CorePrelude

Standard

Operators

($) :: (a -> b) -> a -> b infixr 0

Application operator. This operator is redundant, since ordinary application (f x) means the same as (f $ x). However, $ has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:

    f $ g $ h x  =  f (g (h x))

It is also useful in higher-order situations, such as map ($ 0) xs, or zipWith ($) fs xs.

($!) :: (a -> b) -> a -> b infixr 0

Strict (call-by-value) application, defined in terms of seq.

(&&) :: Bool -> Bool -> Bool infixr 3

Boolean "and"

(||) :: Bool -> Bool -> Bool infixr 2

Boolean "or"

(.) :: Category k cat => forall b c a. cat b c -> cat a b -> cat a c

morphism composition

Functions

not :: Bool -> Bool

Boolean "not"

otherwise :: Bool

otherwise is defined as the value True. It helps to make guards more readable. eg.

 f x | x < 0     = ...
     | otherwise = ...

fst :: (a, b) -> a

Extract the first component of a pair.

snd :: (a, b) -> b

Extract the second component of a pair.

id :: Category k cat => forall a. cat a a

the identity morphism

maybe :: b -> (a -> b) -> Maybe a -> b

The maybe function takes a default value, a function, and a Maybe value. If the Maybe value is Nothing, the function returns the default value. Otherwise, it applies the function to the value inside the Just and returns the result.

either :: (a -> c) -> (b -> c) -> Either a b -> c

Case analysis for the Either type. If the value is Left a, apply the first function to a; if it is Right b, apply the second function to b.

flip :: (a -> b -> c) -> b -> a -> c

flip f takes its (first) two arguments in the reverse order of f.

const :: a -> b -> a

Constant function.

error :: [Char] -> a

error stops execution and displays an error message.

putStr :: MonadIO m => Text -> m ()

putStrLn :: MonadIO m => Text -> m ()

print :: (MonadIO m, Show a) => a -> m ()

getArgs :: MonadIO m => m [Text]

terror :: Text -> a

error applied to Text

Since 0.4.1

odd :: Integral a => a -> Bool

even :: Integral a => a -> Bool

uncurry :: (a -> b -> c) -> (a, b) -> c

uncurry converts a curried function to a function on pairs.

curry :: ((a, b) -> c) -> a -> b -> c

curry converts an uncurried function to a curried function.

swap :: (a, b) -> (b, a)

Swap the components of a pair.

until :: (a -> Bool) -> (a -> a) -> a -> a

until p f yields the result of applying f until p holds.

asTypeOf :: a -> a -> a

asTypeOf is a type-restricted version of const. 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.

undefined :: a

A special case of error. It is expected that compilers will recognize this and insert error messages which are more appropriate to the context in which undefined appears.

seq :: a -> b -> b

Evaluates its first argument to head normal form, and then returns its second argument as the result.

Type classes

class Eq a => Ord a where

The Ord class is used for totally ordered datatypes.

Instances of Ord can be derived for any user-defined datatype whose constituent types are in Ord. The declared order of the constructors in the data declaration determines the ordering in derived Ord instances. The Ordering datatype allows a single comparison to determine the precise ordering of two objects.

Minimal complete definition: either compare or <=. Using compare can be more efficient for complex types.

Minimal complete definition

compare | (<=)

Methods

compare :: a -> a -> Ordering

(<) :: a -> a -> Bool infix 4

(>=) :: a -> a -> Bool infix 4

(>) :: a -> a -> Bool infix 4

(<=) :: a -> a -> Bool infix 4

max :: a -> a -> a

min :: a -> a -> a

Instances

Ord Bool

Ord Char

Ord Double

Ord Float

Ord Int

Ord Int8

Ord Int16

Ord Int32

Ord Int64

Ord Integer

Ord Ordering

Ord Word

Ord Word8

Ord Word16

Ord Word32

Ord Word64

Ord ()

Ord ThreadId

Ord BlockReason

Ord ThreadStatus

Ord AsyncException

Ord ArrayException

Ord ExitCode

Ord ErrorCall

Ord ArithException

Ord All

Ord Any

Ord Arity

Ord Fixity

Ord Associativity

Ord TypeRep

Ord TyCon

Ord ByteString

Ord ByteString

Ord IntSet

Ord Text

Ord Text

Ord a => Ord [a]

Integral a => Ord (Ratio a)

Ord (U1 p)

Ord p => Ord (Par1 p)

Ord a => Ord (ZipList a)

Ord a => Ord (Dual a)

Ord a => Ord (Sum a)

Ord a => Ord (Product a)

Ord a => Ord (First a)

Ord a => Ord (Last a)

Ord a => Ord (Down a)

Ord a => Ord (Maybe a)

Ord a => Ord (IntMap a)

Ord a => Ord (Set a)

Ord a => Ord (Seq a)

Ord a => Ord (ViewL a)

Ord a => Ord (ViewR a)

Ord a => Ord (Identity a)

Ord a => Ord (Vector a)

(Unbox a, Ord a) => Ord (Vector a)

(Storable a, Ord a) => Ord (Vector a)

(Prim a, Ord a) => Ord (Vector a)

(Ord a, Ord b) => Ord (Either a b)

Ord (f p) => Ord (Rec1 f p)

(Ord a, Ord b) => Ord (a, b)

(Ord k, Ord v) => Ord (Map k v)

(Ord1 m, Ord a) => Ord (MaybeT m a)

(Ord1 m, Ord a) => Ord (ListT m a)

(Ord1 f, Ord a) => Ord (IdentityT f a)

Ord a => Ord (Stream Id a)

Ord c => Ord (K1 i c p)

(Ord (f p), Ord (g p)) => Ord ((:+:) f g p)

(Ord (f p), Ord (g p)) => Ord ((:*:) f g p)

Ord (f (g p)) => Ord ((:.:) f g p)

(Ord a, Ord b, Ord c) => Ord (a, b, c)

Ord (Coercion k a b)

Ord ((:~:) k a b)

(Ord w, Ord1 m, Ord a) => Ord (WriterT w m a)

(Ord w, Ord1 m, Ord a) => Ord (WriterT w m a)

(Ord e, Ord1 m, Ord a) => Ord (ErrorT e m a)

(Ord e, Ord1 m, Ord a) => Ord (ExceptT e m a)

Ord (f p) => Ord (M1 i c f p)

(Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d)

(Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e)

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f)

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g)

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h)

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i)

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j)

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k)

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l)

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m)

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n)

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)

class Eq a where

The Eq class defines equality (==) and inequality (/=). All the basic datatypes exported by the Prelude are instances of Eq, and Eq may be derived for any datatype whose constituents are also instances of Eq.

Minimal complete definition: either == or /=.

Minimal complete definition

(==) | (/=)

Methods

(==) :: a -> a -> Bool infix 4

(/=) :: a -> a -> Bool infix 4

Instances

Eq Bool

Eq Char

Eq Double

Eq Float

Eq Int

Eq Int8

Eq Int16

Eq Int32

Eq Int64

Eq Integer

Eq Ordering

Eq Word

Eq Word8

Eq Word16

Eq Word32

Eq Word64

Eq ()

Eq SpecConstrAnnotation

Eq ThreadId

Eq BlockReason

Eq ThreadStatus

Eq AsyncException

Eq ArrayException

Eq ExitCode

Eq IOErrorType

Eq MaskingState

Eq IOException

Eq ErrorCall

Eq ArithException

Eq All

Eq Any

Eq Arity

Eq Fixity

Eq Associativity

Eq TypeRep

Eq TyCon

Eq ByteString

Eq ByteString

Eq IntSet

Eq Text

Eq CodePoint

Eq DecoderState

Eq Text

Eq UnicodeException

Eq a => Eq [a]

Eq a => Eq (Ratio a)

Eq (U1 p)

Eq p => Eq (Par1 p)

Eq a => Eq (Complex a)

Eq a => Eq (ZipList a)

Eq (TVar a)

Eq a => Eq (Dual a)

Eq a => Eq (Sum a)

Eq a => Eq (Product a)

Eq a => Eq (First a)

Eq a => Eq (Last a)

Eq a => Eq (Down a)

Eq a => Eq (Maybe a)

Eq a => Eq (IntMap a)

Eq a => Eq (Set a)

Eq a => Eq (Seq a)

Eq a => Eq (ViewL a)

Eq a => Eq (ViewR a)

Eq a => Eq (Identity a)

(Hashable a, Eq a) => Eq (HashSet a)

Eq a => Eq (Vector a)

(Unbox a, Eq a) => Eq (Vector a)

(Storable a, Eq a) => Eq (Vector a)

(Prim a, Eq a) => Eq (Vector a)

(Eq a, Eq b) => Eq (Either a b)

Eq (f p) => Eq (Rec1 f p)

(Eq a, Eq b) => Eq (a, b)

Eq (m a) => Eq (NonGreedy m a)

(Eq a, Eq b) => Eq ((:&) a b)

(Eq k, Eq a) => Eq (Map k a)

(Eq1 m, Eq a) => Eq (MaybeT m a)

(Eq1 m, Eq a) => Eq (ListT m a)

(Eq1 f, Eq a) => Eq (IdentityT f a)

(Eq k, Eq v) => Eq (Leaf k v)

(Eq k, Eq v) => Eq (HashMap k v)

Eq a => Eq (Stream Id a)

Eq c => Eq (K1 i c p)

(Eq (f p), Eq (g p)) => Eq ((:+:) f g p)

(Eq (f p), Eq (g p)) => Eq ((:*:) f g p)

Eq (f (g p)) => Eq ((:.:) f g p)

(Eq a, Eq b, Eq c) => Eq (a, b, c)

Eq (Coercion k a b)

Eq ((:~:) k a b)

(Eq w, Eq1 m, Eq a) => Eq (WriterT w m a)

(Eq w, Eq1 m, Eq a) => Eq (WriterT w m a)

(Eq e, Eq1 m, Eq a) => Eq (ErrorT e m a)

(Eq e, Eq1 m, Eq a) => Eq (ExceptT e m a)

Eq (f p) => Eq (M1 i c f p)

(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d)

(Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e)

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f)

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g)

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h)

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i)

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j)

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k)

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l)

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m)

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n)

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)

class Bounded a where

The Bounded class is used to name the upper and lower limits of a type. Ord is not a superclass of Bounded since types that are not totally ordered may also have upper and lower bounds.

