Prelude

base-4.2.0.0: Basic libraries

Prelude

Portability	portable
Stability	stable
Maintainer	libraries@haskell.org

Description

The Prelude: a standard module imported by default into all Haskell modules. For more documentation, see the Haskell 98 Report http://www.haskell.org/onlinereport/.

Synopsis

data Bool

= False

| True

(&&) :: Bool -> Bool -> Bool

(||) :: Bool -> Bool -> Bool

not :: Bool -> Bool

otherwise :: Bool

data Maybe a

= Nothing

| Just a

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

data Either a b

= Left a

| Right b

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

data Ordering

= LT

| EQ

| GT

data Char

type String = [Char]

fst :: (a, b) -> a

snd :: (a, b) -> b

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

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

class Eq a where

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

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

class Eq a => Ord a where

compare :: a -> a -> Ordering

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

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

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

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

max :: a -> a -> a

min :: a -> a -> a

class Enum a where

succ :: a -> a

pred :: a -> a

toEnum :: Int -> a

fromEnum :: a -> Int

enumFrom :: a -> [a]

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

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

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

class Bounded a where

minBound :: a

maxBound :: a

data Int

data Integer

data Float

data Double

type Rational = Ratio Integer

class (Eq a, Show a) => Num a where

(+) :: a -> a -> a

(*) :: a -> a -> a

(-) :: a -> a -> a

negate :: a -> a

abs :: a -> a

signum :: a -> a

fromInteger :: Integer -> a

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

toRational :: a -> Rational

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

quot :: a -> a -> a

rem :: a -> a -> a

div :: a -> a -> a

mod :: a -> a -> a

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

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

toInteger :: a -> Integer

class Num a => Fractional a where

(/) :: a -> a -> a

recip :: a -> a

fromRational :: Rational -> a

class Fractional a => Floating a where

pi :: a

exp :: a -> a

sqrt :: a -> a

log :: a -> a

(**) :: a -> a -> a

logBase :: a -> a -> a

sin :: a -> a

tan :: a -> a

cos :: a -> a

asin :: a -> a

atan :: a -> a

acos :: a -> a

sinh :: a -> a

tanh :: a -> a

cosh :: a -> a

asinh :: a -> a

atanh :: a -> a

acosh :: a -> a

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

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

truncate :: Integral b => a -> b

round :: Integral b => a -> b

ceiling :: Integral b => a -> b

floor :: Integral b => a -> b

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

floatRadix :: a -> Integer

floatDigits :: a -> Int

floatRange :: a -> (Int, Int)

decodeFloat :: a -> (Integer, Int)

encodeFloat :: Integer -> Int -> a

exponent :: a -> Int

significand :: a -> a

scaleFloat :: Int -> a -> a

isNaN :: a -> Bool

isInfinite :: a -> Bool

isDenormalized :: a -> Bool

isNegativeZero :: a -> Bool

isIEEE :: a -> Bool

atan2 :: a -> a -> a

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

even :: Integral a => a -> Bool

odd :: Integral a => a -> Bool

gcd :: Integral a => a -> a -> a

lcm :: Integral a => a -> a -> a

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

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

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

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

class Monad m where

(>>=) :: forall a b. m a -> (a -> m b) -> m b

(>>) :: forall a b. m a -> m b -> m b

return :: a -> m a

fail :: String -> m a

class Functor f where

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

mapM :: Monad m => (a -> m b) -> [a] -> m [b]

mapM_ :: Monad m => (a -> m b) -> [a] -> m ()

sequence :: Monad m => [m a] -> m [a]

sequence_ :: Monad m => [m a] -> m ()

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

id :: a -> a

const :: a -> b -> a

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

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

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

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

asTypeOf :: a -> a -> a

error :: [Char] -> a

undefined :: a

seq :: a -> b -> b

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

map :: (a -> b) -> [a] -> [b]

