if the queue is full.
writeTBQueue :: TBQueue a -> a -> STM ()

-- | Put a data item back onto a channel, where it will be the next item
--   read. Blocks if the queue is full.
unGetTBQueue :: TBQueue a -> a -> STM ()

-- | A version of <a>readTBQueue</a> which does not retry. Instead it
--   returns <tt>Nothing</tt> if no value is available.
tryReadTBQueue :: TBQueue a -> STM (Maybe a)

-- | A version of <a>peekTBQueue</a> which does not retry. Instead it
--   returns <tt>Nothing</tt> if no value is available.
tryPeekTBQueue :: TBQueue a -> STM (Maybe a)

-- | Read the next value from the <a>TBQueue</a>.
readTBQueue :: TBQueue a -> STM a

-- | Get the next value from the <tt>TBQueue</tt> without removing it,
--   retrying if the channel is empty.
peekTBQueue :: TBQueue a -> STM a

-- | <tt>IO</tt> version of <a>newTBQueue</a>. This is useful for creating
--   top-level <a>TBQueue</a>s using <a>unsafePerformIO</a>, because using
--   <tt>atomically</tt> inside <a>unsafePerformIO</a> isn't possible.
newTBQueueIO :: Natural -> IO (TBQueue a)

-- | Builds and returns a new instance of <a>TBQueue</a>.
newTBQueue :: Natural -> STM (TBQueue a)

-- | Return the length of a <a>TBQueue</a>.
lengthTBQueue :: TBQueue a -> STM Natural

-- | Returns <a>True</a> if the supplied <a>TBQueue</a> is full.
isFullTBQueue :: TBQueue a -> STM Bool

-- | Returns <a>True</a> if the supplied <a>TBQueue</a> is empty.
isEmptyTBQueue :: TBQueue a -> STM Bool

-- | Efficiently read the entire contents of a <a>TBQueue</a> into a list.
--   This function never retries.
flushTBQueue :: TBQueue a -> STM [a]

-- | A space efficient, packed, unboxed Unicode text type.
data Text
class ISO8601 t

-- | The most commonly used ISO 8601 format for this type.
iso8601Format :: ISO8601 t => Format t

-- | Show in the most commonly used ISO 8601 format.
iso8601Show :: ISO8601 t => t -> String

-- | Parse the most commonly used ISO 8601 format.
iso8601ParseM :: (MonadFail m, ISO8601 t) => String -> m t

-- | Parse a time value given a format string. See <a>parseTimeM</a> for
--   details.
readSTime :: ParseTime t => Bool -> TimeLocale -> String -> ReadS t

-- | Parse a time value given a format string. See <a>parseTimeM</a> for
--   details.
readPTime :: ParseTime t => Bool -> TimeLocale -> String -> ReadP t

-- | Parse a time value given a format string. Fails if the input could not
--   be parsed using the given format. See <a>parseTimeM</a> for details.
parseTimeOrError :: ParseTime t => Bool -> TimeLocale -> String -> String -> t

-- | Parses a time value given a list of pairs of format and input.
--   Resulting value is constructed from all provided specifiers.
parseTimeMultipleM :: (MonadFail m, ParseTime t) => Bool -> TimeLocale -> [(String, String)] -> m t

-- | Parses a time value given a format string. Missing information will be
--   derived from 1970-01-01 00:00 UTC (which was a Thursday). Supports the
--   same %-codes as <tt>formatTime</tt>, including <tt>%-</tt>,
--   <tt>%_</tt> and <tt>%0</tt> modifiers, however padding widths are not
--   supported. Case is not significant in the input string. Some
--   variations in the input are accepted:
--   
--   <ul>
--   <li><i><tt>%z</tt> <tt>%Ez</tt></i> accepts any of <tt>±HHMM</tt> or
--   <tt>±HH:MM</tt>.</li>
--   <li><i><tt>%Z</tt> <tt>%EZ</tt></i> accepts any string of letters, or
--   any of the formats accepted by <tt>%z</tt>.</li>
--   <li><i><tt>%0Y</tt></i> accepts exactly four digits.</li>
--   <li><i><tt>%0G</tt></i> accepts exactly four digits.</li>
--   <li><i><tt>%0C</tt></i> accepts exactly two digits.</li>
--   <li><i><tt>%0f</tt></i> accepts exactly two digits.</li>
--   </ul>
--   
--   For example, to parse a date in YYYY-MM-DD format, while allowing the
--   month and date to have optional leading zeros (notice the <tt>-</tt>
--   modifier used for <tt>%m</tt> and <tt>%d</tt>):
--   
--   <pre>
--   Prelude Data.Time&gt; parseTimeM True defaultTimeLocale "%Y-%-m-%-d" "2010-3-04" :: Maybe Day
--   Just 2010-03-04
--   </pre>
parseTimeM :: (MonadFail m, ParseTime t) => Bool -> TimeLocale -> String -> String -> m t

-- | A local time together with a time zone.
--   
--   There is no <a>Eq</a> instance for <tt>ZonedTime</tt>. If you want to
--   compare local times, use <a>zonedTimeToLocalTime</a>. If you want to
--   compare absolute times, use <a>zonedTimeToUTC</a>.
data ZonedTime
ZonedTime :: LocalTime -> TimeZone -> ZonedTime
[zonedTimeToLocalTime] :: ZonedTime -> LocalTime
[zonedTimeZone] :: ZonedTime -> TimeZone
zonedTimeToUTC :: ZonedTime -> UTCTime
utcToZonedTime :: TimeZone -> UTCTime -> ZonedTime

utcToLocalZonedTime :: UTCTime -> IO ZonedTime
getZonedTime :: IO ZonedTime
class FormatTime t

