Prelude (original) (raw)

Basic data types

data Maybe a Source

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

The [Maybe](Prelude.html#t:Maybe) type is also a monad. It is a simple kind of error monad, where all errors are represented by [Nothing](Prelude.html#v:Nothing). A richer error monad can be built using the [Either](Data-Either.html#t:Either) type.

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

The [maybe](Prelude.html#v:maybe) function takes a default value, a function, and a [Maybe](Prelude.html#t:Maybe) value. If the [Maybe](Prelude.html#t:Maybe) value is [Nothing](Prelude.html#v:Nothing), the function returns the default value. Otherwise, it applies the function to the value inside the [Just](Prelude.html#v:Just) and returns the result.

data Either a b Source

The [Either](Prelude.html#t:Either) type represents values with two possibilities: a value of type `[Either](Prelude.html#t:Either)` a b is either `[Left](Prelude.html#v:Left)` a or `[Right](Prelude.html#v:Right)` b.

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

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

Case analysis for the [Either](Prelude.html#t:Either) type. If the value is `[Left](Prelude.html#v:Left)` a, apply the first function to a; if it is `[Right](Prelude.html#v:Right)` b, apply the second function to b.

data Char [Source](/packages/archive///doc/html/src/GHC-Types.html#Char)

The character type [Char](Prelude.html#t:Char) is an enumeration whose values represent Unicode (or equivalently ISO/IEC 10646) characters (seehttp://www.unicode.org/ for details). This set extends the ISO 8859-1 (Latin-1) character set (the first 256 characters), which is itself an extension of the ASCII character set (the first 128 characters). A character literal in Haskell has type [Char](Prelude.html#t:Char).

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

Tuples

fst :: (a, b) -> aSource

Extract the first component of a pair.

snd :: (a, b) -> bSource

Extract the second component of a pair.

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

[curry](Prelude.html#v:curry) converts an uncurried function to a curried function.

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

[uncurry](Prelude.html#v:uncurry) converts a curried function to a function on pairs.

Basic type classes

class Eq a where[Source](/packages/archive///doc/html/src/GHC-Classes.html#Eq)

The [Eq](Prelude.html#t:Eq) class defines equality ([==](Prelude.html#v:-61--61-)) and inequality ([/=](Prelude.html#v:-47--61-)). All the basic datatypes exported by the Prelude are instances of [Eq](Prelude.html#t:Eq), and [Eq](Prelude.html#t:Eq) may be derived for any datatype whose constituents are also instances of [Eq](Prelude.html#t:Eq).

Minimal complete definition: either [==](Prelude.html#v:-61--61-) or [/=](Prelude.html#v:-47--61-).

Instances

Eq Bool
Eq Char
Eq Double
Eq Float
Eq Int
Eq Int8
Eq Int16
Eq Int32
Eq Int64
Eq Integer
Eq Ordering
Eq Word
Eq Word8
Eq Word16
Eq Word32
Eq Word64
Eq ()
Eq TyCon
Eq TypeRep
Eq ArithException
Eq IOException
Eq MaskingState
Eq Lexeme
Eq Fingerprint
Eq IOMode
Eq SeekMode
Eq IODeviceType
Eq CUIntMax
Eq CIntMax
Eq CUIntPtr
Eq CIntPtr
Eq CSUSeconds
Eq CUSeconds
Eq CTime
Eq CClock
Eq CSigAtomic
Eq CWchar
Eq CSize
Eq CPtrdiff
Eq CDouble
Eq CFloat
Eq CULLong
Eq CLLong
Eq CULong
Eq CLong
Eq CUInt
Eq CInt
Eq CUShort
Eq CShort
Eq CUChar
Eq CSChar
Eq CChar
Eq GeneralCategory
Eq TypeRepKey
Eq Associativity
Eq Fixity
Eq Arity
Eq IntPtr
Eq WordPtr
Eq Any
Eq All
Eq BufferState
Eq CodingProgress
Eq NewlineMode
Eq Newline
Eq BufferMode
Eq Handle
Eq IOErrorType
Eq ExitCode
Eq ArrayException
Eq AsyncException
Eq Errno
Eq ThreadStatus
Eq BlockReason
Eq ThreadId
Eq Fd
Eq CRLim
Eq CTcflag
Eq CSpeed
Eq CCc
Eq CUid
Eq CNlink
Eq CGid
Eq CSsize
Eq CPid
Eq COff
Eq CMode
Eq CIno
Eq CDev
Eq Event
Eq TimeoutKey
Eq FdKey
Eq HandlePosn
Eq Fixity
Eq ConstrRep
Eq DataRep
Eq Constr	Equality of constructors
Eq SpecConstrAnnotation
Eq Unique
Eq QSem
Eq QSemN
Eq Version
Eq a => Eq [a]
Eq a => Eq (Ratio a)
Eq (StablePtr a)
Eq (Ptr a)
Eq (FunPtr a)
Eq a => Eq (Maybe a)
Eq (MVar a)
Eq a => Eq (Down a)
Eq (IORef a)
Eq (ForeignPtr 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)
Eq (TVar a)
Eq (Chan a)
Eq (SampleVar a)
Eq 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)
Eq (STRef s a)
(Eq a, Eq b, Eq c) => Eq (a, b, c)
(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](/packages/archive///doc/html/src/GHC-Classes.html#Ord)

