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 operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.

(&&) :: 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.

Examples

Basic usage:

>>> maybe False odd (Just 3)
True

>>> maybe False odd Nothing
False

Read an integer from a string using readMaybe. If we succeed, return twice the integer; that is, apply (*2) to it. If instead we fail to parse an integer, return 0 by default:

>>> import Text.Read ( readMaybe )
>>> maybe 0 (*2) (readMaybe "5")
10
>>> maybe 0 (*2) (readMaybe "")
0

Apply show to a Maybe Int. If we have Just n, we want to show the underlying Int n. But if we have Nothing, we return the empty string instead of (for example) "Nothing":

>>> maybe "" show (Just 5)
"5"
>>> maybe "" show Nothing
""

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.

Examples

We create two values of type Either String Int, one using the Left constructor and another using the Right constructor. Then we apply "either" the length function (if we have a String) or the "times-two" function (if we have an Int):

>>> let s = Left "foo" :: Either String Int
>>> let n = Right 3 :: Either String Int
>>> either length (*2) s
3
>>> either length (*2) n
6

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]

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

The value of seq a b is bottom if a is bottom, and otherwise equal to b. seq is usually introduced to improve performance by avoiding unneeded laziness.

A note on evaluation order: the expression seq a b does not guarantee that a will be evaluated before b. The only guarantee given by seq is that the both a and b will be evaluated before seq returns a value. In particular, this means that b may be evaluated before a. If you need to guarantee a specific order of evaluation, you must use the function pseq from the "parallel" package.

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 TypeRep

Ord ()

Ord BigNat

Ord Void

Ord ThreadId

Ord BlockReason

Ord ThreadStatus

Ord AsyncException

Ord ArrayException

Ord ExitCode

Ord BufferMode

Ord Newline

Ord NewlineMode

Ord CChar

Ord CSChar

Ord CUChar

Ord CShort

Ord CUShort

Ord CInt

Ord CUInt

Ord CLong

Ord CULong

Ord CLLong

Ord CULLong

Ord CFloat

Ord CDouble

Ord CPtrdiff

Ord CSize

Ord CWchar

Ord CSigAtomic

Ord CClock

Ord CTime

Ord CUSeconds

Ord CSUSeconds

Ord CIntPtr

Ord CUIntPtr

Ord CIntMax

Ord CUIntMax

Ord ErrorCall

Ord ArithException

Ord All

Ord Any

Ord Arity

Ord Fixity

Ord Associativity

Ord TyCon

Ord ByteString

Ord ByteString

Ord IntSet

Ord Root

Ord FilePath

Ord a => Ord [a]

Integral a => Ord (Ratio a)

Ord (U1 p)

Ord p => Ord (Par1 p)

Ord a => Ord (Identity a)

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 (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)

(Ix i, Ord e) => Ord (Array i e)

Ord a => Ord (Const a b)

Ord (Proxy k s)

(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 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 (f a) => Ord (Alt k f a)

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 TypeRep

Eq ()

Eq Handle

Eq BigNat

Eq Void

Eq SpecConstrAnnotation

Eq Version

Eq ThreadId

Eq BlockReason

Eq ThreadStatus

Eq AsyncException

Eq ArrayException

Eq ExitCode

Eq IOErrorType

Eq BufferMode

Eq Newline

Eq NewlineMode

Eq CChar

Eq CSChar

Eq CUChar

Eq CShort

Eq CUShort

Eq CInt

Eq CUInt

Eq CLong

Eq CULong

Eq CLLong

Eq CULLong

Eq CFloat

Eq CDouble

Eq CPtrdiff

Eq CSize

Eq CWchar

Eq CSigAtomic

Eq CClock

Eq CTime

Eq CUSeconds

Eq CSUSeconds

Eq CIntPtr

Eq CUIntPtr

Eq CIntMax

Eq CUIntMax

Eq MaskingState

Eq IOException

Eq ErrorCall

Eq ArithException

Eq All

Eq Any

Eq Arity

Eq Fixity

Eq Associativity

Eq TyCon

Eq ByteString

Eq ByteString

Eq IntSet

Eq Root

Eq FilePath

Eq CodePoint

Eq DecoderState

Eq UnicodeException

Eq a => Eq [a]