The Bounded class may be derived for any enumeration type; minBound is the first constructor listed in the data declaration and maxBound is the last. Bounded may also be derived for single-constructor datatypes whose constituent types are in Bounded.

Methods

minBound :: a

maxBound :: a

Instances

Bounded Bool

Bounded Char

Bounded Int

Bounded Int8

Bounded Int16

Bounded Int32

Bounded Int64

Bounded Ordering

Bounded Word

Bounded Word8

Bounded Word16

Bounded Word32

Bounded Word64

Bounded ()

Bounded All

Bounded Any

Bounded a => Bounded (Dual a)

Bounded a => Bounded (Sum a)

Bounded a => Bounded (Product a)

(Bounded a, Bounded b) => Bounded (a, b)

(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c)

Coercible k a b => Bounded (Coercion k a b)

(~) k a b => Bounded ((:~:) k a b)

(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d)

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e)

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f)

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g)

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h)

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i)

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j)

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k)

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l)

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m)

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n)

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)

class Enum a where

Class Enum defines operations on sequentially ordered types.

The enumFrom... methods are used in Haskell's translation of arithmetic sequences.

Instances of Enum 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 fromEnum from 0 through n-1. See Chapter 10 of the Haskell Report for more details.

For any type that is an instance of class Bounded as well as Enum, the following should hold:

• The calls succ maxBound and pred minBound should result in a runtime error.
• fromEnum and toEnum should give a runtime error if the result value is not representable in the result type. For example, toEnum 7 :: Bool is an error.
• enumFrom and enumFromThen should be defined with an implicit bound, thus:

   enumFrom     x   = enumFromTo     x maxBound
   enumFromThen x y = enumFromThenTo x y bound
     where
       bound | fromEnum y >= fromEnum x = maxBound
             | otherwise                = minBound

Minimal complete definition

toEnum, fromEnum

Methods

succ :: a -> a

the successor of a value. For numeric types, succ adds 1.

pred :: a -> a

the predecessor of a value. For numeric types, pred subtracts 1.

toEnum :: Int -> a

Convert from an Int.

fromEnum :: a -> Int

Convert to an Int. It is implementation-dependent what fromEnum returns when applied to a value that is too large to fit in an Int.

enumFrom :: a -> [a]

Used in Haskell's translation of [n..].

enumFromThen :: a -> a -> [a]

Used in Haskell's translation of [n,n'..].

enumFromTo :: a -> a -> [a]

Used in Haskell's translation of [n..m].

enumFromThenTo :: a -> a -> a -> [a]

Used in Haskell's translation of [n,n'..m].

Instances

Enum Bool

Enum Char

Enum Double

Enum Float

Enum Int

Enum Int8

Enum Int16

Enum Int32

Enum Int64

Enum Integer

Enum Ordering

Enum Word

Enum Word8

Enum Word16

Enum Word32

Enum Word64

Enum ()

Integral a => Enum (Ratio a)

Coercible k a b => Enum (Coercion k a b)

(~) k a b => Enum ((:~:) k a b)

class Show a

Conversion of values to readable Strings.

Minimal complete definition: showsPrec or show.

Derived instances of Show have the following properties, which are compatible with derived instances of Read:

• The result of show 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.
• If the constructor is defined to be an infix operator, then showsPrec will produce infix applications of the constructor.
• the representation will be enclosed in parentheses if the precedence of the top-level constructor in x is less than d (associativity is ignored). Thus, if d is 0 then the result is never surrounded in parentheses; if d is 11 it is always surrounded in parentheses, unless it is an atomic expression.
• If the constructor is defined using record syntax, then show will produce the record-syntax form, with the fields given in the same order as the original declaration.

For example, given the declarations

infixr 5 :^:
data Tree a =  Leaf a  |  Tree a :^: Tree a

the derived instance of Show is equivalent to

instance (Show a) => Show (Tree a) where

       showsPrec d (Leaf m) = showParen (d > app_prec) $
            showString "Leaf " . showsPrec (app_prec+1) m
         where app_prec = 10

       showsPrec d (u :^: v) = showParen (d > up_prec) $
            showsPrec (up_prec+1) u .
            showString " :^: "      .
            showsPrec (up_prec+1) v
         where up_prec = 5

Note that right-associativity of :^: is ignored. For example,

• show (Leaf 1 :^: Leaf 2 :^: Leaf 3) produces the string "Leaf 1 :^: (Leaf 2 :^: Leaf 3)".

Minimal complete definition

showsPrec | show

Instances

Show Bool

Show Char

Show Double

Show Float

Show Int

Show Int8

Show Int16

Show Int32

Show Int64

Show Integer

Show Ordering

Show Word

Show Word8

Show Word16

Show Word32

Show Word64

Show ()

Show ThreadId

Show BlockReason

Show ThreadStatus

Show BlockedIndefinitelyOnMVar

Show BlockedIndefinitelyOnSTM

Show Deadlock

Show AssertionFailed

Show SomeAsyncException

Show AsyncException

Show ArrayException

Show ExitCode

Show IOErrorType

Show MaskingState

Show IOException

Show ErrorCall

Show ArithException

Show All

Show Any

Show Arity

Show Fixity

Show Associativity

Show TypeRep

Show TyCon

Show SomeException

Show ByteString

Show ByteString

Show IntSet

Show Text

Show FilePath

Show CodePoint

Show DecoderState

Show Text

Show Decoding

Show UnicodeException

Show a => Show [a]

(Integral a, Show a) => Show (Ratio a)

Show (U1 p)

Show p => Show (Par1 p)

Show a => Show (Complex a)

Show a => Show (ZipList a)

Show a => Show (Dual a)

Show a => Show (Sum a)

Show a => Show (Product a)

Show a => Show (First a)

Show a => Show (Last a)

Show a => Show (Down a)

Show a => Show (Maybe a)

Show a => Show (IntMap a)

Show a => Show (Set a)

Show a => Show (Seq a)

Show a => Show (ViewL a)

Show a => Show (ViewR a)

Show a => Show (Identity a)

Show a => Show (HashSet a)

Show a => Show (Vector a)

(Show a, Unbox a) => Show (Vector a)

(Show a, Storable a) => Show (Vector a)

(Show a, Prim a) => Show (Vector a)

(Show a, Show b) => Show (Either a b)

Show (f p) => Show (Rec1 f p)

(Show a, Show b) => Show (a, b)

Show (m a) => Show (NonGreedy m a)

(Show a, Show b) => Show ((:&) a b)

Show (ST s a)

(Show k, Show a) => Show (Map k a)

(Show1 m, Show a) => Show (MaybeT m a)

(Show1 m, Show a) => Show (ListT m a)

(Show1 f, Show a) => Show (IdentityT f a)

(Show k, Show v) => Show (HashMap k v)

Show c => Show (K1 i c p)

(Show (f p), Show (g p)) => Show ((:+:) f g p)

(Show (f p), Show (g p)) => Show ((:*:) f g p)

Show (f (g p)) => Show ((:.:) f g p)

(Show a, Show b, Show c) => Show (a, b, c)

Show (Coercion k a b)

Show ((:~:) k a b)

(Show w, Show1 m, Show a) => Show (WriterT w m a)

(Show w, Show1 m, Show a) => Show (WriterT w m a)

(Show e, Show1 m, Show a) => Show (ErrorT e m a)

(Show e, Show1 m, Show a) => Show (ExceptT e m a)

Show (f p) => Show (M1 i c f p)

(Show a, Show b, Show c, Show d) => Show (a, b, c, d)

(Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e)

(Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f)

(Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g)

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h) => Show (a, b, c, d, e, f, g, h)

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i) => Show (a, b, c, d, e, f, g, h, i)

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j) => Show (a, b, c, d, e, f, g, h, i, j)

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k) => Show (a, b, c, d, e, f, g, h, i, j, k)

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l) => Show (a, b, c, d, e, f, g, h, i, j, k, l)

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m)

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n)

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n, Show o) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)

class Read a

Parsing of Strings, producing values.

Minimal complete definition: readsPrec (or, for GHC only, readPrec)

Derived instances of Read make the following assumptions, which derived instances of Show obey:

• If the constructor is defined to be an infix operator, then the derived Read instance will parse only infix applications of the constructor (not the prefix form).
• Associativity is not used to reduce the occurrence of parentheses, although precedence may be.
• If the constructor is defined using record syntax, the derived Read will parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration.
• The derived Read instance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.

For example, given the declarations

infixr 5 :^:
data Tree a =  Leaf a  |  Tree a :^: Tree a

the derived instance of Read in Haskell 2010 is equivalent to

instance (Read a) => Read (Tree a) where

        readsPrec d r =  readParen (d > app_prec)
                         (\r -> [(Leaf m,t) |
                                 ("Leaf",s) <- lex r,
                                 (m,t) <- readsPrec (app_prec+1) s]) r

                      ++ readParen (d > up_prec)
                         (\r -> [(u:^:v,w) |
                                 (u,s) <- readsPrec (up_prec+1) r,
                                 (":^:",t) <- lex s,
                                 (v,w) <- readsPrec (up_prec+1) t]) r

          where app_prec = 10
                up_prec = 5

Note that right-associativity of :^: is unused.