-- | Substitute various time-related information for each %-code in the
--   string, as per <a>formatCharacter</a>.
--   
--   The general form is
--   <tt>%&lt;modifier&gt;&lt;width&gt;&lt;alternate&gt;&lt;specifier&gt;</tt>,
--   where <tt>&lt;modifier&gt;</tt>, <tt>&lt;width&gt;</tt>, and
--   <tt>&lt;alternate&gt;</tt> are optional.
--   
--   <h2><tt>&lt;modifier&gt;</tt></h2>
--   
--   glibc-style modifiers can be used before the specifier (here marked as
--   <tt>z</tt>):
--   
--   <ul>
--   <li><i><tt>%-z</tt></i> no padding</li>
--   <li><i><tt>%_z</tt></i> pad with spaces</li>
--   <li><i><tt>%0z</tt></i> pad with zeros</li>
--   <li><i><tt>%^z</tt></i> convert to upper case</li>
--   <li><i><tt>%#z</tt></i> convert to lower case (consistently, unlike
--   glibc)</li>
--   </ul>
--   
--   <h2><tt>&lt;width&gt;</tt></h2>
--   
--   Width digits can also be used after any modifiers and before the
--   specifier (here marked as <tt>z</tt>), for example:
--   
--   <ul>
--   <li><i><tt>%4z</tt></i> pad to 4 characters (with default padding
--   character)</li>
--   <li><i><tt>%_12z</tt></i> pad with spaces to 12 characters</li>
--   </ul>
--   
--   <h2><tt>&lt;alternate&gt;</tt></h2>
--   
--   An optional <tt>E</tt> character indicates an alternate formatting.
--   Currently this only affects <tt>%Z</tt> and <tt>%z</tt>.
--   
--   <ul>
--   <li><i><tt>%Ez</tt></i> alternate formatting</li>
--   </ul>
--   
--   <h2><tt>&lt;specifier&gt;</tt></h2>
--   
--   For all types (note these three are done by <a>formatTime</a>, not by
--   <a>formatCharacter</a>):
--   
--   <ul>
--   <li><i><tt>%%</tt></i> <tt>%</tt></li>
--   <li><i><tt>%t</tt></i> tab</li>
--   <li><i><tt>%n</tt></i> newline</li>
--   </ul>
--   
--   <h3><tt>TimeZone</tt></h3>
--   
--   For <tt>TimeZone</tt> (and <tt>ZonedTime</tt> and <tt>UTCTime</tt>):
--   
--   <ul>
--   <li><i><tt>%z</tt></i> timezone offset in the format
--   <tt>±HHMM</tt></li>
--   <li><i><tt>%Ez</tt></i> timezone offset in the format
--   <tt>±HH:MM</tt></li>
--   <li><i><tt>%Z</tt></i> timezone name (or else offset in the format
--   <tt>±HHMM</tt>)</li>
--   <li><i><tt>%EZ</tt></i> timezone name (or else offset in the format
--   <tt>±HH:MM</tt>)</li>
--   </ul>
--   
--   <h3><tt>LocalTime</tt></h3>
--   
--   For <tt>LocalTime</tt> (and <tt>ZonedTime</tt> and <tt>UTCTime</tt>
--   and <tt>UniversalTime</tt>):
--   
--   <ul>
--   <li><i><tt>%c</tt></i> as <a>dateTimeFmt</a> <tt>locale</tt> (e.g.
--   <tt>%a %b %e %H:%M:%S %Z %Y</tt>)</li>
--   </ul>
--   
--   <h3><tt>TimeOfDay</tt></h3>
--   
--   For <tt>TimeOfDay</tt> (and <tt>LocalTime</tt> and <tt>ZonedTime</tt>
--   and <tt>UTCTime</tt> and <tt>UniversalTime</tt>):
--   
--   <ul>
--   <li><i><tt>%R</tt></i> same as <tt>%H:%M</tt></li>
--   <li><i><tt>%T</tt></i> same as <tt>%H:%M:%S</tt></li>
--   <li><i><tt>%X</tt></i> as <a>timeFmt</a> <tt>locale</tt> (e.g.
--   <tt>%H:%M:%S</tt>)</li>
--   <li><i><tt>%r</tt></i> as <a>time12Fmt</a> <tt>locale</tt> (e.g.
--   <tt>%I:%M:%S %p</tt>)</li>
--   <li><i><tt>%P</tt></i> day-half of day from (<a>amPm</a>
--   <tt>locale</tt>), converted to lowercase, <tt>am</tt>,
--   <tt>pm</tt></li>
--   <li><i><tt>%p</tt></i> day-half of day from (<a>amPm</a>
--   <tt>locale</tt>), <tt>AM</tt>, <tt>PM</tt></li>
--   <li><i><tt>%H</tt></i> hour of day (24-hour), 0-padded to two chars,
--   <tt>00</tt> - <tt>23</tt></li>
--   <li><i><tt>%k</tt></i> hour of day (24-hour), space-padded to two
--   chars, <tt> 0</tt> - <tt>23</tt></li>
--   <li><i><tt>%I</tt></i> hour of day-half (12-hour), 0-padded to two
--   chars, <tt>01</tt> - <tt>12</tt></li>
--   <li><i><tt>%l</tt></i> hour of day-half (12-hour), space-padded to two
--   chars, <tt> 1</tt> - <tt>12</tt></li>
--   <li><i><tt>%M</tt></i> minute of hour, 0-padded to two chars,
--   <tt>00</tt> - <tt>59</tt></li>