Eq a => Eq (Ratio a)

Eq (U1 p)

Eq p => Eq (Par1 p)

Eq a => Eq (Identity a)

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)

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

(Ix i, Eq e) => Eq (Array i e)

Eq a => Eq (Const a b)

Eq (Proxy k s)

(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 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 (STArray s i e)

Eq (f a) => Eq (Alt k f a)

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 CChar

Bounded CSChar

Bounded CUChar

Bounded CShort

Bounded CUShort

Bounded CInt

Bounded CUInt

Bounded CLong

Bounded CULong

Bounded CLLong

Bounded CULLong

Bounded CPtrdiff

Bounded CSize

Bounded CWchar

Bounded CSigAtomic

Bounded CIntPtr

Bounded CUIntPtr

Bounded CIntMax

Bounded CUIntMax

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 (Proxy k s)

(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 Int

Enum Int8

Enum Int16

Enum Int32

Enum Int64

Enum Integer

Enum Ordering

Enum Word

Enum Word8

Enum Word16

Enum Word32

Enum Word64

Enum ()

Enum CChar

Enum CSChar

Enum CUChar

Enum CShort

Enum CUShort

Enum CInt

Enum CUInt

Enum CLong

Enum CULong

Enum CLLong

Enum CULLong

Enum CFloat

Enum CDouble

Enum CPtrdiff

Enum CSize

Enum CWchar

Enum CSigAtomic

Enum CClock

Enum CTime

Enum CUSeconds

Enum CSUSeconds

Enum CIntPtr

Enum CUIntPtr

Enum CIntMax

Enum CUIntMax

Integral a => Enum (Ratio a)

Enum (Proxy k s)

Enum (f a) => Enum (Alt k f 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.

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 Int

Show Int8

Show Int16

Show Int32

Show Int64

Show Integer

Show Ordering

Show Word

Show Word8

Show Word16

Show Word32

Show Word64

Show TypeRep

Show ()

Show Handle

Show HandleType

Show Void

Show Version

Show ThreadId

Show BlockReason

Show ThreadStatus

Show BlockedIndefinitelyOnMVar

Show BlockedIndefinitelyOnSTM

Show Deadlock

Show AllocationLimitExceeded

Show AssertionFailed

Show SomeAsyncException

Show AsyncException

Show ArrayException

Show ExitCode

Show IOErrorType

Show BufferMode

Show Newline

Show NewlineMode

Show CChar

Show CSChar

Show CUChar

Show CShort

Show CUShort

Show CInt

Show CUInt

Show CLong

Show CULong

Show CLLong

Show CULLong

Show CFloat

Show CDouble

Show CPtrdiff

Show CSize

Show CWchar

Show CSigAtomic

Show CClock

Show CTime

Show CUSeconds

Show CSUSeconds

Show CIntPtr

Show CUIntPtr

Show CIntMax

Show CUIntMax

Show MaskingState

Show IOException

Show ErrorCall

Show ArithException

Show All

Show Any

Show Arity

Show Fixity

Show Associativity

Show TyCon

Show SomeException

Show ByteString

Show ByteString

Show IntSet

Show Root

Show CodePoint

Show DecoderState

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 (Identity a)

This instance would be equivalent to the derived instances of the Identity newtype if the runIdentity field were removed

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 (Rules a)

Show a => Show (HashSet a)

Show 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)

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

Show a => Show (Const a b)

Show (Proxy k s)

(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 (f a) => Show (Alt k f a)

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.

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 Void

Reading a Void value is always a parse error, considering Void as a data type with no constructors.