The derived instance in GHC is equivalent to

instance (Read a) => Read (Tree a) where

        readPrec = parens $ (prec app_prec $ do
                                 Ident "Leaf" <- lexP
                                 m <- step readPrec
                                 return (Leaf m))

                     +++ (prec up_prec $ do
                                 u <- step readPrec
                                 Symbol ":^:" <- lexP
                                 v <- step readPrec
                                 return (u :^: v))

          where app_prec = 10
                up_prec = 5

        readListPrec = readListPrecDefault

Minimal complete definition

readsPrec | readPrec

Instances

Read Bool

Read Char

Read Double

Read Float

Read Int

Read Int8

Read Int16

Read Int32

Read Int64

Read Integer

Read Ordering

Read Word

Read Word8

Read Word16

Read Word32

Read Word64

Read ()

Read ExitCode

Read All

Read Any

Read Arity

Read Fixity

Read Associativity

Read Lexeme

Read ByteString

Read ByteString

Read IntSet

Read Text

Read Text

Read a => Read [a]

(Integral a, Read a) => Read (Ratio a)

Read (U1 p)

Read p => Read (Par1 p)

Read a => Read (Complex a)

Read a => Read (ZipList a)

Read a => Read (Dual a)

Read a => Read (Sum a)

Read a => Read (Product a)

Read a => Read (First a)

Read a => Read (Last a)

Read a => Read (Down a)

Read a => Read (Maybe a)

Read e => Read (IntMap e)

(Read a, Ord a) => Read (Set a)

Read a => Read (Seq a)

Read a => Read (ViewL a)

Read a => Read (ViewR a)

Read a => Read (Identity a)

(Eq a, Hashable a, Read a) => Read (HashSet a)

Read a => Read (Vector a)

(Read a, Unbox a) => Read (Vector a)

(Read a, Storable a) => Read (Vector a)

(Read a, Prim a) => Read (Vector a)

(Read a, Read b) => Read (Either a b)

Read (f p) => Read (Rec1 f p)

(Read a, Read b) => Read (a, b)

(Ix a, Read a, Read b) => Read (Array a b)

(Ord k, Read k, Read e) => Read (Map k e)

(Read1 m, Read a) => Read (MaybeT m a)

(Read1 m, Read a) => Read (ListT m a)

(Read1 f, Read a) => Read (IdentityT f a)

(Eq k, Hashable k, Read k, Read e) => Read (HashMap k e)

Read c => Read (K1 i c p)

(Read (f p), Read (g p)) => Read ((:+:) f g p)

(Read (f p), Read (g p)) => Read ((:*:) f g p)

Read (f (g p)) => Read ((:.:) f g p)

(Read a, Read b, Read c) => Read (a, b, c)

Coercible k a b => Read (Coercion k a b)

(~) k a b => Read ((:~:) k a b)

(Read w, Read1 m, Read a) => Read (WriterT w m a)

(Read w, Read1 m, Read a) => Read (WriterT w m a)

(Read e, Read1 m, Read a) => Read (ErrorT e m a)

(Read e, Read1 m, Read a) => Read (ExceptT e m a)

Read (f p) => Read (M1 i c f p)

(Read a, Read b, Read c, Read d) => Read (a, b, c, d)

(Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e)

(Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f)

(Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g)

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h)

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i)

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j)

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k)

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l)

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m)

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n)

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)

class Functor f where

The Functor class is used for types that can be mapped over. Instances of Functor should satisfy the following laws:

fmap id  ==  id
fmap (f . g)  ==  fmap f . fmap g

The instances of Functor for lists, Maybe and IO satisfy these laws.

Minimal complete definition

fmap

Methods

fmap :: (a -> b) -> f a -> f b

(<$) :: a -> f b -> f a infixl 4

Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.

Instances

Functor []

Functor IO

Functor Id

Functor ZipList

Functor Handler

Functor STM

Functor ReadP

Functor Maybe

Functor Digit

Functor Node

Functor Elem

Functor Id

Functor FingerTree

Functor IntMap

Functor Seq

Functor ViewL

Functor ViewR

Functor Identity

Functor Vector

Functor ((->) r)

Functor (Either a)

Functor ((,) a)

Functor (ST s)

Functor (StateL s)

Functor (StateR s)

Functor (Const m)

Monad m => Functor (WrappedMonad m)

Functor (ST s)

Arrow a => Functor (ArrowMonad a)

Functor (State s)

Functor (Map k)

Functor m => Functor (MaybeT m)

Functor m => Functor (ListT m)

Functor m => Functor (IdentityT m)

Functor (HashMap k)

Arrow a => Functor (WrappedArrow a b)

Functor m => Functor (WriterT w m)

Functor m => Functor (WriterT w m)

Functor m => Functor (ErrorT e m)

Functor m => Functor (ExceptT e m)

Functor m => Functor (StateT s m)

Functor m => Functor (StateT s m)

Functor m => Functor (ReaderT r m)

Functor m => Functor (RWST r w s m)

Functor m => Functor (RWST r w s m)

class Monad m where

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.

Minimal complete definition: >>= and return.

Instances of Monad should satisfy the following laws:

return a >>= k  ==  k a
m >>= return  ==  m
m >>= (\x -> k x >>= h)  ==  (m >>= k) >>= h

Instances of both Monad and Functor should additionally satisfy the law:

fmap f xs  ==  xs >>= return . f

The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.

Minimal complete definition

(>>=), return

Methods

(>>=) :: m a -> (a -> m b) -> m b infixl 1

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

(>>) :: m a -> m b -> m b infixl 1

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

return :: a -> m a

Inject a value into the monadic type.

fail :: String -> m a

Fail with a message. This operation is not part of the mathematical definition of a monad, but is invoked on pattern-match failure in a do expression.

Instances

Monad []

Monad IO

Monad P

Monad STM

Monad ReadP

Monad Maybe

Monad Id

Monad Seq

Monad Identity

Monad Vector

Monad ((->) r)

Monad (Either e)

Monad (ST s)

Monad m => Monad (WrappedMonad m)

Monad (ST s)

ArrowApply a => Monad (ArrowMonad a)

Monad (State s)

Monad m => Monad (MaybeT m)

Monad m => Monad (ListT m)

Monad m => Monad (IdentityT m)

(Monoid w, Monad m) => Monad (WriterT w m)

(Monoid w, Monad m) => Monad (WriterT w m)

(Monad m, Error e) => Monad (ErrorT e m)

Monad m => Monad (ExceptT e m)

Monad m => Monad (StateT s m)

Monad m => Monad (StateT s m)

Monad m => Monad (ReaderT r m)

(Monoid w, Monad m) => Monad (RWST r w s m)

(Monoid w, Monad m) => Monad (RWST r w s m)

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1

Same as >>=, but with the arguments interchanged.

class IsString a where

Class for string-like datastructures; used by the overloaded string extension (-XOverloadedStrings in GHC).

Methods

fromString :: String -> a

Instances

IsString ByteString

IsString ByteString

IsString Builder

IsString Text

IsString FilePath

IsString Text

IsString [Char]

Numeric type classes

class Num a where

Basic numeric class.

Minimal complete definition: all except negate or (-)

Minimal complete definition

(+), (*), abs, signum, fromInteger, (negate | (-))

Methods

(+) :: a -> a -> a infixl 6

(*) :: a -> a -> a infixl 7

(-) :: a -> a -> a infixl 6

negate :: a -> a

Unary negation.

abs :: a -> a

Absolute value.

signum :: a -> a

Sign of a number. The functions abs and signum should satisfy the law:

abs x * signum x == x

For real numbers, the signum is either -1 (negative), 0 (zero) or 1 (positive).

fromInteger :: Integer -> a

Conversion from an Integer. An integer literal represents the application of the function fromInteger to the appropriate value of type Integer, so such literals have type (Num a) => a.

Instances

Num Double

Num Float

Num Int

Num Int8

Num Int16

Num Int32

Num Int64

Num Integer

Num Word

Num Word8

Num Word16

Num Word32

Num Word64

Num CodePoint

Num DecoderState

Integral a => Num (Ratio a)

RealFloat a => Num (Complex a)

Num a => Num (Sum a)

Num a => Num (Product a)

class (Num a, Ord a) => Real a where

Methods

toRational :: a -> Rational

the rational equivalent of its real argument with full precision

Instances

Real Double

Real Float

Real Int

Real Int8

Real Int16

Real Int32

Real Int64

Real Integer

Real Word

Real Word8

Real Word16

Real Word32

Real Word64

Integral a => Real (Ratio a)

class (Real a, Enum a) => Integral a where

Integral numbers, supporting integer division.

Minimal complete definition: quotRem and toInteger

Minimal complete definition

quotRem, toInteger

Methods

quot :: a -> a -> a infixl 7

integer division truncated toward zero

rem :: a -> a -> a infixl 7

integer remainder, satisfying

(x `quot` y)*y + (x `rem` y) == x

div :: a -> a -> a infixl 7

integer division truncated toward negative infinity

mod :: a -> a -> a infixl 7

integer modulus, satisfying

(x `div` y)*y + (x `mod` y) == x

quotRem :: a -> a -> (a, a)

simultaneous quot and rem

divMod :: a -> a -> (a, a)

simultaneous div and mod

toInteger :: a -> Integer

conversion to Integer

Instances

Integral Int

Integral Int8

Integral Int16

Integral Int32

Integral Int64

Integral Integer

Integral Word

Integral Word8

Integral Word16

Integral Word32

Integral Word64

class Num a => Fractional a where

Fractional numbers, supporting real division.

Minimal complete definition: fromRational and (recip or (/))

Minimal complete definition

fromRational, (recip | (/))

Methods

(/) :: a -> a -> a infixl 7

fractional division

recip :: a -> a

reciprocal fraction

fromRational :: Rational -> a

Conversion from a Rational (that is Ratio Integer). A floating literal stands for an application of fromRational to a value of type Rational, so such literals have type (Fractional a) => a.

Instances

Fractional Double

Fractional Float

Integral a => Fractional (Ratio a)

RealFloat a => Fractional (Complex a)

class Fractional a => Floating a where

Trigonometric and hyperbolic functions and related functions.