(++) :: [a] -> [a] -> [a]

filter :: (a -> Bool) -> [a] -> [a]

head :: [a] -> a

last :: [a] -> a

tail :: [a] -> [a]

init :: [a] -> [a]

null :: [a] -> Bool

length :: [a] -> Int

(!!) :: [a] -> Int -> a

reverse :: [a] -> [a]

foldl :: (a -> b -> a) -> a -> [b] -> a

foldl1 :: (a -> a -> a) -> [a] -> a

foldr :: (a -> b -> b) -> b -> [a] -> b

foldr1 :: (a -> a -> a) -> [a] -> a

and :: [Bool] -> Bool

or :: [Bool] -> Bool

any :: (a -> Bool) -> [a] -> Bool

all :: (a -> Bool) -> [a] -> Bool

sum :: Num a => [a] -> a

product :: Num a => [a] -> a

concat :: [[a]] -> [a]

concatMap :: (a -> [b]) -> [a] -> [b]

maximum :: Ord a => [a] -> a

minimum :: Ord a => [a] -> a

scanl :: (a -> b -> a) -> a -> [b] -> [a]

scanl1 :: (a -> a -> a) -> [a] -> [a]

scanr :: (a -> b -> b) -> b -> [a] -> [b]

scanr1 :: (a -> a -> a) -> [a] -> [a]

iterate :: (a -> a) -> a -> [a]

repeat :: a -> [a]

replicate :: Int -> a -> [a]

cycle :: [a] -> [a]

take :: Int -> [a] -> [a]

drop :: Int -> [a] -> [a]

splitAt :: Int -> [a] -> ([a], [a])

takeWhile :: (a -> Bool) -> [a] -> [a]

dropWhile :: (a -> Bool) -> [a] -> [a]

span :: (a -> Bool) -> [a] -> ([a], [a])

break :: (a -> Bool) -> [a] -> ([a], [a])

elem :: Eq a => a -> [a] -> Bool

notElem :: Eq a => a -> [a] -> Bool

lookup :: Eq a => a -> [(a, b)] -> Maybe b

zip :: [a] -> [b] -> [(a, b)]

zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]

zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]

zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]

unzip :: [(a, b)] -> ([a], [b])

unzip3 :: [(a, b, c)] -> ([a], [b], [c])

lines :: String -> [String]

words :: String -> [String]

unlines :: [String] -> String

unwords :: [String] -> String

type ShowS = String -> String

class Show a where

showsPrec :: Int -> a -> ShowS

show :: a -> String

showList :: [a] -> ShowS

shows :: Show a => a -> ShowS

showChar :: Char -> ShowS

showString :: String -> ShowS

showParen :: Bool -> ShowS -> ShowS

type ReadS a = String -> [(a, String)]

class Read a where

readsPrec :: Int -> ReadS a

readList :: ReadS [a]

reads :: Read a => ReadS a

readParen :: Bool -> ReadS a -> ReadS a

read :: Read a => String -> a

lex :: ReadS String

data IO a

putChar :: Char -> IO ()

putStr :: String -> IO ()

putStrLn :: String -> IO ()

print :: Show a => a -> IO ()

getChar :: IO Char

getLine :: IO String

getContents :: IO String

interact :: (String -> String) -> IO ()

type FilePath = String

readFile :: FilePath -> IO String

writeFile :: FilePath -> String -> IO ()

appendFile :: FilePath -> String -> IO ()

readIO :: Read a => String -> IO a

readLn :: Read a => IO a

type IOError = IOException

ioError :: IOError -> IO a

userError :: String -> IOError

catch :: IO a -> (IOError -> IO a) -> IO a

Standard types, classes and related functions

Basic data types

data Bool

Source

Constructors

False
True

Instances

(&&) :: Bool -> Bool -> Bool

Source

Boolean "and"

(||) :: Bool -> Bool -> Bool

Source

Boolean "or"

not :: Bool -> Bool

Source

Boolean "not"

otherwise :: Bool

Source

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

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

data Maybe a

Source

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 Data.Either.Either type.

Constructors

Nothing
Just a

Instances

Eq a => Eq (Maybe a)

Data a => Data (Maybe a)

Ord a => Ord (Maybe a)

Read a => Read (Maybe a)

Show a => Show (Maybe a)

Monoid a => Monoid (Maybe a)

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

Source

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.

data Either a b

Source

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

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

Constructors

Left a
Right b

Instances

Typeable2 Either

Functor (Either a)

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

(Data a, Data b) => Data (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)

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

Source

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.

data Ordering

Source

Constructors

LT
EQ
GT

Instances

data Char

Instances

type String = [Char]

Source

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

Tuples

fst :: (a, b) -> a

Source

Extract the first component of a pair.

snd :: (a, b) -> b

Source

Extract the second component of a pair.

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

Source

curry converts an uncurried function to a curried function.

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

Source

uncurry converts a curried function to a function on pairs.

Basic type classes

class Eq a where

Source

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 /=.