--   <li><i><tt>%S</tt></i> second of minute (without decimal part),
--   0-padded to two chars, <tt>00</tt> - <tt>60</tt></li>
--   <li><i><tt>%q</tt></i> picosecond of second, 0-padded to twelve chars,
--   <tt>000000000000</tt> - <tt>999999999999</tt>.</li>
--   <li><i><tt>%Q</tt></i> decimal point and fraction of second, up to 12
--   second decimals, without trailing zeros. For a whole number of
--   seconds, <tt>%Q</tt> omits the decimal point unless padding is
--   specified.</li>
--   </ul>
--   
--   <h3><tt>UTCTime</tt> and <tt>ZonedTime</tt></h3>
--   
--   For <tt>UTCTime</tt> and <tt>ZonedTime</tt>:
--   
--   <ul>
--   <li><i><tt>%s</tt></i> number of whole seconds since the Unix epoch.
--   For times before the Unix epoch, this is a negative number. Note that
--   in <tt>%s.%q</tt> and <tt>%s%Q</tt> the decimals are positive, not
--   negative. For example, 0.9 seconds before the Unix epoch is formatted
--   as <tt>-1.1</tt> with <tt>%s%Q</tt>.</li>
--   </ul>
--   
--   <h3><tt>DayOfWeek</tt></h3>
--   
--   For <tt>DayOfWeek</tt> (and <tt>Day</tt> and <tt>LocalTime</tt> and
--   <tt>ZonedTime</tt> and <tt>UTCTime</tt> and <tt>UniversalTime</tt>):
--   
--   <ul>
--   <li><i><tt>%u</tt></i> day of week number for Week Date format,
--   <tt>1</tt> (= Monday) - <tt>7</tt> (= Sunday)</li>
--   <li><i><tt>%w</tt></i> day of week number, <tt>0</tt> (= Sunday) -
--   <tt>6</tt> (= Saturday)</li>
--   <li><i><tt>%a</tt></i> day of week, short form (<a>snd</a> from
--   <a>wDays</a> <tt>locale</tt>), <tt>Sun</tt> - <tt>Sat</tt></li>
--   <li><i><tt>%A</tt></i> day of week, long form (<a>fst</a> from
--   <a>wDays</a> <tt>locale</tt>), <tt>Sunday</tt> -
--   <tt>Saturday</tt></li>
--   </ul>
--   
--   <h3><tt>Month</tt></h3>
--   
--   For <tt>Month</tt> (and <tt>Day</tt> and <tt>LocalTime</tt> and
--   <tt>ZonedTime</tt> and <tt>UTCTime</tt> and <tt>UniversalTime</tt>):
--   
--   <ul>
--   <li><i><tt>%Y</tt></i> year, no padding. Note <tt>%0Y</tt> and
--   <tt>%_Y</tt> pad to four chars</li>
--   <li><i><tt>%y</tt></i> year of century, 0-padded to two chars,
--   <tt>00</tt> - <tt>99</tt></li>
--   <li><i><tt>%C</tt></i> century, no padding. Note <tt>%0C</tt> and
--   <tt>%_C</tt> pad to two chars</li>
--   <li><i><tt>%B</tt></i> month name, long form (<a>fst</a> from
--   <a>months</a> <tt>locale</tt>), <tt>January</tt> -
--   <tt>December</tt></li>
--   <li><i><tt>%b</tt>, <tt>%h</tt></i> month name, short form (<a>snd</a>
--   from <a>months</a> <tt>locale</tt>), <tt>Jan</tt> - <tt>Dec</tt></li>
--   <li><i><tt>%m</tt></i> month of year, 0-padded to two chars,
--   <tt>01</tt> - <tt>12</tt></li>
--   </ul>
--   
--   <h3><tt>Day</tt></h3>
--   
--   For <tt>Day</tt> (and <tt>LocalTime</tt> and <tt>ZonedTime</tt> and
--   <tt>UTCTime</tt> and <tt>UniversalTime</tt>):
--   
--   <ul>
--   <li><i><tt>%D</tt></i> same as <tt>%m/%d/%y</tt></li>
--   <li><i><tt>%F</tt></i> same as <tt>%Y-%m-%d</tt></li>
--   <li><i><tt>%x</tt></i> as <a>dateFmt</a> <tt>locale</tt> (e.g.
--   <tt>%m/%d/%y</tt>)</li>
--   <li><i><tt>%d</tt></i> day of month, 0-padded to two chars,
--   <tt>01</tt> - <tt>31</tt></li>
--   <li><i><tt>%e</tt></i> day of month, space-padded to two chars, <tt>
--   1</tt> - <tt>31</tt></li>
--   <li><i><tt>%j</tt></i> day of year, 0-padded to three chars,
--   <tt>001</tt> - <tt>366</tt></li>
--   <li><i><tt>%f</tt></i> century for Week Date format, no padding. Note
--   <tt>%0f</tt> and <tt>%_f</tt> pad to two chars</li>
--   <li><i><tt>%V</tt></i> week of year for Week Date format, 0-padded to
--   two chars, <tt>01</tt> - <tt>53</tt></li>
--   <li><i><tt>%U</tt></i> week of year where weeks start on Sunday (as
--   <tt>sundayStartWeek</tt>), 0-padded to two chars, <tt>00</tt> -
--   <tt>53</tt></li>
--   <li><i><tt>%W</tt></i> week of year where weeks start on Monday (as