Minimal complete definition: pi, exp, log, sin, cos, sinh, cosh, asin, acos, atan, asinh, acosh and atanh

Minimal complete definition

pi, exp, log, sin, cos, asin, atan, acos, sinh, cosh, asinh, atanh, acosh

Methods

pi :: a

exp :: a -> a

sqrt :: a -> a

log :: a -> a

(**) :: a -> a -> a infixr 8

logBase :: a -> a -> a

sin :: a -> a

tan :: a -> a

cos :: a -> a

asin :: a -> a

atan :: a -> a

acos :: a -> a

sinh :: a -> a

tanh :: a -> a

cosh :: a -> a

asinh :: a -> a

atanh :: a -> a

acosh :: a -> a

Instances

Floating Double

Floating Float

RealFloat a => Floating (Complex a)

class (Real a, Fractional a) => RealFrac a where

Extracting components of fractions.

Minimal complete definition: properFraction

Minimal complete definition

properFraction

Methods

properFraction :: Integral b => a -> (b, a)

The function properFraction takes a real fractional number x and returns a pair (n,f) such that x = n+f, and:

• n is an integral number with the same sign as x; and
• f is a fraction with the same type and sign as x, and with absolute value less than 1.

The default definitions of the ceiling, floor, truncate and round functions are in terms of properFraction.

truncate :: Integral b => a -> b

truncate x returns the integer nearest x between zero and x

round :: Integral b => a -> b

round x returns the nearest integer to x; the even integer if x is equidistant between two integers

ceiling :: Integral b => a -> b

ceiling x returns the least integer not less than x

floor :: Integral b => a -> b

floor x returns the greatest integer not greater than x

Instances

RealFrac Double

RealFrac Float

Integral a => RealFrac (Ratio a)

class (RealFrac a, Floating a) => RealFloat a where

Efficient, machine-independent access to the components of a floating-point number.

Minimal complete definition: all except exponent, significand, scaleFloat and atan2

Minimal complete definition

floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE

Methods

floatRadix :: a -> Integer

a constant function, returning the radix of the representation (often 2)

floatDigits :: a -> Int

a constant function, returning the number of digits of floatRadix in the significand

floatRange :: a -> (Int, Int)

a constant function, returning the lowest and highest values the exponent may assume

decodeFloat :: a -> (Integer, Int)

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

encodeFloat :: Integer -> Int -> a

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

exponent :: a -> Int

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

significand :: a -> a

The first component of decodeFloat, scaled to lie in the open interval (-1,1), either 0.0 or of absolute value >= 1/b, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

scaleFloat :: Int -> a -> a

multiplies a floating-point number by an integer power of the radix

isNaN :: a -> Bool

True if the argument is an IEEE "not-a-number" (NaN) value

isInfinite :: a -> Bool

True if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> Bool

True if the argument is too small to be represented in normalized format

isNegativeZero :: a -> Bool

True if the argument is an IEEE negative zero

isIEEE :: a -> Bool

True if the argument is an IEEE floating point number

atan2 :: a -> a -> a

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

Instances

RealFloat Double

RealFloat Float

Data types

data Maybe a :: * -> *

The Maybe type encapsulates an optional value. A value of type Maybe a either contains a value of type a (represented as Just a), or it is empty (represented as Nothing). Using Maybe is a good way to deal with errors or exceptional cases without resorting to drastic measures such as error.

The Maybe type is also a monad. It is a simple kind of error monad, where all errors are represented by Nothing. A richer error monad can be built using the Either type.

Constructors

Nothing

Just a

Instances

Alternative Maybe

Monad Maybe

Functor Maybe

MonadPlus Maybe

Applicative Maybe

Foldable Maybe

Traversable Maybe

Generic1 Maybe

MonadBase Maybe Maybe

MonadBaseControl Maybe Maybe

Eq a => Eq (Maybe a)

Ord a => Ord (Maybe a)

Read a => Read (Maybe a)

Show a => Show (Maybe a)

Generic (Maybe a)

Arguable a => Argument (Maybe a)

use Maybe when it should be parsed from one or zero (greedily)

Monoid a => Monoid (Maybe a)

Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S." Since there is no "Semigroup" typeclass providing just mappend, we use Monoid instead.

Hashable a => Hashable (Maybe a)

Typeable (* -> *) Maybe

type Rep1 Maybe = D1 D1Maybe ((:+:) (C1 C1_0Maybe U1) (C1 C1_1Maybe (S1 NoSelector Par1)))

type StM Maybe a = a

type Rep (Maybe a) = D1 D1Maybe ((:+:) (C1 C1_0Maybe U1) (C1 C1_1Maybe (S1 NoSelector (Rec0 a))))

type (==) (Maybe k) a b = EqMaybe k a b

data Ordering :: *

Constructors

LT

EQ

GT

Instances

Bounded Ordering

Enum Ordering

Eq Ordering

Ord Ordering

Read Ordering

Show Ordering

Generic Ordering

Monoid Ordering

Hashable Ordering

Typeable * Ordering

type Rep Ordering = D1 D1Ordering ((:+:) (C1 C1_0Ordering U1) ((:+:) (C1 C1_1Ordering U1) (C1 C1_2Ordering U1)))

type (==) Ordering a b = EqOrdering a b

data Bool :: *

Constructors

False

True

Instances

Bounded Bool

Enum Bool

Eq Bool

Ord Bool

Read Bool

Show Bool

Generic Bool

Storable Bool

Hashable Bool

Unbox Bool

Typeable * Bool

Vector Vector Bool

MVector MVector Bool

type Rep Bool = D1 D1Bool ((:+:) (C1 C1_0Bool U1) (C1 C1_1Bool U1))

data Vector Bool = V_Bool (Vector Word8)

data MVector s Bool = MV_Bool (MVector s Word8)

type (==) Bool a b = EqBool a b

data Char :: *

The character type Char is an enumeration whose values represent Unicode (or equivalently ISO/IEC 10646) characters (see http://www.unicode.org/ 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 Char.

To convert a Char to or from the corresponding Int value defined by Unicode, use toEnum and fromEnum from the Enum class respectively (or equivalently ord and chr).

Instances

Bounded Char

Enum Char

Eq Char

Ord Char

Read Char

Show Char

Generic Char

Arguable Char

char is a special case, so that we don't force the user to single-quote their input

Arguable String

string is a special case, so that we don't force the user to double-quote their input

Argument String

make sure strings are handled as a separate type, not a list of chars

Storable Char

Hashable Char

ErrorList Char

Unbox Char

Typeable * Char

Vector Vector Char

MVector MVector Char

IsString [Char]

type Rep Char = D1 D_Char (C1 C_Char (S1 NoSelector (Rec0 Char)))

data Vector Char = V_Char (Vector Char)

data MVector s Char = MV_Char (MVector s Char)

data IO a :: * -> *

A value of type IO a is a computation which, when performed, does some I/O before returning a value of type a.

There is really only one way to "perform" an I/O action: bind it to Main.main 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 IO monad and called at some point, directly or indirectly, from Main.main.

IO is a monad, so IO actions can be combined using either the do-notation or the >> and >>= operations from the Monad class.

Instances

Alternative IO

Monad IO

Functor IO

MonadPlus IO

Applicative IO

PrimMonad IO

PrimBase IO

MonadIO IO

MonadBase IO IO

MonadBaseControl IO IO

Typeable (* -> *) IO

type PrimState IO = RealWorld

type StM IO a = a

data Either a b :: * -> * -> *

The Either type represents values with two possibilities: a value of type Either a b is either Left a or Right b.

The Either type is sometimes used to represent a value which is either correct or an error; by convention, the Left constructor is used to hold an error value and the Right constructor is used to hold a correct value (mnemonic: "right" also means "correct").

Constructors

Left a

Right b

Instances

Error e => Alternative (Either e)

Monad (Either e)

Functor (Either a)

Error e => MonadPlus (Either e)

Applicative (Either e)

Foldable (Either a)

Traversable (Either a)

Generic1 (Either a)

MonadBase (Either e) (Either e)

MonadBaseControl (Either e) (Either e)

(Eq a, Eq b) => Eq (Either a b)

(Ord a, Ord b) => Ord (Either a b)

(Read a, Read b) => Read (Either a b)

(Show a, Show b) => Show (Either a b)

Generic (Either a b)

(Hashable a, Hashable b) => Hashable (Either a b)

Typeable (* -> * -> *) Either

type Rep1 (Either a) = D1 D1Either ((:+:) (C1 C1_0Either (S1 NoSelector (Rec0 a))) (C1 C1_1Either (S1 NoSelector Par1)))

type StM (Either e) a = a

type Rep (Either a b) = D1 D1Either ((:+:) (C1 C1_0Either (S1 NoSelector (Rec0 a))) (C1 C1_1Either (S1 NoSelector (Rec0 b))))

type (==) (Either k k1) a b = EqEither k k1 a b

Re-exports

Packed reps

data ByteString :: *

A space-efficient representation of a Word8 vector, supporting many efficient operations.

A ByteString contains 8-bit bytes, or by using the operations from Data.ByteString.Char8 it can be interpreted as containing 8-bit characters.

Instances

Eq ByteString

Data ByteString

Ord ByteString

Read ByteString

Show ByteString

IsString ByteString

Monoid ByteString

NFData ByteString

Hashable ByteString

Typeable * ByteString

type LByteString = ByteString

data Text :: *

A space efficient, packed, unboxed Unicode text type.

Instances

IsList Text

Eq Text

Data Text

This instance preserves data abstraction at the cost of inefficiency. We omit reflection services for the sake of data abstraction.

This instance was created by copying the updated behavior of Data.Set.Set and Data.Map.Map. If you feel a mistake has been made, please feel free to submit improvements.

The original discussion is archived here: could we get a Data instance for Data.Text.Text?

The followup discussion that changed the behavior of Set and Map is archived here: Proposal: Allow gunfold for Data.Map, ...