Methods

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

Source

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

Instances

Eq ()

Eq Inserts

Eq HashData

Eq KeyPr

Eq Key

Eq Finalizers

Eq Timeout

Eq a => Eq [a]

Integral a => Eq (Ratio a)

Eq (StablePtr a)

Eq (Ptr a)

Eq (FunPtr a)

Eq a => Eq ([::] a)

Eq a => Eq (Maybe a)

Eq (MVar a)

Eq (IORef a)

Eq (ForeignPtr a)

Eq (TVar a)

Eq a => Eq (Down a)

Eq a => Eq (Last a)

Eq a => Eq (First a)

Eq a => Eq (Product a)

Eq a => Eq (Sum a)

Eq a => Eq (Dual a)

RealFloat a => Eq (Complex a)

Eq (Fixed a)

Eq (StableName a)

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

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

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

Eq (IOArray i e)

Eq (STRef s a)

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

Eq (STArray s i e)

(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 Eq a => Ord a where

Source

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.

Methods

compare :: a -> a -> Ordering

Source

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

Source

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

Source

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

Source

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

Source

max :: a -> a -> a

Source

min :: a -> a -> a

Instances

Ord ()

Ord a => Ord [a]

Integral a => Ord (Ratio a)

Ord (Ptr a)

Ord (FunPtr a)

Ord a => Ord ([::] a)

Ord a => Ord (Maybe a)

Ord (ForeignPtr a)

Ord a => Ord (Down a)

Ord a => Ord (Last a)

Ord a => Ord (First a)

Ord a => Ord (Product a)

Ord a => Ord (Sum a)

Ord a => Ord (Dual a)

Ord (Fixed a)

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

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

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

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

(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 Enum a where

Source

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

Methods

succ :: a -> a

Source

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

pred :: a -> a

Source

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

toEnum :: Int -> a

Source

Convert from an Int.

fromEnum :: a -> Int

Source

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]

Source

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

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

Source

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

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

Source

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

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

Source

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

Instances

class Bounded a where

Source

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 ()

Bounded GeneralCategory

Bounded a => Bounded (Product a)

Bounded a => Bounded (Sum a)

Bounded a => Bounded (Dual a)

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

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

(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)

Numbers

Numeric types

data Int

Source

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 Prelude.minBound and Prelude.maxBound from the Prelude.Bounded class.

Instances

data Integer

Arbitrary-precision integers.

Instances

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

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

type Rational = Ratio Integer

Source

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

Numeric type classes

class (Eq a, Show a) => Num a where

Source

Basic numeric class.

Minimal complete definition: all except negate or (-)

Methods

(+) :: a -> a -> a

Source

(*) :: a -> a -> a

Source

(-) :: a -> a -> a

Source

negate :: a -> a

Source

Unary negation.

abs :: a -> a

Source

Absolute value.

signum :: a -> a

Source

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

Source

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

Integral a => Num (Ratio a)

RealFloat a => Num (Complex a)

HasResolution a => Num (Fixed a)

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

Source

Methods

toRational :: a -> Rational

Source

the rational equivalent of its real argument with full precision

Instances

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

Source

Integral numbers, supporting integer division.

Minimal complete definition: quotRem and toInteger

Methods

quot :: a -> a -> a

Source

integer division truncated toward zero

rem :: a -> a -> a

Source

integer remainder, satisfying

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

div :: a -> a -> a

Source

integer division truncated toward negative infinity

mod :: a -> a -> a

Source

integer modulus, satisfying

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

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

Source

simultaneous quot and rem

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

Source

simultaneous div and mod

toInteger :: a -> Integer

Source

conversion to Integer

Instances

class Num a => Fractional a where

Source

Fractional numbers, supporting real division.

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

Methods

(/) :: a -> a -> a

Source

fractional division

recip :: a -> a

Source

reciprocal fraction

fromRational :: Rational -> a

Source

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

Integral a => Fractional (Ratio a)

RealFloat a => Fractional (Complex a)

HasResolution a => Fractional (Fixed a)

class Fractional a => Floating a where

Source

Trigonometric and hyperbolic functions and related functions.

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

Methods

pi :: a

exp :: a -> a

sqrt :: a -> a

log :: a -> a

(**) :: a -> a -> a

Source

logBase :: a -> a -> a

sin :: a -> a

tan :: a -> a

cos :: a -> a

asin :: a -> a

atan :: a -> a

acos :: a -> a

sinh :: a -> a

tanh :: a -> a

cosh :: a -> a

asinh :: a -> a

atanh :: a -> a

acosh :: a -> a

Instances

RealFloat a => Floating (Complex a)

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

Source

Extracting components of fractions.

