haskell98-2.0.0.3: Compatibility with Haskell 98

Safe HaskellTrustworthy
LanguageHaskell98

Prelude

Contents

Description

The Haskell 98 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

Standard types, classes and related functions

Basic data types

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

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

not :: Bool -> Bool

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 Either type.

Constructors

Nothing 
Just a 

Instances

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

Monad (Either e) 
Functor (Either a) 
Applicative (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) 
Typeable (* -> * -> *) Either 
type (==) (Either k k1) a b = EqEither k k1 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.

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

Minimal complete definition

(==) | (/=)

Methods

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

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

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 () 
Eq Handle 
Eq HandlePosn 
Eq IOMode 
Eq Errno 
Eq AsyncException 
Eq ArrayException 
Eq ExitCode 
Eq IOErrorType 
Eq BufferMode 
Eq Newline 
Eq NewlineMode 
Eq IODeviceType 
Eq SeekMode 
Eq WordPtr 
Eq IntPtr 
Eq GeneralCategory 
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 Lexeme 
Eq Number 
Eq Permissions 
Eq TimeLocale 
Eq Month 
Eq Day 
Eq ClockTime 
Eq CalendarTime 
Eq TimeDiff 
Eq LocalTime 
Eq UTCTime 
Eq NominalDiffTime 
Eq UniversalTime 
Eq DiffTime 
Eq Permissions 
Eq a => Eq [a] 
Eq a => Eq (Ratio a) 
Eq a => Eq (Complex a) 
Eq a => Eq (ZipList a) 
Eq (IORef a) 
Eq a => Eq (Maybe 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 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

Minimal complete definition

compare | (<=)

Methods

compare :: a -> a -> Ordering

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

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

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

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

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 () 
Ord IOMode 
Ord AsyncException 
Ord ArrayException 
Ord ExitCode 
Ord BufferMode 
Ord Newline 
Ord NewlineMode 
Ord SeekMode 
Ord WordPtr 
Ord IntPtr 
Ord GeneralCategory 
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 Permissions 
Ord TimeLocale 
Ord Month 
Ord Day 
Ord ClockTime 
Ord CalendarTime 
Ord TimeDiff 
Ord LocalTime 
Ord UTCTime 
Ord NominalDiffTime 
Ord UniversalTime 
Ord DiffTime 
Ord Permissions 
Ord a => Ord [a] 
Integral a => Ord (Ratio a) 
Ord a => Ord (ZipList a) 
Ord a => Ord (Maybe 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:

   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 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].

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 Source

maxBound :: a Source

Instances

Bounded Bool 
Bounded Char 
Bounded Int 
Bounded Int8 
Bounded Int16 
Bounded Int32 
Bounded Int64 
Bounded Ordering 
Bounded Word 
Bounded () 
Bounded WordPtr 
Bounded IntPtr 
Bounded GeneralCategory 
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 Month 
Bounded Day 
(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

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 Num a where Source

Basic numeric class.

Minimal complete definition: all except negate or (-)

Minimal complete definition

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

Methods

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

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

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

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

Integral numbers, supporting integer division.

Minimal complete definition: quotRem and toInteger

Minimal complete definition

quotRem, toInteger

Methods

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

integer division truncated toward zero

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

integer remainder, satisfying

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

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

integer division truncated toward negative infinity

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

class Num a => Fractional a where Source

Fractional numbers, supporting real division.

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

Minimal complete definition

fromRational, (recip | (/))

Methods

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

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

Minimal complete definition

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

Methods

pi :: a Source

exp :: a -> a Source

sqrt :: a -> a Source

log :: a -> a Source

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

logBase :: a -> a -> a Source

sin :: a -> a Source

tan :: a -> a Source

cos :: a -> a Source

asin :: a -> a Source

atan :: a -> a Source

acos :: a -> a Source

sinh :: a -> a Source

tanh :: a -> a Source

cosh :: a -> a Source

asinh :: a -> a Source

atanh :: a -> a Source

acosh :: a -> a Source

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

Extracting components of fractions.

Minimal complete definition: properFraction

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

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) <= 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 Source

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 Source

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 Source

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 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.