Ord Text

Read Text

Show Text

IsString Text

Arguable Text

Text is a special case, so that we don't force the user to double-quote their input

Monoid Text

Binary Text

NFData Text

Hashable Text

Typeable * Text

type Item Text = Char

type LText = Text

Containers

data Map k a :: * -> * -> *

A Map from keys k to values a.

Instances

Functor (Map k)

Foldable (Map k)

Traversable (Map k)

(Eq k, Eq a) => Eq (Map k a)

(Data k, Data a, Ord k) => Data (Map k a)

(Ord k, Ord v) => Ord (Map k v)

(Ord k, Read k, Read e) => Read (Map k e)

(Show k, Show a) => Show (Map k a)

Ord k => Monoid (Map k v)

(NFData k, NFData a) => NFData (Map k a)

Typeable (* -> * -> *) Map

data HashMap k v :: * -> * -> *

A map from keys to values. A map cannot contain duplicate keys; each key can map to at most one value.

Instances

Functor (HashMap k)

Foldable (HashMap k)

Traversable (HashMap k)

(Eq k, Hashable k) => IsList (HashMap k v)

(Eq k, Eq v) => Eq (HashMap k v)

(Data k, Data v, Eq k, Hashable k) => Data (HashMap k v)

(Eq k, Hashable k, Read k, Read e) => Read (HashMap k e)

(Show k, Show v) => Show (HashMap k v)

(Eq k, Hashable k) => Monoid (HashMap k v)

(NFData k, NFData v) => NFData (HashMap k v)

Typeable (* -> * -> *) HashMap

type Item (HashMap k v) = (k, v)

data IntMap a :: * -> *

A map of integers to values a.

Instances

Functor IntMap

Foldable IntMap

Traversable IntMap

Eq a => Eq (IntMap a)

Data a => Data (IntMap a)

Ord a => Ord (IntMap a)

Read e => Read (IntMap e)

Show a => Show (IntMap a)

Monoid (IntMap a)

NFData a => NFData (IntMap a)

Typeable (* -> *) IntMap

data Set a :: * -> *

A set of values a.

Instances

Foldable Set

Eq a => Eq (Set a)

(Data a, Ord a) => Data (Set a)

Ord a => Ord (Set a)

(Read a, Ord a) => Read (Set a)

Show a => Show (Set a)

Ord a => Monoid (Set a)

NFData a => NFData (Set a)

Typeable (* -> *) Set

data HashSet a :: * -> *

A set of values. A set cannot contain duplicate values.

Instances

Foldable HashSet

(Eq a, Hashable a) => IsList (HashSet a)

(Hashable a, Eq a) => Eq (HashSet a)

(Data a, Eq a, Hashable a) => Data (HashSet a)

(Eq a, Hashable a, Read a) => Read (HashSet a)

Show a => Show (HashSet a)

(Hashable a, Eq a) => Monoid (HashSet a)

NFData a => NFData (HashSet a)

Typeable (* -> *) HashSet

type Item (HashSet a) = a

data IntSet :: *

A set of integers.

Instances

Eq IntSet

Data IntSet

Ord IntSet

Read IntSet

Show IntSet

Monoid IntSet

NFData IntSet

Typeable * IntSet

data Seq a :: * -> *

General-purpose finite sequences.

Instances

Alternative Seq

Monad Seq

Functor Seq

MonadPlus Seq

Applicative Seq

Foldable Seq

Traversable Seq

Eq a => Eq (Seq a)

Data a => Data (Seq a)

Ord a => Ord (Seq a)

Read a => Read (Seq a)

Show a => Show (Seq a)

Monoid (Seq a)

NFData a => NFData (Seq a)

Typeable (* -> *) Seq

data Vector a :: * -> *

Boxed vectors, supporting efficient slicing.

Instances

Alternative Vector

Monad Vector

Functor Vector

MonadPlus Vector

Applicative Vector

Foldable Vector

Traversable Vector

Vector Vector a

IsList (Vector a)

Eq a => Eq (Vector a)

Data a => Data (Vector a)

Ord a => Ord (Vector a)

Read a => Read (Vector a)

Show a => Show (Vector a)

Monoid (Vector a)

NFData a => NFData (Vector a)

Typeable (* -> *) Vector

type Mutable Vector = MVector

type Item (Vector a) = a

type UVector = Vector

class (Vector Vector a, MVector MVector a) => Unbox a

Instances

Unbox Bool

Unbox Char

Unbox Double

Unbox Float

Unbox Int

Unbox Int8

Unbox Int16

Unbox Int32

Unbox Int64

Unbox Word

Unbox Word8

Unbox Word16

Unbox Word32

Unbox Word64

Unbox ()

(RealFloat a, Unbox a) => Unbox (Complex a)

(Unbox a, Unbox b) => Unbox (a, b)

(Unbox a, Unbox b, Unbox c) => Unbox (a, b, c)

(Unbox a, Unbox b, Unbox c, Unbox d) => Unbox (a, b, c, d)

(Unbox a, Unbox b, Unbox c, Unbox d, Unbox e) => Unbox (a, b, c, d, e)

(Unbox a, Unbox b, Unbox c, Unbox d, Unbox e, Unbox f) => Unbox (a, b, c, d, e, f)

type SVector = Vector

class Storable a

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 Ptr a, for some a which is an instance of class Storable. The type argument to Ptr 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 Storable facilitates this manipulation on all types for which it is instantiated, which are the standard basic types of Haskell, the fixed size Int types (Int8, Int16, Int32, Int64), the fixed size Word types (Word8, Word16, Word32, Word64), StablePtr, all types from Foreign.C.Types, as well as Ptr.

Minimal complete definition: sizeOf, alignment, one of peek, peekElemOff and peekByteOff, and one of poke, pokeElemOff and pokeByteOff.

Minimal complete definition

sizeOf, alignment, (peek | peekElemOff | peekByteOff), (poke | pokeElemOff | pokeByteOff)

Instances

Storable Bool

Storable Char

Storable Double

Storable Float

Storable Int

Storable Int8

Storable Int16

Storable Int32

Storable Int64

Storable Word

Storable Word8

Storable Word16

Storable Word32

Storable Word64

Storable Fingerprint

Storable CodePoint

Storable DecoderState

Storable (StablePtr a)

Storable (Ptr a)

Storable (FunPtr a)

class Hashable a where

The class of types that can be converted to a hash value.

Minimal implementation: hashWithSalt.

Minimal complete definition

Nothing

Methods

hashWithSalt :: Int -> a -> Int infixl 0

Return a hash value for the argument, using the given salt.

The general contract of hashWithSalt is:

• If two values are equal according to the == method, then applying the hashWithSalt method on each of the two values must produce the same integer result if the same salt is used in each case.
• It is not required that if two values are unequal according to the == method, then applying the hashWithSalt 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.
• 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 hashWithSalt must make use of the salt in its implementation.

hash :: a -> Int

Like hashWithSalt, but no salt is used. The default implementation uses hashWithSalt with some default salt. Instances might want to implement this method to provide a more efficient implementation than the default implementation.

Instances

Hashable Bool

Hashable Char

Hashable Double

Hashable Float

Hashable Int

Hashable Int8

Hashable Int16

Hashable Int32

Hashable Int64

Hashable Integer

Hashable Ordering

Hashable Word

Hashable Word8

Hashable Word16

Hashable Word32

Hashable Word64

Hashable ()

Hashable ThreadId

Hashable TypeRep

Hashable ByteString

Hashable ByteString

Hashable ShortByteString

Hashable Text

Hashable Text

Hashable a => Hashable [a]

(Integral a, Hashable a) => Hashable (Ratio a)

Hashable (StableName a)

Hashable a => Hashable (Maybe a)

(Hashable a, Hashable b) => Hashable (Either a b)

(Hashable a1, Hashable a2) => Hashable (a1, a2)

(Hashable a1, Hashable a2, Hashable a3) => Hashable (a1, a2, a3)

(Hashable a1, Hashable a2, Hashable a3, Hashable a4) => Hashable (a1, a2, a3, a4)

(Hashable a1, Hashable a2, Hashable a3, Hashable a4, Hashable a5) => Hashable (a1, a2, a3, a4, a5)

(Hashable a1, Hashable a2, Hashable a3, Hashable a4, Hashable a5, Hashable a6) => Hashable (a1, a2, a3, a4, a5, a6)

(Hashable a1, Hashable a2, Hashable a3, Hashable a4, Hashable a5, Hashable a6, Hashable a7) => Hashable (a1, a2, a3, a4, a5, a6, a7)

Numbers

data Word :: *

A Word is an unsigned integral type, with the same size as Int.

Instances

Bounded Word

Enum Word

Eq Word

Integral Word

Num Word

Ord Word

Read Word

Real Word

Show Word

Storable Word

Hashable Word

Unbox Word

Typeable * Word

Vector Vector Word

MVector MVector Word

data Vector Word = V_Word (Vector Word)

data MVector s Word = MV_Word (MVector s Word)

data Word8 :: *

8-bit unsigned integer type

Instances

Bounded Word8

Enum Word8

Eq Word8

Integral Word8

Num Word8

Ord Word8

Read Word8

Real Word8

Show Word8

Ix Word8

Storable Word8

Bits Word8

FiniteBits Word8

Hashable Word8

Unbox Word8

Typeable * Word8

Vector Vector Word8

MVector MVector Word8

data Vector Word8 = V_Word8 (Vector Word8)

data MVector s Word8 = MV_Word8 (MVector s Word8)

data Word32 :: *

32-bit unsigned integer type

Instances

Bounded Word32

Enum Word32

Eq Word32

Integral Word32

Num Word32

Ord Word32

Read Word32

Real Word32

Show Word32

Ix Word32

Storable Word32

Bits Word32

FiniteBits Word32

Hashable Word32

Unbox Word32

Typeable * Word32

Vector Vector Word32

MVector MVector Word32

data Vector Word32 = V_Word32 (Vector Word32)

data MVector s Word32 = MV_Word32 (MVector s Word32)