Minimal complete definition: properFraction

Methods

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

Source

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

Source

truncate x returns the integer nearest x between zero and x

round :: Integral b => a -> b

Source

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

ceiling :: Integral b => a -> b

Source

ceiling x returns the least integer not less than x

floor :: Integral b => a -> b

Source

floor x returns the greatest integer not greater than x

Instances

Integral a => RealFrac (Ratio a)

HasResolution a => RealFrac (Fixed a)

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

Source

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

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

Methods

floatRadix :: a -> Integer

Source

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

floatDigits :: a -> Int

Source

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

floatRange :: a -> (Int, Int)

Source

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

decodeFloat :: a -> (Integer, Int)

Source

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) <= m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0).

encodeFloat :: Integer -> Int -> a

Source

encodeFloat performs the inverse of decodeFloat

exponent :: a -> Int

Source

the second component of decodeFloat.

significand :: a -> a

Source

the first component of decodeFloat, scaled to lie in the open interval (-1,1)

scaleFloat :: Int -> a -> a

Source

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

isNaN :: a -> Bool

Source

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

isInfinite :: a -> Bool

Source

True if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> Bool

Source

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

isNegativeZero :: a -> Bool

Source

True if the argument is an IEEE negative zero

isIEEE :: a -> Bool

Source

True if the argument is an IEEE floating point number

atan2 :: a -> a -> a

Source

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

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

Source

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.

even :: Integral a => a -> Bool

Source

odd :: Integral a => a -> Bool

Source

gcd :: Integral a => a -> a -> a

Source

gcd x y is the greatest (positive) integer that divides both x and y; for example gcd (-3) 6 = 3, gcd (-3) (-6) = 3, gcd 0 4 = 4. gcd 0 0 raises a runtime error.

lcm :: Integral a => a -> a -> a

Source

lcm x y is the smallest positive integer that both x and y divide.

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

Source

raise a number to a non-negative integral power

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

Source

raise a number to an integral power

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

Source

general coercion from integral types

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

Source

general coercion to fractional types

Monads and functors

class Monad m where

Source

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

Minimal complete definition: >>= and return.

Instances of Monad should satisfy the following laws:

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

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

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

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

Methods

(>>=) :: forall a b. m a -> (a -> m b) -> m b

Source

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

(>>) :: forall a b. m a -> m b -> m b

Source

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

Source

Inject a value into the monadic type.

fail :: String -> m a

Source

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 [::]

Monad P

Monad ((->) r)

Monad (ST s)

ArrowApply a => Monad (ArrowMonad a)

Monad (ST s)

class Functor f where

Source

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, Data.Maybe.Maybe and System.IO.IO defined in the Prelude satisfy these laws.

Methods

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

Source

Instances

Functor []

Functor [::]

Functor Id

Functor ((->) r)

Functor (Either a)

Functor ((,) a)

Functor (ST s)

Ix i => Functor (Array i)

Monad m => Functor (WrappedMonad m)

Functor (Const m)

Functor (StateR s)

Functor (StateL s)

Functor (ST s)

Arrow a => Functor (WrappedArrow a b)

mapM :: Monad m => (a -> m b) -> [a] -> m [b]

Source

mapM f is equivalent to sequence . map f.

mapM_ :: Monad m => (a -> m b) -> [a] -> m ()

Source

mapM_ f is equivalent to sequence_ . map f.

sequence :: Monad m => [m a] -> m [a]

Source

Evaluate each action in the sequence from left to right, and collect the results.

sequence_ :: Monad m => [m a] -> m ()

Source

Evaluate each action in the sequence from left to right, and ignore the results.

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

Source

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

Miscellaneous functions

id :: a -> a

Source

Identity function.

const :: a -> b -> a

Source

Constant function.

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

Source

Function composition.

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

Source

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

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

Source

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 Data.List.zipWith ($) fs xs.

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

Source

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

asTypeOf :: a -> a -> a

Source

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.

error :: [Char] -> a

Source

error stops execution and displays an error message.

undefined :: a

Source

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

Source

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

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

Source

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

List operations

map :: (a -> b) -> [a] -> [b]

Source

map f xs is the list obtained by applying f to each element of xs, i.e.,

 map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
 map f [x1, x2, ...] == [f x1, f x2, ...]

