basic-prelude-0.5.1: An enhanced core prelude; a common foundation for alternate preludes.

Safe HaskellNone
LanguageHaskell98

CorePrelude

Contents

Synopsis

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 () Source

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

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

terror :: Text -> a Source

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

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 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 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:

   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].

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 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 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

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:

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

The above laws imply:

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

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.

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

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.

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

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

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

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

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.

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 
Traversable 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.

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) 
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) 
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.

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 

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) 
(Hashable k, Hashable v) => Hashable (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) 
Hashable a => Hashable (HashSet a) 
type Item (HashSet a) = a 

data IntSet :: *

A set of integers.

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.

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) 

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)

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.

Numbers

data Word :: *

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

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.

data Integer :: *

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

Useful properties resulting from the invariants:

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.

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.

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

Folds and traversals

class Foldable t

Data structures that can be folded.

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

Foldable instances are expected to satisfy the following laws:

foldr f z t = appEndo (foldMap (Endo . f) t ) z
foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z
fold = foldMap id

sum, product, maximum, and minimum should all be essentially equivalent to foldMap forms, such as

sum = getSum . foldMap Sum

but may be less defined.

If the type is also a Functor instance, it should satisfy

foldMap f = fold . fmap f

which implies that

foldMap f . fmap g = foldMap (f . g)

Minimal complete definition

foldMap | foldr

asum :: (Foldable t, Alternative f) => t (f a) -> f a

The sum of a collection of actions, generalizing concat.

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

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

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.

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:

Minimal complete definition

traverse | sequenceA

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 Source

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:

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

If f is also a Monad, it should satisfy

(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.

(<$>) :: 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:

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

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.

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.

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_.

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

Join two values with a path separator. For examples and caveats see the equivalent function combine.

Posix:   "/directory" </> "file.ext" == "/directory/file.ext"
Windows: "/directory" </> "file.ext" == "/directory\\file.ext"

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

Add an extension, even if there is already one there, equivalent to addExtension.

"/directory/path" <.> "ext" == "/directory/path.ext"
"/directory/path" <.> ".ext" == "/directory/path.ext"

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