Numeric functions

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 infixr 8 Source

raise a number to a non-negative integral power

(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 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, Maybe and IO defined in the Prelude satisfy these laws.

Minimal complete definition

(>>=), return

Methods

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

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 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

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, Maybe and IO satisfy these laws.

Methods

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

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 infixr 1 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 infixr 9 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 infixr 0 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 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

($!) :: (a -> b) -> a -> b infixr 0 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] infixr 5 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

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

(!!) :: [a] -> Int -> a infixl 9 Source

List index (subscript) operator, starting from 0. It is an instance of the more general 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 :: (b -> a -> b) -> b -> [a] -> b 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. For the result to be False, the list must be finite; True, however, results from a True value for the predicate applied to an element at a finite index of a finite or infinite list.

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

Applied to a predicate and a list, all determines if all elements of the list satisfy the predicate. For the result to be True, the list must be finite; False, however, results from a False value for the predicate applied to an element at a finite index of a finite or infinite list.

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 :: (b -> a -> b) -> b -> [a] -> [b] 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 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 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 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 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 infix 4 Source

elem is the list membership predicate, usually written in infix form, e.g., x `elem` xs. For the result to be False, the list must be finite; True, however, results from an element equal to x found at a finite index of a finite or infinite list.

notElem :: Eq a => a -> [a] -> Bool infix 4 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 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

Methods

showsPrec Source

Arguments

:: 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 Read and Show satisfy the following:

That is, 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 Bool 
Show Char 
Show Double 
Show Float 
Show Int 
Show Int8 
Show Int16 
Show Int32 
Show Int64 
Show Integer 
Show Ordering 
Show Word 
Show () 
Show Handle 
Show HandleType 
Show HandlePosn 
Show IOMode 
Show PatternMatchFail 
Show RecSelError 
Show RecConError 
Show RecUpdError 
Show NoMethodError 
Show NonTermination 
Show NestedAtomically 
Show BlockedIndefinitelyOnMVar 
Show BlockedIndefinitelyOnSTM 
Show Deadlock 
Show AssertionFailed 
Show SomeAsyncException 
Show AsyncException 
Show ArrayException 
Show ExitCode 
Show IOErrorType 
Show BufferMode 
Show Newline 
Show NewlineMode 
Show SeekMode 
Show WordPtr 
Show IntPtr 
Show GeneralCategory 
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 Lexeme 
Show Number 
Show SomeException 
Show Permissions 
Show TimeLocale 
Show Month 
Show Day 
Show ClockTime 
Show CalendarTime 
Show TimeDiff 
Show Padding 
Show DateFormatSpec 
Show LocalTime 
Show ZonedTime 
Show UTCTime 
Show NominalDiffTime 
Show Day 
Show DiffTime 
Show Permissions 
Show StdGen 
Show a => Show [a] 
(Integral a, Show a) => Show (Ratio a) 
Show a => Show (Complex a) 
Show a => Show (ZipList a) 
Show a => Show (Maybe a) 
(Show a, Show b) => Show (Either a b) 
(Show a, Show b) => Show (a, b) 
(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 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

Methods

readsPrec Source

Arguments

:: 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 Show satisfy the following:

That is, readsPrec parses the string produced by showsPrec, and delivers the value that 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 Bool 
Read Char 
Read Double 
Read Float 
Read Int 
Read Int8 
Read Int16 
Read Int32 
Read Int64 
Read Integer 
Read Ordering 
Read Word 
Read () 
Read IOMode 
Read ExitCode 
Read BufferMode 
Read Newline 
Read NewlineMode 
Read SeekMode 
Read WordPtr 
Read IntPtr 
Read GeneralCategory 
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 Lexeme 
Read Permissions 
Read Month 
Read Day 
Read CalendarTime 
Read TimeDiff 
Read LocalTime 
Read ZonedTime 
Read TimeOfDay 
Read TimeZone 
Read UTCTime 
Read Day 
Read Permissions 
Read StdGen 
Read a => Read [a] 
(Integral a, Read a) => Read (Ratio a) 
Read a => Read (Complex a) 
Read a => Read (ZipList a) 
Read a => Read (Maybe 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 :: * -> *

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 2010 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 2010, 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 one of the exception handling functions. 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 catch from Control.Exception.