(++) :: [a] -> [a] -> [a]

Source

Append two lists, i.e.,

 [x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn]
 [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]

If the first list is not finite, the result is the first list.

filter :: (a -> Bool) -> [a] -> [a]

Source

filter, applied to a predicate and a list, returns the list of those elements that satisfy the predicate; i.e.,

 filter p xs = [ x | x <- xs, p x]

head :: [a] -> a

Source

Extract the first element of a list, which must be non-empty.

last :: [a] -> a

Source

Extract the last element of a list, which must be finite and non-empty.

tail :: [a] -> [a]

Source

Extract the elements after the head of a list, which must be non-empty.

init :: [a] -> [a]

Source

Return all the elements of a list except the last one. The list must be non-empty.

null :: [a] -> Bool

Source

Test whether a list is empty.

length :: [a] -> Int

Source

length returns the length of a finite list as an Int. It is an instance of the more general Data.List.genericLength, the result type of which may be any kind of number.

(!!) :: [a] -> Int -> a

Source

List index (subscript) operator, starting from 0. It is an instance of the more general Data.List.genericIndex, which takes an index of any integral type.

reverse :: [a] -> [a]

Source

reverse xs returns the elements of xs in reverse order. xs must be finite.

Reducing lists (folds)

foldl :: (a -> b -> a) -> a -> [b] -> a

Source

foldl, applied to a binary operator, a starting value (typically the left-identity of the operator), and a list, reduces the list using the binary operator, from left to right:

 foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn

The list must be finite.

foldl1 :: (a -> a -> a) -> [a] -> a

Source

foldl1 is a variant of foldl that has no starting value argument, and thus must be applied to non-empty lists.

foldr :: (a -> b -> b) -> b -> [a] -> b

Source

foldr, applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left:

 foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)

foldr1 :: (a -> a -> a) -> [a] -> a

Source

foldr1 is a variant of foldr that has no starting value argument, and thus must be applied to non-empty lists.

Special folds

and :: [Bool] -> Bool

Source

and returns the conjunction of a Boolean list. For the result to be True, the list must be finite; False, however, results from a False value at a finite index of a finite or infinite list.

or :: [Bool] -> Bool

Source

or returns the disjunction of a Boolean list. For the result to be False, the list must be finite; True, however, results from a True value at a finite index of a finite or infinite list.

any :: (a -> Bool) -> [a] -> Bool

Source

Applied to a predicate and a list, any determines if any element of the list satisfies the predicate.

all :: (a -> Bool) -> [a] -> Bool

Source

Applied to a predicate and a list, all determines if all elements of the list satisfy the predicate.

sum :: Num a => [a] -> a

Source

The sum function computes the sum of a finite list of numbers.

product :: Num a => [a] -> a

Source

The product function computes the product of a finite list of numbers.

concat :: [[a]] -> [a]

Source

Concatenate a list of lists.

concatMap :: (a -> [b]) -> [a] -> [b]

Source

Map a function over a list and concatenate the results.

maximum :: Ord a => [a] -> a

Source

maximum returns the maximum value from a list, which must be non-empty, finite, and of an ordered type. It is a special case of maximumBy, which allows the programmer to supply their own comparison function.

minimum :: Ord a => [a] -> a

Source

minimum returns the minimum value from a list, which must be non-empty, finite, and of an ordered type. It is a special case of minimumBy, which allows the programmer to supply their own comparison function.

Building lists

Scans

scanl :: (a -> b -> a) -> a -> [b] -> [a]

Source

scanl is similar to foldl, but returns a list of successive reduced values from the left:

 scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]

Note that

 last (scanl f z xs) == foldl f z xs.

scanl1 :: (a -> a -> a) -> [a] -> [a]

Source

scanl1 is a variant of scanl that has no starting value argument:

 scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]

scanr :: (a -> b -> b) -> b -> [a] -> [b]

Source

scanr is the right-to-left dual of scanl. Note that

 head (scanr f z xs) == foldr f z xs.

scanr1 :: (a -> a -> a) -> [a] -> [a]

Source

scanr1 is a variant of scanr that has no starting value argument.