data Word64 :: *

64-bit unsigned integer type

Instances

Bounded Word64

Enum Word64

Eq Word64

Integral Word64

Num Word64

Ord Word64

Read Word64

Real Word64

Show Word64

Ix Word64

Storable Word64

Bits Word64

FiniteBits Word64

Hashable Word64

Unbox Word64

Typeable * Word64

Vector Vector Word64

MVector MVector Word64

data Vector Word64 = V_Word64 (Vector Word64)

data MVector s Word64 = MV_Word64 (MVector s Word64)

data Int :: *

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

Instances

Bounded Int

Enum Int

Eq Int

Integral Int

Num Int

Ord Int

Read Int

Real Int

Show Int

Generic Int

Storable Int

Hashable Int

Unbox Int

Typeable * Int

Vector Vector Int

MVector MVector Int

type Rep Int = D1 D_Int (C1 C_Int (S1 NoSelector (Rec0 Int)))

data Vector Int = V_Int (Vector Int)

data MVector s Int = MV_Int (MVector s Int)

data Int32 :: *

32-bit signed integer type

Instances

Bounded Int32

Enum Int32

Eq Int32

Integral Int32

Num Int32

Ord Int32

Read Int32

Real Int32

Show Int32

Ix Int32

Storable Int32

Bits Int32

FiniteBits Int32

Hashable Int32

Unbox Int32

Typeable * Int32

Vector Vector Int32

MVector MVector Int32

data Vector Int32 = V_Int32 (Vector Int32)

data MVector s Int32 = MV_Int32 (MVector s Int32)

data Int64 :: *

64-bit signed integer type

Instances

Bounded Int64

Enum Int64

Eq Int64

Integral Int64

Num Int64

Ord Int64

Read Int64

Real Int64

Show Int64

Ix Int64

Storable Int64

Bits Int64

FiniteBits Int64

Hashable Int64

Unbox Int64

Typeable * Int64

Vector Vector Int64

MVector MVector Int64

data Vector Int64 = V_Int64 (Vector Int64)

data MVector s Int64 = MV_Int64 (MVector s Int64)

data Integer :: *

Arbitrary-precision integers.

Instances

Enum Integer

Eq Integer

Integral Integer

Num Integer

Ord Integer

Read Integer

Real Integer

Show Integer

Hashable Integer

Typeable * Integer

type Rational = Ratio Integer

Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.

data Float :: *

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.

Instances

Enum Float

Eq Float

Floating Float

Fractional Float

Num Float

Ord Float

Read Float

Real Float

RealFloat Float

RealFrac Float

Show Float

Generic Float

Storable Float

Hashable Float

Unbox Float

Typeable * Float

Vector Vector Float

MVector MVector Float

type Rep Float = D1 D_Float (C1 C_Float (S1 NoSelector (Rec0 Float)))

data Vector Float = V_Float (Vector Float)

data MVector s Float = MV_Float (MVector s Float)

data Double :: *

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.

Instances

Enum Double

Eq Double

Floating Double

Fractional Double

Num Double

Ord Double

Read Double

Real Double

RealFloat Double

RealFrac Double

Show Double

Generic Double

Storable Double

Hashable Double

Unbox Double

Typeable * Double

Vector Vector Double

MVector MVector Double

type Rep Double = D1 D_Double (C1 C_Double (S1 NoSelector (Rec0 Double)))

data Vector Double = V_Double (Vector Double)

data MVector s Double = MV_Double (MVector s Double)

Numeric functions

(^) :: (Num a, Integral b) => a -> b -> a infixr 8

raise a number to a non-negative integral power

(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8

raise a number to an integral power

subtract :: Num a => a -> a -> a

the same as flip (-).

Because - is treated specially in the Haskell grammar, (- e) is not a section, but an application of prefix negation. However, (subtract exp) is equivalent to the disallowed section.

fromIntegral :: (Integral a, Num b) => a -> b

general coercion from integral types

realToFrac :: (Real a, Fractional b) => a -> b

general coercion to fractional types

Monoids

class Monoid a where

The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:

• mappend mempty x = x

• mappend x mempty = x

• mappend x (mappend y z) = mappend (mappend x y) z

• mconcat = foldr mappend mempty

The method names refer to the monoid of lists under concatenation, but there are many other instances.

Minimal complete definition: mempty and mappend.

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 newtypes and make those instances of Monoid, e.g. Sum and Product.

Minimal complete definition

mempty, mappend

Methods

mempty :: a

Identity of mappend

mappend :: a -> a -> a

An associative operation

mconcat :: [a] -> a

Fold a list using the monoid. For most types, the default definition for mconcat will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.

Instances

Monoid Ordering

Monoid ()

Monoid All

Monoid Any

Monoid ByteString

Monoid ByteString

Monoid IntSet

Monoid Text

Monoid FilePath

Monoid Text

Monoid [a]

Monoid a => Monoid (Dual a)

Monoid (Endo a)

Num a => Monoid (Sum a)

Num a => Monoid (Product a)

Monoid (First a)

Monoid (Last a)

Monoid a => Monoid (Maybe a)

Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S." Since there is no "Semigroup" typeclass providing just mappend, we use Monoid instead.

Monoid (IntMap a)

Ord a => Monoid (Set a)

Monoid (Seq a)

(Hashable a, Eq a) => Monoid (HashSet a)

Monoid (Vector a)

Unbox a => Monoid (Vector a)

Storable a => Monoid (Vector a)

Prim a => Monoid (Vector a)

Monoid b => Monoid (a -> b)

(Monoid a, Monoid b) => Monoid (a, b)

Monoid a => Monoid (Const a b)

Monoid (Proxy * s)

Ord k => Monoid (Map k v)

(Eq k, Hashable k) => Monoid (HashMap k v)

Typeable (* -> Constraint) Monoid

(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)

(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d)

(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e)

(<>) :: Monoid m => m -> m -> m infixr 6

An infix synonym for mappend.

Since: 4.5.0.0

Folds and traversals

class Foldable t

Data structures that can be folded.

Minimal complete definition: foldMap or foldr.

For example, given a data type

data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be

instance Foldable Tree where
   foldMap f Empty = mempty
   foldMap f (Leaf x) = f x
   foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r

This is suitable even for abstract types, as the monoid is assumed to satisfy the monoid laws. Alternatively, one could define foldr:

instance Foldable Tree where
   foldr f z Empty = z
   foldr f z (Leaf x) = f x z
   foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l

Minimal complete definition

foldMap | foldr

Instances

Foldable []

Foldable Maybe

Foldable Digit

Foldable Node

Foldable Elem

Foldable FingerTree

Foldable IntMap

Foldable Set

Foldable Seq

Foldable ViewL

Foldable ViewR

Foldable Identity

Foldable HashSet

Foldable Vector

Foldable (Either a)

Foldable ((,) a)

Ix i => Foldable (Array i)

Foldable (Const m)

Foldable (Proxy *)

Foldable (Map k)

Foldable f => Foldable (MaybeT f)

Foldable f => Foldable (ListT f)

Foldable f => Foldable (IdentityT f)

Foldable (HashMap k)

Foldable f => Foldable (WriterT w f)

Foldable f => Foldable (WriterT w f)

Foldable f => Foldable (ErrorT e f)

Foldable f => Foldable (ExceptT e f)

class (Functor t, Foldable t) => Traversable t

Functors representing data structures that can be traversed from left to right.

Minimal complete definition: traverse or sequenceA.

A definition of traverse must satisfy the following laws:

naturality

t . traverse f = traverse (t . f) for every applicative transformation t

identity

traverse Identity = Identity

composition

traverse (Compose . fmap g . f) = Compose . fmap (traverse g) . traverse f

A definition of sequenceA must satisfy the following laws:

naturality

t . sequenceA = sequenceA . fmap t for every applicative transformation t

identity

sequenceA . fmap Identity = Identity

composition

sequenceA . fmap Compose = Compose . fmap sequenceA . sequenceA

where an applicative transformation is a function

t :: (Applicative f, Applicative g) => f a -> g a

preserving the Applicative operations, i.e.

• t (pure x) = pure x

• t (x <*> y) = t x <*> t y

and the identity functor Identity and composition of functors Compose are defined as

  newtype Identity a = Identity a

  instance Functor Identity where
    fmap f (Identity x) = Identity (f x)

  instance Applicative Indentity where
    pure x = Identity x
    Identity f <*> Identity x = Identity (f x)

  newtype Compose f g a = Compose (f (g a))

  instance (Functor f, Functor g) => Functor (Compose f g) where
    fmap f (Compose x) = Compose (fmap (fmap f) x)

  instance (Applicative f, Applicative g) => Applicative (Compose f g) where
    pure x = Compose (pure (pure x))
    Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)

(The naturality law is implied by parametricity.)

Instances are similar to Functor, e.g. given a data type

data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be

instance Traversable Tree where
   traverse f Empty = pure Empty
   traverse f (Leaf x) = Leaf <$> f x
   traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r

This is suitable even for abstract types, as the laws for <*> imply a form of associativity.

The superclass instances should satisfy the following:

• In the Functor instance, fmap should be equivalent to traversal with the identity applicative functor (fmapDefault).
• In the Foldable instance, foldMap should be equivalent to traversal with a constant applicative functor (foldMapDefault).

Minimal complete definition

traverse | sequenceA

Instances

Traversable []

Traversable Maybe

Traversable Digit

Traversable Node

Traversable Elem

Traversable FingerTree

Traversable IntMap

Traversable Seq

Traversable ViewL

Traversable ViewR

Traversable Identity

Traversable Vector

Traversable (Either a)

Traversable ((,) a)

Ix i => Traversable (Array i)

Traversable (Const m)

Traversable (Proxy *)

Traversable (Map k)

Traversable f => Traversable (MaybeT f)

Traversable f => Traversable (ListT f)

Traversable f => Traversable (IdentityT f)

Traversable (HashMap k)

Traversable f => Traversable (WriterT w f)

Traversable f => Traversable (WriterT w f)

Traversable f => Traversable (ErrorT e f)

Traversable f => Traversable (ExceptT e f)

arrow

first :: Arrow a => forall b c d. a b c -> a (b, d) (c, d)

Send the first component of the input through the argument arrow, and copy the rest unchanged to the output.

second :: Arrow a => forall b c d. a b c -> a (d, b) (d, c)

A mirror image of first.