Read Version

Read ExitCode

Read BufferMode

Read Newline

Read NewlineMode

Read CChar

Read CSChar

Read CUChar

Read CShort

Read CUShort

Read CInt

Read CUInt

Read CLong

Read CULong

Read CLLong

Read CULLong

Read CFloat

Read CDouble

Read CPtrdiff

Read CSize

Read CWchar

Read CSigAtomic

Read CClock

Read CTime

Read CUSeconds

Read CSUSeconds

Read CIntPtr

Read CUIntPtr

Read CIntMax

Read CUIntMax

Read All

Read Any

Read Arity

Read Fixity

Read Associativity

Read Lexeme

Read ByteString

Read ByteString

Read IntSet

Read a => Read [a]

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

Read (U1 p)

Read p => Read (Par1 p)

Read a => Read (Identity a)

This instance would be equivalent to the derived instances of the Identity newtype if the runIdentity field were removed

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)

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

Read 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)

Read a => Read (Const a b)

Read (Proxy k s)

(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)

Read (f a) => Read (Alt k f a)

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 P

Functor Identity

Functor ZipList

Functor Handler

Functor STM

Functor First

Functor Last

Functor ReadP

Functor Maybe

Functor Digit

Functor Node

Functor Elem

Functor FingerTree

Functor IntMap

Functor Seq

Functor ViewL

Functor ViewR

Functor Vector

Functor ((->) r)

Functor (Either a)

Functor ((,) a)

Functor (ST s)

Ix i => Functor (Array i)

Functor (ST s)

Functor (Const m)

Monad m => Functor (WrappedMonad m)

Arrow a => Functor (ArrowMonad a)

Functor (Proxy *)

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 f => Functor (Alt * f)

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 Applicative m => 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.

Instances of Monad should satisfy the following laws:

• return a >>= k  =  k a

• m >>= return  =  m

• m >>= (x -> k x >>= h)  =  (m >>= k) >>= h

Furthermore, the Monad and Applicative operations should relate as follows:

• pure = return

• (<*>) = ap

The above laws imply:

• fmap f xs  =  xs >>= return . f

• (>>) = (*>)

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

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

Minimal complete definition

(>>=)

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 Identity

Monad STM

Monad First

Monad Last

Monad ReadP

Monad Maybe

Monad Seq

Monad Vector

Monad ((->) r)

Monad (Either e)

Monad (ST s)

Monad (ST s)

Monad m => Monad (WrappedMonad m)

ArrowApply a => Monad (ArrowMonad a)

Monad (Proxy *)

Monad (State s)

Monad m => Monad (MaybeT m)

Monad m => Monad (ListT m)

Monad m => Monad (IdentityT m)

Monad f => Monad (Alt * f)

(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 [Char]

Numeric type classes

class Num a where

Basic numeric class.

Minimal complete definition

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

Methods

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

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

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

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 Int

Num Int8

Num Int16

Num Int32

Num Int64

Num Integer

Num Word

Num Word8

Num Word16

Num Word32

Num Word64

Num CChar

Num CSChar

Num CUChar

Num CShort

Num CUShort

Num CInt

Num CUInt

Num CLong

Num CULong

Num CLLong

Num CULLong

Num CFloat

Num CDouble

Num CPtrdiff

Num CSize

Num CWchar

Num CSigAtomic

Num CClock

Num CTime

Num CUSeconds

Num CSUSeconds

Num CIntPtr

Num CUIntPtr

Num CIntMax

Num CUIntMax

Num CodePoint

Num DecoderState

Integral a => Num (Ratio a)

RealFloat a => Num (Complex a)

Num a => Num (Sum a)

Num a => Num (Product a)

Num (f a) => Num (Alt k f 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 Int

Real Int8

Real Int16

Real Int32

Real Int64

Real Integer

Real Word

Real Word8

Real Word16

Real Word32

Real Word64

Real CChar

Real CSChar

Real CUChar

Real CShort

Real CUShort

Real CInt

Real CUInt

Real CLong

Real CULong

Real CLLong

Real CULLong

Real CFloat

Real CDouble

Real CPtrdiff

Real CSize

Real CWchar

Real CSigAtomic

Real CClock

Real CTime

Real CUSeconds

Real CSUSeconds

Real CIntPtr

Real CUIntPtr

Real CIntMax

Real CUIntMax

Integral a => Real (Ratio a)

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

Integral numbers, supporting integer division.