Infinite lists

iterate :: (a -> a) -> a -> [a]

Source

iterate f x returns an infinite list of repeated applications of f to x:

 iterate f x == [x, f x, f (f x), ...]

repeat :: a -> [a]

Source

repeat x is an infinite list, with x the value of every element.

replicate :: Int -> a -> [a]

Source

replicate n x is a list of length n with x the value of every element. It is an instance of the more general Data.List.genericReplicate, in which n may be of any integral type.

cycle :: [a] -> [a]

Source

cycle ties a finite list into a circular one, or equivalently, the infinite repetition of the original list. It is the identity on infinite lists.

Sublists

take :: Int -> [a] -> [a]

Source

take n, applied to a list xs, returns the prefix of xs of length n, or xs itself if n > length xs:

 take 5 "Hello World!" == "Hello"
 take 3 [1,2,3,4,5] == [1,2,3]
 take 3 [1,2] == [1,2]
 take 3 [] == []
 take (-1) [1,2] == []
 take 0 [1,2] == []

It is an instance of the more general Data.List.genericTake, in which n may be of any integral type.

drop :: Int -> [a] -> [a]

Source

drop n xs returns the suffix of xs after the first n elements, or [] if n > length xs:

 drop 6 "Hello World!" == "World!"
 drop 3 [1,2,3,4,5] == [4,5]
 drop 3 [1,2] == []
 drop 3 [] == []
 drop (-1) [1,2] == [1,2]
 drop 0 [1,2] == [1,2]

It is an instance of the more general Data.List.genericDrop, in which n may be of any integral type.

splitAt :: Int -> [a] -> ([a], [a])

Source

splitAt n xs returns a tuple where first element is xs prefix of length n and second element is the remainder of the list:

 splitAt 6 "Hello World!" == ("Hello ","World!")
 splitAt 3 [1,2,3,4,5] == ([1,2,3],[4,5])
 splitAt 1 [1,2,3] == ([1],[2,3])
 splitAt 3 [1,2,3] == ([1,2,3],[])
 splitAt 4 [1,2,3] == ([1,2,3],[])
 splitAt 0 [1,2,3] == ([],[1,2,3])
 splitAt (-1) [1,2,3] == ([],[1,2,3])

It is equivalent to (take n xs, drop n xs). splitAt is an instance of the more general Data.List.genericSplitAt, in which n may be of any integral type.

takeWhile :: (a -> Bool) -> [a] -> [a]

Source

takeWhile, applied to a predicate p and a list xs, returns the longest prefix (possibly empty) of xs of elements that satisfy p:

 takeWhile (< 3) [1,2,3,4,1,2,3,4] == [1,2]
 takeWhile (< 9) [1,2,3] == [1,2,3]
 takeWhile (< 0) [1,2,3] == []

dropWhile :: (a -> Bool) -> [a] -> [a]

Source

dropWhile p xs returns the suffix remaining after takeWhile p xs:

 dropWhile (< 3) [1,2,3,4,5,1,2,3] == [3,4,5,1,2,3]
 dropWhile (< 9) [1,2,3] == []
 dropWhile (< 0) [1,2,3] == [1,2,3]

span :: (a -> Bool) -> [a] -> ([a], [a])

Source

span, applied to a predicate p and a list xs, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that satisfy p and second element is the remainder of the list:

 span (< 3) [1,2,3,4,1,2,3,4] == ([1,2],[3,4,1,2,3,4])
 span (< 9) [1,2,3] == ([1,2,3],[])
 span (< 0) [1,2,3] == ([],[1,2,3])

span p xs is equivalent to (takeWhile p xs, dropWhile p xs)

break :: (a -> Bool) -> [a] -> ([a], [a])

Source

break, applied to a predicate p and a list xs, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that do not satisfy p and second element is the remainder of the list:

 break (> 3) [1,2,3,4,1,2,3,4] == ([1,2,3],[4,1,2,3,4])
 break (< 9) [1,2,3] == ([],[1,2,3])
 break (> 9) [1,2,3] == ([1,2,3],[])

break p is equivalent to span (not . p).

Searching lists

elem :: Eq a => a -> [a] -> Bool

Source

elem is the list membership predicate, usually written in infix form, e.g., x `elem` xs.

notElem :: Eq a => a -> [a] -> Bool

Source

notElem is the negation of elem.

lookup :: Eq a => a -> [(a, b)] -> Maybe b

Source

lookup key assocs looks up a key in an association list.