The default definition may be overridden with a more efficient version if desired.

(***) :: Arrow a => forall b c b' c'. a b c -> a b' c' -> a (b, b') (c, 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 => forall b c c'. a b c -> a b c' -> a 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.

Maybe

mapMaybe :: (a -> Maybe b) -> [a] -> [b]

The mapMaybe function is a version of map which can throw out elements. In particular, the functional argument returns something of type Maybe b. If this is Nothing, no element is added on to the result list. If it just Just b, then b is included in the result list.

catMaybes :: [Maybe a] -> [a]

The catMaybes function takes a list of Maybes and returns a list of all the Just values.

fromMaybe :: a -> Maybe a -> a

The fromMaybe function takes a default value and and Maybe value. If the Maybe is Nothing, it returns the default values; otherwise, it returns the value contained in the Maybe.

isJust :: Maybe a -> Bool

The isJust function returns True iff its argument is of the form Just _.

isNothing :: Maybe a -> Bool

The isNothing function returns True iff its argument is Nothing.

listToMaybe :: [a] -> Maybe a

The listToMaybe function returns Nothing on an empty list or Just a where a is the first element of the list.

maybeToList :: Maybe a -> [a]

The maybeToList function returns an empty list when given Nothing or a singleton list when not given Nothing.

Either

partitionEithers :: [Either a b] -> ([a], [b])

Partitions a list of Either into two lists All the Left elements are extracted, in order, to the first component of the output. Similarly the Right elements are extracted to the second component of the output.

lefts :: [Either a b] -> [a]

Extracts from a list of Either all the Left elements All the Left elements are extracted in order.

rights :: [Either a b] -> [b]

Extracts from a list of Either all the Right elements All the Right elements are extracted in order.

Ord

on :: (b -> b -> c) -> (a -> b) -> a -> a -> c infixl 0

(*) `on` f = \x y -> f x * f y.

Typical usage: sortBy (compare `on` fst).

Algebraic properties:

• (*) `on` id = (*) (if (*) ∉ {⊥, const ⊥})

• ((*) `on` f) `on` g = (*) `on` (f . g)

• flip on f . flip on g = flip on (g . f)

comparing :: Ord a => (b -> a) -> b -> b -> Ordering

comparing p x y = compare (p x) (p y)

Useful combinator for use in conjunction with the xxxBy family of functions from Data.List, for example:

  ... sortBy (comparing fst) ...

equating :: Eq a => (b -> a) -> b -> b -> Bool

newtype Down a :: * -> *

The Down type allows you to reverse sort order conveniently. A value of type Down a contains a value of type a (represented as Down a). If a has an Ord 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: then sortWith by Down x

Provides Show and Read instances (since: 4.7.0.0).

Since: 4.6.0.0

Constructors

Down a

Instances

Eq a => Eq (Down a)

Ord a => Ord (Down a)

Read a => Read (Down a)

Show a => Show (Down a)

Applicative

class Functor f => Applicative f where

A functor with application, providing operations to

• embed pure expressions (pure), and
• sequence computations and combine their results (<*>).

A minimal complete definition must include implementations of these functions satisfying the following laws:

identity

pure id <*> v = v

composition

pure (.) <*> u <*> v <*> w = u <*> (v <*> w)

homomorphism

pure f <*> pure x = pure (f x)

interchange

u <*> pure y = pure ($ y) <*> u

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

• u *> v = pure (const id) <*> u <*> v

• u <* v = pure const <*> u <*> v

As a consequence of these laws, the Functor instance for f will satisfy

• fmap f x = pure f <*> x

If f is also a Monad, it should satisfy

• pure = return

• (<*>) = ap

(which implies that pure and <*> satisfy the applicative functor laws).

Minimal complete definition

pure, (<*>)

Methods

pure :: a -> f a

Lift a value.

(<*>) :: f (a -> b) -> f a -> f b infixl 4

Sequential application.

(*>) :: f a -> f b -> f b infixl 4

Sequence actions, discarding the value of the first argument.

(<*) :: f a -> f b -> f a infixl 4

Sequence actions, discarding the value of the second argument.

Instances

Applicative []

Applicative IO

Applicative Id

Applicative ZipList

Applicative STM

Applicative ReadPrec

Applicative ReadP

Applicative Maybe

Applicative Id

Applicative Seq

Applicative Identity

Applicative Vector

Applicative ((->) a)

Applicative (Either e)

Monoid a => Applicative ((,) a)

Applicative (ST s)

Applicative (StateL s)

Applicative (StateR s)

Monoid m => Applicative (Const m)

Monad m => Applicative (WrappedMonad m)

Applicative (ST s)

Arrow a => Applicative (ArrowMonad a)

Applicative (Proxy *)

Applicative (State s)

(Functor m, Monad m) => Applicative (MaybeT m)

Applicative m => Applicative (ListT m)

Applicative m => Applicative (IdentityT m)

Arrow a => Applicative (WrappedArrow a b)

(Monoid w, Applicative m) => Applicative (WriterT w m)

(Monoid w, Applicative m) => Applicative (WriterT w m)

(Functor m, Monad m) => Applicative (ErrorT e m)

(Functor m, Monad m) => Applicative (ExceptT e m)

(Functor m, Monad m) => Applicative (StateT s m)

(Functor m, Monad m) => Applicative (StateT s m)

Applicative m => Applicative (ReaderT r m)

Typeable ((* -> *) -> Constraint) Applicative

(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m)

(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m)

(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4

An infix synonym for fmap.

(<|>) :: Alternative f => forall a. f a -> f a -> f a

An associative binary operation

Monad

(>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c infixr 1

Left-to-right Kleisli composition of monads.

Transformers

lift :: MonadTrans t => forall m a. Monad m => m a -> t m a

Lift a computation from the argument monad to the constructed monad.

class Monad m => MonadIO m where

Monads in which IO computations may be embedded. Any monad built by applying a sequence of monad transformers to the IO monad will be an instance of this class.

Instances should satisfy the following laws, which state that liftIO is a transformer of monads:

• liftIO . return = return

• liftIO (m >>= f) = liftIO m >>= (liftIO . f)

Methods

liftIO :: IO a -> m a

Lift a computation from the IO monad.

Instances

MonadIO IO

MonadIO m => MonadIO (MaybeT m)

MonadIO m => MonadIO (ListT m)

MonadIO m => MonadIO (IdentityT m)

(Monoid w, MonadIO m) => MonadIO (WriterT w m)

(Monoid w, MonadIO m) => MonadIO (WriterT w m)

(Error e, MonadIO m) => MonadIO (ErrorT e m)

MonadIO m => MonadIO (ExceptT e m)

MonadIO m => MonadIO (StateT s m)

MonadIO m => MonadIO (StateT s m)

MonadIO m => MonadIO (ReaderT r m)

(Monoid w, MonadIO m) => MonadIO (RWST r w s m)

(Monoid w, MonadIO m) => MonadIO (RWST r w s m)

liftIO :: MonadIO m => forall a. IO a -> m a

Lift a computation from the IO monad.

Exceptions

class (Typeable * e, Show e) => Exception e where

Any type that you wish to throw or catch as an exception must be an instance of the Exception class. The simplest case is a new exception type directly below the root:

data MyException = ThisException | ThatException
    deriving (Show, Typeable)

instance Exception MyException

The default method definitions in the Exception class do what we need in this case. You can now throw and catch ThisException and ThatException as exceptions:

*Main> throw ThisException `catch` \e -> putStrLn ("Caught " ++ show (e :: MyException))
Caught ThisException

In more complicated examples, you may wish to define a whole hierarchy of exceptions:

---------------------------------------------------------------------
-- Make the root exception type for all the exceptions in a compiler

data SomeCompilerException = forall e . Exception e => SomeCompilerException e
    deriving Typeable

instance Show SomeCompilerException where
    show (SomeCompilerException e) = show e

instance Exception SomeCompilerException

compilerExceptionToException :: Exception e => e -> SomeException
compilerExceptionToException = toException . SomeCompilerException

compilerExceptionFromException :: Exception e => SomeException -> Maybe e
compilerExceptionFromException x = do
    SomeCompilerException a <- fromException x
    cast a

---------------------------------------------------------------------
-- Make a subhierarchy for exceptions in the frontend of the compiler

data SomeFrontendException = forall e . Exception e => SomeFrontendException e
    deriving Typeable

instance Show SomeFrontendException where
    show (SomeFrontendException e) = show e

instance Exception SomeFrontendException where
    toException = compilerExceptionToException
    fromException = compilerExceptionFromException

frontendExceptionToException :: Exception e => e -> SomeException
frontendExceptionToException = toException . SomeFrontendException

frontendExceptionFromException :: Exception e => SomeException -> Maybe e
frontendExceptionFromException x = do
    SomeFrontendException a <- fromException x
    cast a

---------------------------------------------------------------------
-- Make an exception type for a particular frontend compiler exception

data MismatchedParentheses = MismatchedParentheses
    deriving (Typeable, Show)

instance Exception MismatchedParentheses where
    toException   = frontendExceptionToException
    fromException = frontendExceptionFromException

We can now catch a MismatchedParentheses exception as MismatchedParentheses, SomeFrontendException or SomeCompilerException, but not other types, e.g. IOException:

*Main> throw MismatchedParentheses catch e -> putStrLn ("Caught " ++ show (e :: MismatchedParentheses))
Caught MismatchedParentheses
*Main> throw MismatchedParentheses catch e -> putStrLn ("Caught " ++ show (e :: SomeFrontendException))
Caught MismatchedParentheses
*Main> throw MismatchedParentheses catch e -> putStrLn ("Caught " ++ show (e :: SomeCompilerException))
Caught MismatchedParentheses
*Main> throw MismatchedParentheses catch e -> putStrLn ("Caught " ++ show (e :: IOException))
*** Exception: MismatchedParentheses

Minimal complete definition

Nothing

Methods

toException :: e -> SomeException

fromException :: SomeException -> Maybe e

Instances

Exception BlockedIndefinitelyOnMVar

Exception BlockedIndefinitelyOnSTM

Exception Deadlock

Exception AssertionFailed

Exception SomeAsyncException

Exception AsyncException

Exception ArrayException

Exception ExitCode

Exception IOException

Exception ErrorCall

Exception ArithException

Exception SomeException

Exception UnicodeException

class Typeable a

The class Typeable allows a concrete representation of a type to be calculated.