--   <tt>mondayStartWeek</tt>), 0-padded to two chars, <tt>00</tt> -
--   <tt>53</tt></li>
--   </ul>
--   
--   <h2>Duration types</h2>
--   
--   The specifiers for <tt>DiffTime</tt>, <tt>NominalDiffTime</tt>,
--   <tt>CalendarDiffDays</tt>, and <tt>CalendarDiffTime</tt> are
--   semantically separate from the other types. Specifiers on negative
--   time differences will generally be negative (think <a>rem</a> rather
--   than <a>mod</a>).
--   
--   <h3><tt>NominalDiffTime</tt> and <tt>DiffTime</tt></h3>
--   
--   Note that a "minute" of <tt>DiffTime</tt> is simply 60 SI seconds,
--   rather than a minute of civil time. Use <tt>NominalDiffTime</tt> to
--   work with civil time, ignoring any leap seconds.
--   
--   For <tt>NominalDiffTime</tt> and <tt>DiffTime</tt>:
--   
--   <ul>
--   <li><i><tt>%w</tt></i> total whole weeks</li>
--   <li><i><tt>%d</tt></i> total whole days</li>
--   <li><i><tt>%D</tt></i> whole days of week</li>
--   <li><i><tt>%h</tt></i> total whole hours</li>
--   <li><i><tt>%H</tt></i> whole hours of day</li>
--   <li><i><tt>%m</tt></i> total whole minutes</li>
--   <li><i><tt>%M</tt></i> whole minutes of hour</li>
--   <li><i><tt>%s</tt></i> total whole seconds</li>
--   <li><i><tt>%Es</tt></i> total seconds, with decimal point and up to
--   &lt;width&gt; (default 12) decimal places, without trailing zeros. For
--   a whole number of seconds, <tt>%Es</tt> omits the decimal point unless
--   padding is specified.</li>
--   <li><i><tt>%0Es</tt></i> total seconds, with decimal point and
--   &lt;width&gt; (default 12) decimal places.</li>
--   <li><i><tt>%S</tt></i> whole seconds of minute</li>
--   <li><i><tt>%ES</tt></i> seconds of minute, with decimal point and up
--   to &lt;width&gt; (default 12) decimal places, without trailing zeros.
--   For a whole number of seconds, <tt>%ES</tt> omits the decimal point
--   unless padding is specified.</li>
--   <li><i><tt>%0ES</tt></i> seconds of minute as two digits, with decimal
--   point and &lt;width&gt; (default 12) decimal places.</li>
--   </ul>
--   
--   <h3><tt>CalendarDiffDays</tt></h3>
--   
--   For <tt>CalendarDiffDays</tt> (and <tt>CalendarDiffTime</tt>):
--   
--   <ul>
--   <li><i><tt>%y</tt></i> total years</li>
--   <li><i><tt>%b</tt></i> total months</li>
--   <li><i><tt>%B</tt></i> months of year</li>
--   <li><i><tt>%w</tt></i> total weeks, not including months</li>
--   <li><i><tt>%d</tt></i> total days, not including months</li>
--   <li><i><tt>%D</tt></i> days of week</li>
--   </ul>
--   
--   <h3><tt>CalendarDiffTime</tt></h3>
--   
--   For <tt>CalendarDiffTime</tt>:
--   
--   <ul>
--   <li><i><tt>%h</tt></i> total hours, not including months</li>
--   <li><i><tt>%H</tt></i> hours of day</li>
--   <li><i><tt>%m</tt></i> total minutes, not including months</li>
--   <li><i><tt>%M</tt></i> minutes of hour</li>
--   <li><i><tt>%s</tt></i> total whole seconds, not including months</li>
--   <li><i><tt>%Es</tt></i> total seconds, not including months, with
--   decimal point and up to &lt;width&gt; (default 12) decimal places,
--   without trailing zeros. For a whole number of seconds, <tt>%Es</tt>
--   omits the decimal point unless padding is specified.</li>
--   <li><i><tt>%0Es</tt></i> total seconds, not including months, with
--   decimal point and &lt;width&gt; (default 12) decimal places.</li>
--   <li><i><tt>%S</tt></i> whole seconds of minute</li>
--   <li><i><tt>%ES</tt></i> seconds of minute, with decimal point and up
--   to &lt;width&gt; (default 12) decimal places, without trailing zeros.
--   For a whole number of seconds, <tt>%ES</tt> omits the decimal point
--   unless padding is specified.</li>
--   <li><i><tt>%0ES</tt></i> seconds of minute as two digits, with decimal
--   point and &lt;width&gt; (default 12) decimal places.</li>
--   </ul>
formatTime :: FormatTime t => TimeLocale -> String -> t -> String