The [Ord](Prelude.html#t:Ord) class is used for totally ordered datatypes.

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

Minimal complete definition: either [compare](Prelude.html#v:compare) or [<=](Prelude.html#v:-60--61-). Using [compare](Prelude.html#v:compare) can be more efficient for complex types.

Instances

| Ord Bool | | | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | | | Ord Char | | | Ord Double | | | Ord Float | | | Ord Int | | | Ord Int8 | | | Ord Int16 | | | Ord Int32 | | | Ord Int64 | | | Ord Integer | | | Ord Ordering | | | Ord Word | | | Ord Word8 | | | Ord Word16 | | | Ord Word32 | | | Ord Word64 | | | Ord () | | | Ord TyCon | | | Ord TypeRep | | | Ord ArithException | | | Ord Fingerprint | | | Ord IOMode | | | Ord SeekMode | | | Ord CUIntMax | | | Ord CIntMax | | | Ord CUIntPtr | | | Ord CIntPtr | | | Ord CSUSeconds | | | Ord CUSeconds | | | Ord CTime | | | Ord CClock | | | Ord CSigAtomic | | | Ord CWchar | | | Ord CSize | | | Ord CPtrdiff | | | Ord CDouble | | | Ord CFloat | | | Ord CULLong | | | Ord CLLong | | | Ord CULong | | | Ord CLong | | | Ord CUInt | | | Ord CInt | | | Ord CUShort | | | Ord CShort | | | Ord CUChar | | | Ord CSChar | | | Ord CChar | | | Ord GeneralCategory | | | Ord TypeRepKey | | | Ord Associativity | | | Ord Fixity | | | Ord Arity | | | Ord IntPtr | | | Ord WordPtr | | | Ord Any | | | Ord All | | | Ord NewlineMode | | | Ord Newline | | | Ord BufferMode | | | Ord ExitCode | | | Ord ArrayException | | | Ord AsyncException | | | Ord ThreadStatus | | | Ord BlockReason | | | Ord ThreadId | | | Ord Fd | | | Ord CRLim | | | Ord CTcflag | | | Ord CSpeed | | | Ord CCc | | | Ord CUid | | | Ord CNlink | | | Ord CGid | | | Ord CSsize | | | Ord CPid | | | Ord COff | | | Ord CMode | | | Ord CIno | | | Ord CDev | | | Ord Unique | | | Ord Version | | | Ord a => Ord [a] | | | Integral a => Ord (Ratio a) | | | Ord (Ptr a) | | | Ord (FunPtr a) | | | Ord a => Ord (Maybe a) | | | Ord a => Ord (Down a) | | | Ord (ForeignPtr 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) | | | (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 whereSource

Class [Enum](Prelude.html#t:Enum) defines operations on sequentially ordered types.

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

Instances of [Enum](Prelude.html#t: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](Prelude.html#v: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](Prelude.html#t:Bounded) as well as [Enum](Prelude.html#t:Enum), the following should hold:

The calls `[succ](Prelude.html#v:succ)` `[maxBound](Prelude.html#v:maxBound)` and `[pred](Prelude.html#v:pred)` `[minBound](Prelude.html#v:minBound)` should result in a runtime error.
[fromEnum](Prelude.html#v:fromEnum) and [toEnum](Prelude.html#v:toEnum) should give a runtime error if the result value is not representable in the result type. For example, `[toEnum](Prelude.html#v:toEnum)` 7 :: `[Bool](Prelude.html#t:Bool)` is an error.
[enumFrom](Prelude.html#v:enumFrom) and [enumFromThen](Prelude.html#v: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

class Bounded a whereSource

The [Bounded](Prelude.html#t:Bounded) class is used to name the upper and lower limits of a type. [Ord](Prelude.html#t:Ord) is not a superclass of [Bounded](Prelude.html#t:Bounded) since types that are not totally ordered may also have upper and lower bounds.