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

Integral CChar

Integral CSChar

Integral CUChar

Integral CShort

Integral CUShort

Integral CInt

Integral CUInt

Integral CLong

Integral CULong

Integral CLLong

Integral CULLong

Integral CPtrdiff

Integral CSize

Integral CWchar

Integral CSigAtomic

Integral CIntPtr

Integral CUIntPtr

Integral CIntMax

Integral CUIntMax

class Num a => Fractional a where

Fractional numbers, supporting real division.

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 CFloat

Fractional CDouble

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, asin, acos, atan, sinh, cosh, asinh, acosh, atanh

Methods

pi :: a

exp :: a -> a

log :: a -> a

sqrt :: a -> a

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

logBase :: a -> a -> a

sin :: a -> a

cos :: a -> a

tan :: a -> a

asin :: a -> a

acos :: a -> a

atan :: a -> a

sinh :: a -> a

cosh :: a -> a

tanh :: a -> a

asinh :: a -> a

acosh :: a -> a

atanh :: a -> a

Instances

Floating Double

Floating Float

Floating CFloat

Floating CDouble

RealFloat a => Floating (Complex a)

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

Extracting components of fractions.

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 CFloat

RealFrac CDouble

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

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

RealFloat CFloat

RealFloat CDouble

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

Monad Maybe

Functor Maybe

Applicative Maybe

Foldable Maybe

Generic1 Maybe

Alternative Maybe

MonadPlus 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)

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

Ix Ordering

Generic Ordering

Monoid Ordering

Hashable 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

Ix Bool

Generic Bool

Storable Bool

Hashable Bool

Unbox 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

Ix 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

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

Monad IO

Functor IO

Applicative IO

PrimMonad IO

PrimBase IO

MonadIO IO

MonadBase IO IO

MonadBaseControl IO 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").

Examples

The type Either String Int is the type of values which can be either a String or an Int. The Left constructor can be used only on Strings, and the Right constructor can be used only on Ints:

>>> let s = Left "foo" :: Either String Int
>>> s
Left "foo"
>>> let n = Right 3 :: Either String Int
>>> n
Right 3
>>> :type s
s :: Either String Int
>>> :type n
n :: Either String Int

The fmap from our Functor instance will ignore Left values, but will apply the supplied function to values contained in a Right:

>>> let s = Left "foo" :: Either String Int
>>> let n = Right 3 :: Either String Int
>>> fmap (*2) s
Left "foo"
>>> fmap (*2) n
Right 6

The Monad instance for Either 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 Int from a Char, or fail.

>>> import Data.Char ( digitToInt, isDigit )
>>> :{
    let parseEither :: Char -> Either String Int
        parseEither c
          | isDigit c = Right (digitToInt c)
          | otherwise = Left "parse error"
>>> :}

The following should work, since both '1' and '2' can be parsed as Ints.

>>> :{
    let parseMultiple :: Either String Int
        parseMultiple = do
          x <- parseEither '1'
          y <- parseEither '2'
          return (x + y)
>>> :}

>>> parseMultiple
Right 3

But the following should fail overall, since the first operation where we attempt to parse 'm' as an Int will fail:

>>> :{
    let parseMultiple :: Either String Int
        parseMultiple = do
          x <- parseEither 'm'
          y <- parseEither '2'
          return (x + y)
>>> :}

>>> parseMultiple
Left "parse error"

Constructors

Left a

Right b

Instances

Monad (Either e)

Functor (Either a)

Applicative (Either e)

Foldable (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)

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

type LByteString = ByteString

data Text :: *

A space efficient, packed, unboxed Unicode text type.

Instances

Arguable Text

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

Hashable 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)

Ord k => IsList (Map k v)

(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)

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

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)

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

data IntMap a :: * -> *

A map of integers to values a.

Instances

Functor IntMap

Foldable IntMap

Traversable IntMap

IsList (IntMap a)

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)

type Item (IntMap a) = (Key, a)

data Set a :: * -> *

A set of values a.

Instances

Foldable Set

Ord a => IsList (Set a)

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)

type Item (Set a) = a

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)

type Item (HashSet a) = a

data IntSet :: *

A set of integers.