-- | The class of types which can be parsed given a UNIX-style time format
--   string.
class ParseTime t
data TimeLocale
TimeLocale :: [(String, String)] -> [(String, String)] -> (String, String) -> String -> String -> String -> String -> [TimeZone] -> TimeLocale

-- | full and abbreviated week days, starting with Sunday
[wDays] :: TimeLocale -> [(String, String)]

-- | full and abbreviated months
[months] :: TimeLocale -> [(String, String)]

-- | AM/PM symbols
[amPm] :: TimeLocale -> (String, String)

-- | formatting strings
[dateTimeFmt] :: TimeLocale -> String

-- | formatting strings
[dateFmt] :: TimeLocale -> String

-- | formatting strings
[timeFmt] :: TimeLocale -> String

-- | formatting strings
[time12Fmt] :: TimeLocale -> String

-- | time zones known by name
[knownTimeZones] :: TimeLocale -> [TimeZone]

-- | Format string according to <a>RFC822</a>.
rfc822DateFormat :: String

-- | Construct format string according to <a>ISO-8601</a>.
--   
--   The <tt>Maybe String</tt> argument allows to supply an optional time
--   specification. E.g.:
--   
--   <pre>
--   <a>iso8601DateFormat</a> Nothing            == "%Y-%m-%d"           -- i.e. <tt><i>YYYY-MM-DD</i></tt>
--   <a>iso8601DateFormat</a> (Just "%H:%M:%S")  == "%Y-%m-%dT%H:%M:%S"  -- i.e. <tt><i>YYYY-MM-DD</i>T<i>HH:MM:SS</i></tt>
--   </pre>
iso8601DateFormat :: Maybe String -> String

-- | Locale representing American usage.
--   
--   <a>knownTimeZones</a> contains only the ten time-zones mentioned in
--   RFC 802 sec. 5: "UT", "GMT", "EST", "EDT", "CST", "CDT", "MST", "MDT",
--   "PST", "PDT". Note that the parsing functions will regardless parse
--   "UTC", single-letter military time-zones, and +HHMM format.
defaultTimeLocale :: TimeLocale

-- | A simple day and time aggregate, where the day is of the specified
--   parameter, and the time is a TimeOfDay. Conversion of this (as local
--   civil time) to UTC depends on the time zone. Conversion of this (as
--   local mean time) to UT1 depends on the longitude.
data LocalTime
LocalTime :: Day -> TimeOfDay -> LocalTime
[localDay] :: LocalTime -> Day
[localTimeOfDay] :: LocalTime -> TimeOfDay

-- | Get the local time of a UTC time in a time zone.
utcToLocalTime :: TimeZone -> UTCTime -> LocalTime

-- | Get the local time of a UT1 time on a particular meridian (in degrees,
--   positive is East).
ut1ToLocalTime :: Rational -> UniversalTime -> LocalTime

-- | Get the UTC time of a local time in a time zone.
localTimeToUTC :: TimeZone -> LocalTime -> UTCTime

-- | Get the UT1 time of a local time on a particular meridian (in degrees,
--   positive is East).
localTimeToUT1 :: Rational -> LocalTime -> UniversalTime

-- | diffLocalTime a b = a - b
diffLocalTime :: LocalTime -> LocalTime -> NominalDiffTime

-- | addLocalTime a b = a + b
addLocalTime :: NominalDiffTime -> LocalTime -> LocalTime

-- | Time of day as represented in hour, minute and second (with
--   picoseconds), typically used to express local time of day.
data TimeOfDay
TimeOfDay :: Int -> Int -> Pico -> TimeOfDay

-- | range 0 - 23
[todHour] :: TimeOfDay -> Int

-- | range 0 - 59
[todMin] :: TimeOfDay -> Int

-- | Note that 0 &lt;= <a>todSec</a> &lt; 61, accomodating leap seconds.
--   Any local minute may have a leap second, since leap seconds happen in
--   all zones simultaneously
[todSec] :: TimeOfDay -> Pico

-- | Convert a time of day in UTC to a time of day in some timezone,
--   together with a day adjustment.
utcToLocalTimeOfDay :: TimeZone -> TimeOfDay -> (Integer, TimeOfDay)

-- | Get the time of day given a time since midnight. Time more than 24h
--   will be converted to leap-seconds.
timeToTimeOfDay :: DiffTime -> TimeOfDay

-- | Convert a period of time into a count of days and a time of day since
--   midnight. The time of day will never have a leap second.
timeToDaysAndTimeOfDay :: NominalDiffTime -> (Integer, TimeOfDay)

-- | Get the time since midnight for a given time of day.
timeOfDayToTime :: TimeOfDay -> DiffTime

-- | Get the fraction of a day since midnight given a time of day.
timeOfDayToDayFraction :: TimeOfDay -> Rational

-- | Same as <a>timeOfDayToTime</a>.
sinceMidnight :: TimeOfDay -> DiffTime

-- | Same as <a>timeToTimeOfDay</a>.
pastMidnight :: DiffTime -> TimeOfDay

-- | Hour zero
midnight :: TimeOfDay

-- | Hour twelve
midday :: TimeOfDay
makeTimeOfDayValid :: Int -> Int -> Pico -> Maybe TimeOfDay

-- | Convert a time of day in some timezone to a time of day in UTC,
--   together with a day adjustment.
localToUTCTimeOfDay :: TimeZone -> TimeOfDay -> (Integer, TimeOfDay)

-- | Convert a count of days and a time of day since midnight into a period
--   of time.
daysAndTimeOfDayToTime :: Integer -> TimeOfDay -> NominalDiffTime

-- | Get the time of day given the fraction of a day since midnight.
dayFractionToTimeOfDay :: Rational -> TimeOfDay

-- | A TimeZone is a whole number of minutes offset from UTC, together with
--   a name and a "just for summer" flag.
data TimeZone
TimeZone :: Int -> Bool -> String -> TimeZone

-- | The number of minutes offset from UTC. Positive means local time will
--   be later in the day than UTC.
[timeZoneMinutes] :: TimeZone -> Int

-- | Is this time zone just persisting for the summer?
[timeZoneSummerOnly] :: TimeZone -> Bool

-- | The name of the zone, typically a three- or four-letter acronym.
[timeZoneName] :: TimeZone -> String