The [Bounded](Prelude.html#t:Bounded) class may be derived for any enumeration type;[minBound](Prelude.html#v:minBound) is the first constructor listed in the data declaration and [maxBound](Prelude.html#v:maxBound) is the last.[Bounded](Prelude.html#t:Bounded) may also be derived for single-constructor datatypes whose constituent types are in [Bounded](Prelude.html#t:Bounded).

Instances

| Bounded Bool | | | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | | Bounded Char | | | Bounded Int | | | Bounded Int8 | | | Bounded Int16 | | | Bounded Int32 | | | Bounded Int64 | | | Bounded Ordering | | | Bounded Word | | | Bounded Word8 | | | Bounded Word16 | | | Bounded Word32 | | | Bounded Word64 | | | Bounded () | | | Bounded CUIntMax | | | Bounded CIntMax | | | Bounded CUIntPtr | | | Bounded CIntPtr | | | Bounded CSigAtomic | | | Bounded CWchar | | | Bounded CSize | | | Bounded CPtrdiff | | | Bounded CULLong | | | Bounded CLLong | | | Bounded CULong | | | Bounded CLong | | | Bounded CUInt | | | Bounded CInt | | | Bounded CUShort | | | Bounded CShort | | | Bounded CUChar | | | Bounded CSChar | | | Bounded CChar | | | Bounded GeneralCategory | | | Bounded IntPtr | | | Bounded WordPtr | | | Bounded Any | | | Bounded All | | | Bounded Fd | | | Bounded CRLim | | | Bounded CTcflag | | | Bounded CUid | | | Bounded CNlink | | | Bounded CGid | | | Bounded CSsize | | | Bounded CPid | | | Bounded COff | | | Bounded CMode | | | Bounded CIno | | | Bounded CDev | | | 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](/packages/archive///doc/html/src/GHC-Types.html#Int)

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

data Float [Source](/packages/archive///doc/html/src/GHC-Types.html#Float)

Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.

data Double [Source](/packages/archive///doc/html/src/GHC-Types.html#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.

type Rational = Ratio Integer Source

Arbitrary-precision rational numbers, represented as a ratio of two [Integer](Prelude.html#t:Integer) values. A rational number may be constructed using the [%](Data-Ratio.html#v:-37-) operator.

Numeric type classes

class Num a whereSource

Basic numeric class.

Minimal complete definition: all except [negate](Prelude.html#v:negate) or (-)

class Fractional a => Floating a whereSource

Trigonometric and hyperbolic functions and related functions.

Minimal complete definition:[pi](Prelude.html#v:pi), [exp](Prelude.html#v:exp), [log](Prelude.html#v:log), [sin](Prelude.html#v:sin), [cos](Prelude.html#v:cos), [sinh](Prelude.html#v:sinh), [cosh](Prelude.html#v:cosh),[asin](Prelude.html#v:asin), [acos](Prelude.html#v:acos), [atan](Prelude.html#v:atan), [asinh](Prelude.html#v:asinh), [acosh](Prelude.html#v:acosh) and [atanh](Prelude.html#v:atanh)

Methods

pi :: aSource

exp, sqrt, log :: a -> aSource

(**), logBase :: a -> a -> aSource

sin, tan, cos :: a -> aSource

asin, atan, acos :: a -> aSource

sinh, tanh, cosh :: a -> aSource

asinh, atanh, acosh :: a -> aSource

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

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](Prelude.html#v: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](Prelude.html#v:decodeFloat) applied to a real floating-point number returns the significand expressed as an [Integer](Prelude.html#t:Integer) and an appropriately scaled exponent (an [Int](Prelude.html#t:Int)). If `[decodeFloat](Prelude.html#v: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](Prelude.html#v:abs)` m < b^d, where d is the value of `[floatDigits](Prelude.html#v:floatDigits)` x. In particular, `[decodeFloat](Prelude.html#v:decodeFloat)` 0 = (0,0). If the type contains a negative zero, also `[decodeFloat](Prelude.html#v:decodeFloat)` (-0.0) = (0,0).The result of `[decodeFloat](Prelude.html#v:decodeFloat)` x is unspecified if either of `[isNaN](Prelude.html#v:isNaN)` x or `[isInfinite](Prelude.html#v:isInfinite)` x is [True](Prelude.html#v:True).