Zipping and unzipping lists

zip :: [a] -> [b] -> [(a, b)]

Source

zip takes two lists and returns a list of corresponding pairs. If one input list is short, excess elements of the longer list are discarded.

zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]

Source

zip3 takes three lists and returns a list of triples, analogous to zip.

zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]

Source

zipWith generalises zip by zipping with the function given as the first argument, instead of a tupling function. For example, zipWith (+) is applied to two lists to produce the list of corresponding sums.

zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]

Source

The zipWith3 function takes a function which combines three elements, as well as three lists and returns a list of their point-wise combination, analogous to zipWith.

unzip :: [(a, b)] -> ([a], [b])

Source

unzip transforms a list of pairs into a list of first components and a list of second components.

unzip3 :: [(a, b, c)] -> ([a], [b], [c])

Source

The unzip3 function takes a list of triples and returns three lists, analogous to unzip.

Functions on strings

lines :: String -> [String]

Source

lines breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.

words :: String -> [String]

Source

words breaks a string up into a list of words, which were delimited by white space.

unlines :: [String] -> String

Source

unlines is an inverse operation to lines. It joins lines, after appending a terminating newline to each.

unwords :: [String] -> String

Source

unwords is an inverse operation to words. It joins words with separating spaces.

Converting to and from String

Converting to String

type ShowS = String -> String

Source

The shows functions return a function that prepends the output String to an existing String. This allows constant-time concatenation of results using function composition.

class Show a where

Source

Conversion of values to readable Strings.

Minimal complete definition: showsPrec or show.

Derived instances of Show have the following properties, which are compatible with derived instances of Text.Read.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)".

Methods

showsPrec

Source

:: Int	the operator precedence of the enclosing context (a number from `0` to `11`). Function application has precedence `10`.
-> a	the value to be converted to a `String`
-> ShowS
Convert a value to a readable `String`. `showsPrec` should satisfy the law showsPrec d x r ++ s == showsPrec d x (r ++ s) Derived instances of Text.Read.Read and `Show` satisfy the following: `(x,"")` is an element of `(Text.Read.readsPrec d (showsPrec d x ""))`. That is, Text.Read.readsPrec parses the string produced by `showsPrec`, and delivers the value that `showsPrec` started with.

show :: a -> String

Source

A specialised variant of showsPrec, using precedence context zero, and returning an ordinary String.

showList :: [a] -> ShowS

Source

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

Instances

Show ()

Show HashData

Show HandleType

Show BlockedIndefinitelyOnSTM

Show BlockedIndefinitelyOnMVar

Show BlockedIndefinitely

Show BlockedOnDeadMVar

Show NestedAtomically

Show PatternMatchFail

Show FD

Show Timeout

Show a => Show [a]

Integral a => Show (Ratio a)

Show (Ptr a)

Show (FunPtr a)

Show a => Show ([::] a)

Show a => Show (Maybe a)

Show (ForeignPtr a)

Show a => Show (Last a)

Show a => Show (First a)

Show a => Show (Product a)

Show a => Show (Sum a)

Show a => Show (Dual a)

RealFloat a => Show (Complex a)

HasResolution a => Show (Fixed a)

Show (a -> b)

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

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

Show (ST s a)

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

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

(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)

shows :: Show a => a -> ShowS

Source

equivalent to showsPrec with a precedence of 0.

showChar :: Char -> ShowS

Source

utility function converting a Char to a show function that simply prepends the character unchanged.

showString :: String -> ShowS

Source

utility function converting a String to a show function that simply prepends the string unchanged.

showParen :: Bool -> ShowS -> ShowS

Source

utility function that surrounds the inner show function with parentheses when the Bool parameter is True.

Converting from String

type ReadS a = String -> [(a, String)]

Source

A parser for a type a, represented as a function that takes a String and returns a list of possible parses as (a,String) pairs.

Note that this kind of backtracking parser is very inefficient; reading a large structure may be quite slow (cf ReadP).

class Read a where

Source

Parsing of Strings, producing values.

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

Derived instances of Read make the following assumptions, which derived instances of Text.Show.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 98 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

Methods

readsPrec

Source

:: Int the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10.

-> ReadS a

attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.

Derived instances of Read and Text.Show.Show satisfy the following:

(x,"") is an element of (readsPrec d (Text.Show.showsPrec d x "")).