-- | The UTC time zone.
utc :: TimeZone

-- | Text representing the offset of this timezone, such as "-0800" or
--   "+0400" (like <tt>%z</tt> in formatTime), with arbitrary padding.
timeZoneOffsetString' :: Maybe Char -> TimeZone -> String

-- | Text representing the offset of this timezone, such as "-0800" or
--   "+0400" (like <tt>%z</tt> in formatTime).
timeZoneOffsetString :: TimeZone -> String

-- | Create a nameless non-summer timezone for this number of minutes.
minutesToTimeZone :: Int -> TimeZone

-- | Create a nameless non-summer timezone for this number of hours.
hoursToTimeZone :: Int -> TimeZone

-- | Get the local time-zone for a given time (varying as per summertime
--   adjustments).
getTimeZone :: UTCTime -> IO TimeZone

-- | Get the current time-zone.
getCurrentTimeZone :: IO TimeZone
data CalendarDiffTime
CalendarDiffTime :: Integer -> NominalDiffTime -> CalendarDiffTime
[ctMonths] :: CalendarDiffTime -> Integer
[ctTime] :: CalendarDiffTime -> NominalDiffTime

-- | Scale by a factor. Note that <tt>scaleCalendarDiffTime (-1)</tt> will
--   not perfectly invert a duration, due to variable month lengths.
scaleCalendarDiffTime :: Integer -> CalendarDiffTime -> CalendarDiffTime
calendarTimeTime :: NominalDiffTime -> CalendarDiffTime
calendarTimeDays :: CalendarDiffDays -> CalendarDiffTime

-- | diffUTCTime a b = a - b
diffUTCTime :: UTCTime -> UTCTime -> NominalDiffTime

-- | addUTCTime a b = a + b
addUTCTime :: NominalDiffTime -> UTCTime -> UTCTime
utcTimeToPOSIXSeconds :: UTCTime -> POSIXTime
systemToPOSIXTime :: SystemTime -> POSIXTime
posixSecondsToUTCTime :: POSIXTime -> UTCTime

-- | Get the current POSIX time from the system clock.
getPOSIXTime :: IO POSIXTime

-- | Get the current <a>UTCTime</a> from the system clock.
getCurrentTime :: IO UTCTime

-- | Convert <a>UTCTime</a> to <a>SystemTime</a>, matching zero
--   <a>SystemTime</a> to midnight of <a>systemEpochDay</a> UTC.
utcToSystemTime :: UTCTime -> SystemTime

-- | Map leap-second values to the start of the following second. The
--   resulting <a>systemNanoseconds</a> will always be in the range 0 to
--   1E9-1.
truncateSystemTimeLeapSecond :: SystemTime -> SystemTime

-- | Convert <a>SystemTime</a> to <a>UTCTime</a>, matching zero
--   <a>SystemTime</a> to midnight of <a>systemEpochDay</a> UTC.
systemToUTCTime :: SystemTime -> UTCTime

-- | Convert <a>SystemTime</a> to <a>AbsoluteTime</a>, matching zero
--   <a>SystemTime</a> to midnight of <a>systemEpochDay</a> TAI.
systemToTAITime :: SystemTime -> AbsoluteTime

-- | The day of the epoch of <a>SystemTime</a>, 1970-01-01
systemEpochDay :: Day

-- | The Modified Julian Date is the day with the fraction of the day,
--   measured from UT midnight. It's used to represent UT1, which is time
--   as measured by the earth's rotation, adjusted for various wobbles.
newtype UniversalTime
ModJulianDate :: Rational -> UniversalTime
[getModJulianDate] :: UniversalTime -> Rational

-- | This is the simplest representation of UTC. It consists of the day
--   number, and a time offset from midnight. Note that if a day has a leap
--   second added to it, it will have 86401 seconds.
data UTCTime
UTCTime :: Day -> DiffTime -> UTCTime

-- | the day
[utctDay] :: UTCTime -> Day

-- | the time from midnight, 0 &lt;= t &lt; 86401s (because of
--   leap-seconds)
[utctDayTime] :: UTCTime -> DiffTime

-- | <a>SystemTime</a> is time returned by system clock functions. Its
--   semantics depends on the clock function, but the epoch is typically
--   the beginning of 1970. Note that <a>systemNanoseconds</a> of 1E9 to
--   2E9-1 can be used to represent leap seconds.
data SystemTime
MkSystemTime :: {-# UNPACK #-} !Int64 -> {-# UNPACK #-} !Word32 -> SystemTime
[systemSeconds] :: SystemTime -> {-# UNPACK #-} !Int64
[systemNanoseconds] :: SystemTime -> {-# UNPACK #-} !Word32

-- | The resolution of <a>getSystemTime</a>, <tt>getCurrentTime</tt>,
--   <tt>getPOSIXTime</tt>. On UNIX systems this uses
--   <tt>clock_getres</tt>, which may be <a>wrong on WSL2</a>.
getTime_resolution :: DiffTime

-- | Get the system time, epoch start of 1970 UTC, leap-seconds ignored.
--   <a>getSystemTime</a> is typically much faster than
--   <tt>getCurrentTime</tt>.
getSystemTime :: IO SystemTime

-- | POSIX time is the nominal time since 1970-01-01 00:00 UTC
--   
--   To convert from a <a>CTime</a> or <tt>System.Posix.EpochTime</tt>, use
--   <a>realToFrac</a>.
type POSIXTime = NominalDiffTime