Instances

IsList IntSet

Eq IntSet

Data IntSet

Ord IntSet

Read IntSet

Show IntSet

Monoid IntSet

NFData IntSet

type Item IntSet = Key

data Seq a :: * -> *

General-purpose finite sequences.

Instances

Monad Seq

Functor Seq

Applicative Seq

Foldable Seq

Traversable Seq

Alternative Seq

MonadPlus Seq

IsList (Seq a)

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)

type Item (Seq a) = a

data Vector a :: * -> *

Boxed vectors, supporting efficient slicing.

Instances

Monad Vector

Functor Vector

Applicative Vector

Foldable Vector

Traversable Vector

Alternative Vector

MonadPlus 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)

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, (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 CChar

Storable CSChar

Storable CUChar

Storable CShort

Storable CUShort

Storable CInt

Storable CUInt

Storable CLong

Storable CULong

Storable CLLong

Storable CULLong

Storable CFloat

Storable CDouble

Storable CPtrdiff

Storable CSize

Storable CWchar

Storable CSigAtomic

Storable CClock

Storable CTime

Storable CUSeconds

Storable CSUSeconds

Storable CIntPtr

Storable CUIntPtr

Storable CIntMax

Storable CUIntMax

Storable Fingerprint

Storable CodePoint

Storable DecoderState

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

Storable (StablePtr a)

Storable (Ptr a)

Storable (FunPtr a)

Storable a => Storable (Complex 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 TypeRep

Hashable ()

Hashable BigNat

Hashable Void

Hashable Natural

Hashable ThreadId

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

Ix Word

Storable Word

Hashable Word

Unbox 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

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

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

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

Ix Int

Generic Int

Storable Int

Hashable Int

Unbox 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

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

Vector Vector Int64

MVector MVector Int64

data Vector Int64 = V_Int64 (Vector Int64)

data MVector s Int64 = MV_Int64 (MVector s Int64)

data Integer :: *

Invariant: Jn# and Jp# are used iff value doesn't fit in S#

Useful properties resulting from the invariants:

• abs (S# _) <= abs (Jp# _)

• abs (S# _) <  abs (Jn# _)

Instances

Enum Integer

Eq Integer

Integral Integer

Num Integer

Ord Integer

Read Integer

Real Integer

Show Integer

Ix Integer

Hashable 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

Eq Float

Floating Float

Ord Float

Read Float

RealFloat Float

Generic Float

Storable Float

Hashable Float

Unbox 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

Eq Double

Floating Double

Ord Double

Read Double

RealFloat Double

Generic Double

Storable Double

Hashable Double

Unbox 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.

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 [a]

Ord a => Monoid (Max a)

Ord a => Monoid (Min 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)

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 k s)

Ord k => Monoid (Map k v)

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

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

Alternative f => Monoid (Alt * f a)

(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

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 is Just b, then b is included in the result list.

Examples

Using mapMaybe f x is a shortcut for catMaybes $ map f x in most cases:

>>> import Text.Read ( readMaybe )
>>> let readMaybeInt = readMaybe :: String -> Maybe Int
>>> mapMaybe readMaybeInt ["1", "Foo", "3"]
[1,3]
>>> catMaybes $ map readMaybeInt ["1", "Foo", "3"]
[1,3]

If we map the Just constructor, the entire list should be returned:

>>> mapMaybe Just [1,2,3]
[1,2,3]

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

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

Examples

Basic usage:

>>> catMaybes [Just 1, Nothing, Just 3]
[1,3]

When constructing a list of Maybe values, catMaybes can be used to return all of the "success" results (if the list is the result of a map, then mapMaybe would be more appropriate):

>>> import Text.Read ( readMaybe )
>>> [readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ]
[Just 1,Nothing,Just 3]
>>> catMaybes $ [readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ]
[1,3]

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.

Examples

Basic usage:

>>> fromMaybe "" (Just "Hello, World!")
"Hello, World!"