That is, readsPrec parses the string produced by Text.Show.showsPrec, and delivers the value that Text.Show.showsPrec started with.

readList :: ReadS [a]

Source

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

Instances

Read ()

Read a => Read [a]

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

Read a => Read ([::] a)

Read a => Read (Maybe a)

Read a => Read (Last a)

Read a => Read (First a)

Read a => Read (Product a)

Read a => Read (Sum a)

Read a => Read (Dual a)

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

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

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

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

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

(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)

reads :: Read a => ReadS a

Source

equivalent to readsPrec with a precedence of 0.

readParen :: Bool -> ReadS a -> ReadS a

Source

readParen True p parses what p parses, but surrounded with parentheses.

readParen False p parses what p parses, but optionally surrounded with parentheses.

read :: Read a => String -> a

Source

The read function reads input from a string, which must be completely consumed by the input process.

lex :: ReadS String

Source

The lex function reads a single lexeme from the input, discarding initial white space, and returning the characters that constitute the lexeme. If the input string contains only white space, lex returns a single successful `lexeme' consisting of the empty string. (Thus lex "" = [("","")].) If there is no legal lexeme at the beginning of the input string, lex fails (i.e. returns []).

This lexer is not completely faithful to the Haskell lexical syntax in the following respects:

Qualified names are not handled properly
Octal and hexadecimal numerics are not recognized as a single token
Comments are not treated properly

Basic Input and output

data IO a

Source

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

HPrintfType (IO a)

PrintfType (IO a)

Simple I/O operations

Output functions

putChar :: Char -> IO ()

Source

Write a character to the standard output device (same as hPutChar stdout).

putStr :: String -> IO ()

Source

Write a string to the standard output device (same as hPutStr stdout).

putStrLn :: String -> IO ()

Source

The same as putStr, but adds a newline character.

print :: Show a => a -> IO ()

Source

The print function outputs a value of any printable type to the standard output device. Printable types are those that are instances of class Show; print converts values to strings for output using the show operation and adds a newline.

For example, a program to print the first 20 integers and their powers of 2 could be written as:

 main = print ([(n, 2^n) | n <- [0..19]])

Input functions

getChar :: IO Char

Source

Read a character from the standard input device (same as hGetChar stdin).

getLine :: IO String

Source

Read a line from the standard input device (same as hGetLine stdin).

getContents :: IO String

Source

The getContents operation returns all user input as a single string, which is read lazily as it is needed (same as hGetContents stdin).

interact :: (String -> String) -> IO ()

Source

The interact function takes a function of type String->String as its argument. The entire input from the standard input device is passed to this function as its argument, and the resulting string is output on the standard output device.

Files

type FilePath = String

Source

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.

readFile :: FilePath -> IO String

Source

The readFile function reads a file and returns the contents of the file as a string. The file is read lazily, on demand, as with getContents.

writeFile :: FilePath -> String -> IO ()

Source

The computation writeFile file str function writes the string str, to the file file.

appendFile :: FilePath -> String -> IO ()

Source

The computation appendFile file str function appends the string str, to the file file.

Note that writeFile and appendFile write a literal string to a file. To write a value of any printable type, as with print, use the show function to convert the value to a string first.

 main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])

readIO :: Read a => String -> IO a

Source

The readIO function is similar to read except that it signals parse failure to the IO monad instead of terminating the program.

readLn :: Read a => IO a

Source

The readLn function combines getLine and readIO.

Exception handling in the I/O monad

type IOError = IOException

Source

The Haskell 98 type for exceptions in the IO monad. Any I/O operation may raise an IOError instead of returning a result. For a more general type of exception, including also those that arise in pure code, see Control.Exception.Exception.

In Haskell 98, this is an opaque type.

ioError :: IOError -> IO a

Source

Raise an IOError in the IO monad.

userError :: String -> IOError

Source

Construct an IOError value with a string describing the error. The fail method of the IO instance of the Monad class raises a userError, thus:

 instance Monad IO where 
   ...
   fail s = ioError (userError s)

catch :: IO a -> (IOError -> IO a) -> IO a

Source

The catch function establishes a handler that receives any IOError raised in the action protected by catch. An IOError is caught by the most recent handler established by catch. These handlers are not selective: all IOErrors are caught. Exception propagation must be explicitly provided in a handler by re-raising any unwanted exceptions. For example, in

 f = catch g (\e -> if IO.isEOFError e then return [] else ioError e)

the function f returns [] when an end-of-file exception (cf. isEOFError) occurs in g; otherwise, the exception is propagated to the next outer handler.

When an exception propagates outside the main program, the Haskell system prints the associated IOError value and exits the program.

Non-I/O exceptions are not caught by this variant; to catch all exceptions, use Control.Exception.catch from Control.Exception.

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