-- | 86400 nominal seconds in every day
posixDayLength :: NominalDiffTime

-- | This is a length of time, as measured by UTC. It has a precision of
--   10^-12 s.
--   
--   Conversion functions such as <a>fromInteger</a> and <a>realToFrac</a>
--   will treat it as seconds. For example, <tt>(0.010 ::
--   NominalDiffTime)</tt> corresponds to 10 milliseconds.
--   
--   It has a precision of one picosecond (= 10^-12 s). Enumeration
--   functions will treat it as picoseconds.
--   
--   It ignores leap-seconds, so it's not necessarily a fixed amount of
--   clock time. For instance, 23:00 UTC + 2 hours of NominalDiffTime =
--   01:00 UTC (+ 1 day), regardless of whether a leap-second intervened.
data NominalDiffTime

-- | Create a <a>NominalDiffTime</a> from a number of seconds.
secondsToNominalDiffTime :: Pico -> NominalDiffTime

-- | Get the seconds in a <a>NominalDiffTime</a>.
nominalDiffTimeToSeconds :: NominalDiffTime -> Pico

-- | One day in <a>NominalDiffTime</a>.
nominalDay :: NominalDiffTime

-- | This is a length of time, as measured by a clock. Conversion functions
--   such as <a>fromInteger</a> and <a>realToFrac</a> will treat it as
--   seconds. For example, <tt>(0.010 :: DiffTime)</tt> corresponds to 10
--   milliseconds.
--   
--   It has a precision of one picosecond (= 10^-12 s). Enumeration
--   functions will treat it as picoseconds.
data DiffTime

-- | Create a <a>DiffTime</a> which represents an integral number of
--   seconds.
secondsToDiffTime :: Integer -> DiffTime

-- | Create a <a>DiffTime</a> from a number of picoseconds.
picosecondsToDiffTime :: Integer -> DiffTime

-- | Get the number of picoseconds in a <a>DiffTime</a>.
diffTimeToPicoseconds :: DiffTime -> Integer
data DayOfWeek
Monday :: DayOfWeek
Tuesday :: DayOfWeek
Wednesday :: DayOfWeek
Thursday :: DayOfWeek
Friday :: DayOfWeek
Saturday :: DayOfWeek
Sunday :: DayOfWeek

-- | The first day-of-week on or after some day
firstDayOfWeekOnAfter :: DayOfWeek -> Day -> Day

-- | <tt>dayOfWeekDiff a b = a - b</tt> in range 0 to 6. The number of days
--   from b to the next a.
dayOfWeekDiff :: DayOfWeek -> DayOfWeek -> Int
dayOfWeek :: Day -> DayOfWeek

-- | Convert to proleptic Gregorian calendar.
toGregorian :: Day -> (Year, MonthOfYear, DayOfMonth)

-- | Show in ISO 8601 format (yyyy-mm-dd)
showGregorian :: Day -> String

-- | The number of days in a given month according to the proleptic
--   Gregorian calendar.
gregorianMonthLength :: Year -> MonthOfYear -> DayOfMonth

-- | Convert from proleptic Gregorian calendar. Invalid values will return
--   Nothing
fromGregorianValid :: Year -> MonthOfYear -> DayOfMonth -> Maybe Day

-- | Convert from proleptic Gregorian calendar. Invalid values will be
--   clipped to the correct range, month first, then day.
fromGregorian :: Year -> MonthOfYear -> DayOfMonth -> Day

-- | Calendrical difference, with as many whole months as possible. Same as
--   <a>diffGregorianDurationClip</a> for positive durations.
diffGregorianDurationRollOver :: Day -> Day -> CalendarDiffDays

-- | Calendrical difference, with as many whole months as possible
diffGregorianDurationClip :: Day -> Day -> CalendarDiffDays

-- | Add years, matching month and day, with Feb 29th rolled over to Mar
--   1st if necessary. For instance, 2004-02-29 + 2 years = 2006-03-01.
addGregorianYearsRollOver :: Integer -> Day -> Day

-- | Add years, matching month and day, with Feb 29th clipped to Feb 28th
--   if necessary. For instance, 2004-02-29 + 2 years = 2006-02-28.
addGregorianYearsClip :: Integer -> Day -> Day

-- | Add months, with days past the last day of the month rolling over to
--   the next month. For instance, 2005-01-30 + 1 month = 2005-03-02.
addGregorianMonthsRollOver :: Integer -> Day -> Day

-- | Add months, with days past the last day of the month clipped to the
--   last day. For instance, 2005-01-30 + 1 month = 2005-02-28.
addGregorianMonthsClip :: Integer -> Day -> Day

-- | Add months (rolling over to next month), then add days
addGregorianDurationRollOver :: CalendarDiffDays -> Day -> Day

-- | Add months (clipped to last day), then add days
addGregorianDurationClip :: CalendarDiffDays -> Day -> Day

-- | Bidirectional abstract constructor for the proleptic Gregorian
--   calendar. Invalid values will be clipped to the correct range, month
--   first, then day.
pattern YearMonthDay :: Year -> MonthOfYear -> DayOfMonth -> Day

-- | Is this year a leap year according to the proleptic Gregorian
--   calendar?
isLeapYear :: Year -> Bool

-- | Year of Common Era.
type Year = Integer

-- | Month of year, in range 1 (January) to 12 (December).
type MonthOfYear = Int