Minimal complete definition

typeRep#

Instances

Typeable * Bool

Typeable * Char

Typeable * Double

Typeable * Float

Typeable * Int

Typeable * Int8

Typeable * Int16

Typeable * Int32

Typeable * Int64

Typeable * Integer

Typeable * Ordering

Typeable * RealWorld

Typeable * Word

Typeable * Word8

Typeable * Word16

Typeable * Word32

Typeable * Word64

Typeable * ()

Typeable * SpecConstrAnnotation

Typeable * ThreadId

Typeable * BlockedIndefinitelyOnMVar

Typeable * BlockedIndefinitelyOnSTM

Typeable * Deadlock

Typeable * AssertionFailed

Typeable * SomeAsyncException

Typeable * AsyncException

Typeable * ArrayException

Typeable * ExitCode

Typeable * IOException

Typeable * ErrorCall

Typeable * ArithException

Typeable * TypeRep

Typeable * TyCon

Typeable * SomeException

Typeable * ByteString

Typeable * ByteString

Typeable * IntSet

Typeable * Text

Typeable * Text

Typeable * UnicodeException

(Typeable (k1 -> k) s, Typeable k1 a) => Typeable k (s a)

Kind-polymorphic Typeable instance for type application

Typeable ((* -> *) -> Constraint) Alternative

Typeable ((* -> *) -> Constraint) Applicative

Typeable (* -> * -> * -> * -> * -> * -> * -> *) (,,,,,,)

Typeable (* -> * -> * -> * -> * -> * -> *) (,,,,,)

Typeable (* -> * -> * -> * -> * -> *) (,,,,)

Typeable (* -> * -> * -> * -> *) (,,,)

Typeable (* -> * -> * -> *) (,,)

Typeable (* -> * -> * -> *) STArray

Typeable (* -> * -> *) (->)

Typeable (* -> * -> *) Either

Typeable (* -> * -> *) (,)

Typeable (* -> * -> *) ST

Typeable (* -> * -> *) Array

Typeable (* -> * -> *) STRef

Typeable (* -> * -> *) Map

Typeable (* -> * -> *) HashMap

Typeable (* -> * -> *) MVector

Typeable (* -> * -> *) MVector

Typeable (* -> * -> *) MVector

Typeable (* -> * -> *) MVector

Typeable (* -> *) []

Typeable (* -> *) Ratio

Typeable (* -> *) IO

Typeable (* -> *) Ptr

Typeable (* -> *) FunPtr

Typeable (* -> *) Complex

Typeable (* -> *) STM

Typeable (* -> *) TVar

Typeable (* -> *) Maybe

Typeable (* -> *) IntMap

Typeable (* -> *) Set

Typeable (* -> *) Seq

Typeable (* -> *) ViewL

Typeable (* -> *) ViewR

Typeable (* -> *) HashSet

Typeable (* -> *) Vector

Typeable (* -> *) Vector

Typeable (* -> *) Vector

Typeable (* -> *) Vector

Typeable (* -> Constraint) Monoid

Typeable (k -> *) (Proxy k)

Typeable (k -> k -> *) (Coercion k)

Typeable (k -> k -> *) ((:~:) k)

data SomeException :: *

The SomeException type is the root of the exception type hierarchy. When an exception of type e is thrown, behind the scenes it is encapsulated in a SomeException.

Instances

Show SomeException

Exception SomeException

Typeable * SomeException

data IOException :: *

Exceptions that occur in the IO monad. An IOException records a more specific error type, a descriptive string and maybe the handle that was used when the error was flagged.

Instances

Eq IOException

Show IOException

Exception IOException

Error IOException

Typeable * IOException

throwIO :: (MonadBase IO m, Exception e) => e -> m a

Generalized version of throwIO.

try :: (MonadBaseControl IO m, Exception e) => m a -> m (Either e a)

Generalized version of try.

Note, when the given computation throws an exception any monadic side effects in m will be discarded.

tryJust :: (MonadBaseControl IO m, Exception e) => (e -> Maybe b) -> m a -> m (Either b a)

Generalized version of tryJust.

Note, when the given computation throws an exception any monadic side effects in m will be discarded.

catch

Arguments

:: forall (m :: * -> *). (MonadBaseControl IO m, Exception e)

=> m a

The computation to run

-> (e -> m a)

Handler to invoke if an exception is raised

-> m a

Generalized version of catch.

Note, when the given computation throws an exception any monadic side effects in m will be discarded.

catchJust

Arguments

:: forall (m :: * -> *). (MonadBaseControl IO m, Exception e)

=> (e -> Maybe b)

Predicate to select exceptions

-> m a

Computation to run

-> (b -> m a)

Handler

-> m a

Generalized version of catchJust.

Note, when the given computation throws an exception any monadic side effects in m will be discarded.

handle :: (MonadBaseControl IO m, Exception e) => (e -> m a) -> m a -> m a

Generalized version of handle.

Note, when the given computation throws an exception any monadic side effects in m will be discarded.

handleJust :: (MonadBaseControl IO m, Exception e) => (e -> Maybe b) -> (b -> m a) -> m a -> m a

Generalized version of handleJust.

Note, when the given computation throws an exception any monadic side effects in m will be discarded.

bracket

Arguments

:: forall (m :: * -> *). MonadBaseControl IO m

=> m a

computation to run first ("acquire resource")

-> (a -> m b)

computation to run last ("release resource")

-> (a -> m c)

computation to run in-between

-> m c

Generalized version of bracket.

Note:

• When the "acquire" or "release" computations throw exceptions any monadic side effects in m will be discarded.
• When the "in-between" computation throws an exception any monadic side effects in m produced by that computation will be discarded but the side effects of the "acquire" or "release" computations will be retained.
• Also, any monadic side effects in m of the "release" computation will be discarded; it is run only for its side effects in IO.

Note that when your acquire and release computations are of type IO it will be more efficient to write:

liftBaseOp (bracket acquire release)

bracket_

Arguments

:: forall (m :: * -> *). MonadBaseControl IO m

=> m a

computation to run first ("acquire resource")

-> m b

computation to run last ("release resource")

-> m c

computation to run in-between

-> m c

Generalized version of bracket_.

Note any monadic side effects in m of both the "acquire" and "release" computations will be discarded. To keep the monadic side effects of the "acquire" computation, use bracket with constant functions instead.

Note that when your acquire and release computations are of type IO it will be more efficient to write:

liftBaseOp_ (bracket_ acquire release)

bracketOnError

Arguments

:: forall (m :: * -> *). MonadBaseControl IO m

=> m a

computation to run first ("acquire resource")

-> (a -> m b)

computation to run last ("release resource")

-> (a -> m c)

computation to run in-between

-> m c

Generalized version of bracketOnError.

Note:

• When the "acquire" or "release" computations throw exceptions any monadic side effects in m will be discarded.
• When the "in-between" computation throws an exception any monadic side effects in m produced by that computation will be discarded but the side effects of the "acquire" computation will be retained.
• Also, any monadic side effects in m of the "release" computation will be discarded; it is run only for its side effects in IO.

Note that when your acquire and release computations are of type IO it will be more efficient to write:

liftBaseOp (bracketOnError acquire release)

onException :: MonadBaseControl IO m => m a -> m b -> m a

Generalized version of onException.

Note, any monadic side effects in m of the "afterward" computation will be discarded.

finally

Arguments

:: forall (m :: * -> *). MonadBaseControl IO m

=> m a

computation to run first

-> m b

computation to run afterward (even if an exception was raised)

-> m a

Generalized version of finally.

Note, any monadic side effects in m of the "afterward" computation will be discarded.

mask :: MonadBaseControl IO m => ((forall a. m a -> m a) -> m b) -> m b

Generalized version of mask.

mask_ :: MonadBaseControl IO m => m a -> m a

Generalized version of mask_.

uninterruptibleMask :: MonadBaseControl IO m => ((forall a. m a -> m a) -> m b) -> m b

Generalized version of uninterruptibleMask.

uninterruptibleMask_ :: MonadBaseControl IO m => m a -> m a

Generalized version of uninterruptibleMask_.

module System.IO.Error

Files

type FilePath = String

File and directory names are values of type String, 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.

(</>) :: FilePath -> FilePath -> FilePath infixr 5

A nice alias for combine.

(<.>) :: FilePath -> String -> FilePath infixr 7

Alias to addExtension, for people who like that sort of thing.

Strings

type String = [Char]

A String is a list of characters. String constants in Haskell are values of type String.

Hashing

hash :: Hashable a => a -> Int

Like hashWithSalt, but no salt is used. The default implementation uses hashWithSalt with some default salt. Instances might want to implement this method to provide a more efficient implementation than the default implementation.

hashWithSalt :: Hashable a => Int -> a -> Int

Return a hash value for the argument, using the given salt.

The general contract of hashWithSalt is:

• If two values are equal according to the == method, then applying the hashWithSalt method on each of the two values must produce the same integer result if the same salt is used in each case.
• It is not required that if two values are unequal according to the == method, then applying the hashWithSalt 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.
• 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 hashWithSalt must make use of the salt in its implementation.

Command line args

readArgs :: (MonadIO m, ArgumentTuple a) => m a