>>> fromMaybe "" Nothing
""

Read an integer from a string using readMaybe. If we fail to parse an integer, we want to return 0 by default:

>>> import Text.Read ( readMaybe )
>>> fromMaybe 0 (readMaybe "5")
5
>>> fromMaybe 0 (readMaybe "")
0

isJust :: Maybe a -> Bool

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

Examples

Basic usage:

>>> isJust (Just 3)
True

>>> isJust (Just ())
True

>>> isJust Nothing
False

Only the outer constructor is taken into consideration:

>>> isJust (Just Nothing)
True

isNothing :: Maybe a -> Bool

The isNothing function returns True iff its argument is Nothing.

Examples

Basic usage:

>>> isNothing (Just 3)
False

>>> isNothing (Just ())
False

>>> isNothing Nothing
True

Only the outer constructor is taken into consideration:

>>> isNothing (Just Nothing)
False

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.

Examples

Basic usage:

>>> listToMaybe []
Nothing

>>> listToMaybe [9]
Just 9

>>> listToMaybe [1,2,3]
Just 1

Composing maybeToList with listToMaybe should be the identity on singleton/empty lists:

>>> maybeToList $ listToMaybe [5]
[5]
>>> maybeToList $ listToMaybe []
[]

But not on lists with more than one element:

>>> maybeToList $ listToMaybe [1,2,3]
[1]

maybeToList :: Maybe a -> [a]

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

Examples

Basic usage:

>>> maybeToList (Just 7)
[7]

>>> maybeToList Nothing
[]

One can use maybeToList to avoid pattern matching when combined with a function that (safely) works on lists:

>>> import Text.Read ( readMaybe )
>>> sum $ maybeToList (readMaybe "3")
3
>>> sum $ maybeToList (readMaybe "")
0

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.

Examples

Basic usage:

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> partitionEithers list
(["foo","bar","baz"],[3,7])

The pair returned by partitionEithers x should be the same pair as (lefts x, rights x):

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> partitionEithers list == (lefts list, rights list)
True

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

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

Examples

Basic usage:

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> lefts list
["foo","bar","baz"]

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

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

Examples

Basic usage:

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> rights list
[3,7]

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 P

Applicative Identity

Applicative ZipList

Applicative STM

Applicative First

Applicative Last

Applicative ReadP

Applicative Maybe

Applicative Seq

Applicative Vector

Applicative ((->) a)

Applicative (Either e)

Monoid a => Applicative ((,) a)

Applicative (ST s)

Applicative (ST s)

Monoid m => Applicative (Const m)

Monad m => Applicative (WrappedMonad m)

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)

Applicative f => Applicative (Alt * f)

(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)

(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.

Examples

Convert from a Maybe Int to a Maybe String using show:

>>> show <$> Nothing
Nothing
>>> show <$> Just 3
Just "3"

Convert from an Either Int Int to an Either Int String using show:

>>> show <$> Left 17
Left 17
>>> show <$> Right 17
Right "17"

Double each element of a list:

>>> (*2) <$> [1,2,3]
[2,4,6]

Apply even to the second element of a pair:

>>> even <$> (2,2)
(2,True)

(<|>) :: 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

displayException :: e -> String

Render this exception value in a human-friendly manner.

Default implementation: show.

Since: 4.8.0.0

Instances

Exception Void

Exception BlockedIndefinitelyOnMVar

Exception BlockedIndefinitelyOnSTM

Exception Deadlock

Exception AllocationLimitExceeded

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#

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

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

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

data FilePath :: *

Instances

Eq FilePath

Data FilePath

Ord FilePath

Arguable FilePath

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

NFData FilePath

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

An alias for append.

(<.>) :: FilePath -> Text -> FilePath

An alias for addExtension.

hasExtension :: FilePath -> Text -> Bool

Get whether a FilePath’s last extension is the predicate.

basename :: FilePath -> FilePath

Retrieve a FilePath’s basename component.

basename "foo/bar.txt" == "bar"

filename :: FilePath -> FilePath

Retrieve a FilePath’s filename component.

filename "foo/bar.txt" == "bar.txt"

directory :: FilePath -> FilePath

Retrieves the FilePath’s directory. If the path is already a directory, it is returned unchanged.

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