-- | Day of month, in range 1 to 31.
type DayOfMonth = Int

-- | The Modified Julian Day is a standard count of days, with zero being
--   the day 1858-11-17.
newtype Day
ModifiedJulianDay :: Integer -> Day
[toModifiedJulianDay] :: Day -> Integer
diffDays :: Day -> Day -> Integer
addDays :: Integer -> Day -> Day
data CalendarDiffDays
CalendarDiffDays :: Integer -> Integer -> CalendarDiffDays
[cdMonths] :: CalendarDiffDays -> Integer
[cdDays] :: CalendarDiffDays -> Integer

-- | Scale by a factor. Note that <tt>scaleCalendarDiffDays (-1)</tt> will
--   not perfectly invert a duration, due to variable month lengths.
scaleCalendarDiffDays :: Integer -> CalendarDiffDays -> CalendarDiffDays
calendarYear :: CalendarDiffDays
calendarWeek :: CalendarDiffDays
calendarMonth :: CalendarDiffDays
calendarDay :: CalendarDiffDays

-- | Convert a <a>MaybeT</a> computation to <a>ExceptT</a>, with a default
--   exception value.
maybeToExceptT :: forall (m :: Type -> Type) e a. Functor m => e -> MaybeT m a -> ExceptT e m a

-- | Transform the computation inside a <tt>MaybeT</tt>.
--   
--   <ul>
--   <li><pre><a>runMaybeT</a> (<a>mapMaybeT</a> f m) = f (<a>runMaybeT</a>
--   m)</pre></li>
--   </ul>
mapMaybeT :: (m (Maybe a) -> n (Maybe b)) -> MaybeT m a -> MaybeT n b

-- | Convert a <a>ExceptT</a> computation to <a>MaybeT</a>, discarding the
--   value of any exception.
exceptToMaybeT :: forall (m :: Type -> Type) e a. Functor m => ExceptT e m a -> MaybeT m a

-- | Constructor for computations in the exception monad. (The inverse of
--   <a>runExcept</a>).
except :: forall (m :: Type -> Type) e a. Monad m => Either e a -> ExceptT e m a

-- | <tt><a>shiftT</a> f</tt> captures the continuation up to the nearest
--   enclosing <a>resetT</a> and passes it to <tt>f</tt>:
--   
--   <ul>
--   <li><pre><a>resetT</a> (<a>shiftT</a> f &gt;&gt;= k) = <a>resetT</a>
--   (f (<a>evalContT</a> . k))</pre></li>
--   </ul>
shiftT :: Monad m => ((a -> m r) -> ContT r m r) -> ContT r m a

-- | <tt><a>resetT</a> m</tt> delimits the continuation of any
--   <a>shiftT</a> inside <tt>m</tt>.
--   
--   <ul>
--   <li><pre><a>resetT</a> (<a>lift</a> m) = <a>lift</a> m</pre></li>
--   </ul>
resetT :: forall (m :: Type -> Type) r r'. Monad m => ContT r m r -> ContT r' m r

-- | <tt><a>reset</a> m</tt> delimits the continuation of any <a>shift</a>
--   inside <tt>m</tt>.
--   
--   <ul>
--   <li><pre><a>reset</a> (<a>return</a> m) = <a>return</a> m</pre></li>
--   </ul>
reset :: Cont r r -> Cont r' r

-- | <tt><a>liftLocal</a> ask local</tt> yields a <tt>local</tt> function
--   for <tt><a>ContT</a> r m</tt>.
liftLocal :: Monad m => m r' -> ((r' -> r') -> m r -> m r) -> (r' -> r') -> ContT r m a -> ContT r m a

-- | The result of running a CPS computation with <a>return</a> as the
--   final continuation.
--   
--   <ul>
--   <li><pre><a>evalContT</a> (<a>lift</a> m) = m</pre></li>
--   </ul>
evalContT :: Monad m => ContT r m r -> m r

-- | The result of running a CPS computation with the identity as the final
--   continuation.
--   
--   <ul>
--   <li><pre><a>evalCont</a> (<a>return</a> x) = x</pre></li>
--   </ul>
evalCont :: Cont r r -> r

-- | A set of values. A set cannot contain duplicate values.
data HashSet a

-- | A map from keys to values. A map cannot contain duplicate keys; each
--   key can map to at most one value.
data HashMap k v

-- | Type representing <a>Universally Unique Identifiers (UUID)</a> as
--   specified in <a>RFC 4122</a>.
data UUID

-- | Boxed vectors, supporting efficient slicing.
data Vector a

-- | If <a>Void</a> is uninhabited then any <a>Monad</a> that holds values
--   of type <a>Void</a> is holding no values.
--   
--   This is only safe for valid monads that do not perform GADT-like
--   analysis on the argument.
unsafeVacuousM :: Monad m => m Void -> m a

-- | If <a>Void</a> is uninhabited than any <a>Functor</a> that holds only
--   values of the type <a>Void</a> is holding no values.
--   
--   This is only safe for valid functors that do not perform GADT-like
--   analysis on the argument.
unsafeVacuous :: Functor f => f Void -> f a

-- | A more meaningful and conflict-free alias for <a>first</a>.
mapLeft :: Bifunctor p => (a -> b) -> p a c -> p b c

-- | A more meaningful and conflict-free alias for <a>second</a>.
mapRight :: Bifunctor p => (b -> c) -> p a b -> p a c

-- | If you're not a fan of magical or special cases, you probably have
--   already been looking for this alias.
type List = []

-- | A more meaningful name for the non-empty list. Follows the convention
--   behind such names as <tt>foldr1</tt>.
type List1 = NonEmpty
sappend :: Semigroup a => a -> a -> a