encodeFloat :: Integer -> Int -> aSource

[encodeFloat](Prelude.html#v:encodeFloat) performs the inverse of [decodeFloat](Prelude.html#v:decodeFloat) in the sense that for finite x with the exception of -0.0,`uncurry` `[encodeFloat](Prelude.html#v:encodeFloat)` (`[decodeFloat](Prelude.html#v:decodeFloat)` x) = x.`[encodeFloat](Prelude.html#v: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](Prelude.html#v:exponent) corresponds to the second component of [decodeFloat](Prelude.html#v:decodeFloat).`[exponent](Prelude.html#v:exponent)` 0 = 0 and for finite nonzero x,`[exponent](Prelude.html#v:exponent)` x = snd (`[decodeFloat](Prelude.html#v:decodeFloat)` x) + `[floatDigits](Prelude.html#v:floatDigits)` x. If x is a finite floating-point number, it is equal in value to`[significand](Prelude.html#v:significand)` x * b ^^ `[exponent](Prelude.html#v:exponent)` x, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

significand :: a -> aSource

The first component of [decodeFloat](Prelude.html#v: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 -> aSource

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

isNaN :: a -> Bool Source

[True](Prelude.html#v:True) if the argument is an IEEE "not-a-number" (NaN) value

isInfinite :: a -> Bool Source

[True](Prelude.html#v:True) if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> Bool Source

[True](Prelude.html#v:True) if the argument is too small to be represented in normalized format

isNegativeZero :: a -> Bool Source

[True](Prelude.html#v:True) if the argument is an IEEE negative zero

isIEEE :: a -> Bool Source

[True](Prelude.html#v:True) if the argument is an IEEE floating point number

atan2 :: a -> a -> aSource

a version of arctangent taking two real floating-point arguments. For real floating x and y, `[atan2](Prelude.html#v:atan2)` y x computes the angle (from the positive x-axis) of the vector from the origin to the point (x,y). `[atan2](Prelude.html#v: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](Prelude.html#v:atan2)` y 1, with y in a type that is [RealFloat](Prelude.html#t:RealFloat), should return the same value as `[atan](Prelude.html#v:atan)` y. A default definition of [atan2](Prelude.html#v:atan2) is provided, but implementors can provide a more accurate implementation.

Numeric functions

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

the same as `[flip](Prelude.html#v:flip)` (`[-](Prelude.html#v:-45-)`).

Because - is treated specially in the Haskell grammar,(- e) is not a section, but an application of prefix negation. However, (`[subtract](Prelude.html#v:subtract)` exp) is equivalent to the disallowed section.

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

`[gcd](Prelude.html#v:gcd)` x y is the non-negative factor of both x and y of which every common factor of x and y is also a factor; for example`[gcd](Prelude.html#v:gcd)` 4 2 = 2, `[gcd](Prelude.html#v:gcd)` (-4) 6 = 2, `[gcd](Prelude.html#v:gcd)` 0 4 = 4. `[gcd](Prelude.html#v:gcd)` 0 0 = 0. (That is, the common divisor that is "greatest" in the divisibility preordering.)

Note: Since for signed fixed-width integer types, `[abs](Prelude.html#v:abs)` `[minBound](Prelude.html#v:minBound)` < 0, the result may be negative if one of the arguments is `[minBound](Prelude.html#v:minBound)` (and necessarily is if the other is 0 or `[minBound](Prelude.html#v:minBound)`) for such types.

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

`[lcm](Prelude.html#v:lcm)` x y is the smallest positive integer that both x and y divide.

Monads and functors

class Monad m whereSource

The [Monad](Prelude.html#t: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: [>>=](Prelude.html#v:-62--62--61-) and [return](Prelude.html#v:return).

Instances of [Monad](Prelude.html#t: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](Prelude.html#t:Monad) and [Functor](Prelude.html#t:Functor) should additionally satisfy the law:

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

The instances of [Monad](Prelude.html#t:Monad) for lists, [Maybe](Data-Maybe.html#t:Maybe) and [IO](System-IO.html#t:IO)defined in the Prelude satisfy these laws.

Methods

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

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 bSource

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

return :: a -> m aSource

Inject a value into the monadic type.

fail :: String -> m aSource

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.

class Functor f whereSource

The [Functor](Prelude.html#t:Functor) class is used for types that can be mapped over. Instances of [Functor](Prelude.html#t:Functor) should satisfy the following laws:

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

The instances of [Functor](Prelude.html#t:Functor) for lists, [Maybe](Data-Maybe.html#t:Maybe) and [IO](System-IO.html#t:IO)satisfy these laws.

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 bSource

Same as [>>=](Prelude.html#v:-62--62--61-), but with the arguments interchanged.

Miscellaneous functions

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

Function composition.

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

`[flip](Prelude.html#v:flip)` f takes its (first) two arguments in the reverse order of f.

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

Application operator. This operator is redundant, since ordinary application (f x) means the same as (f `[$](Prelude.html#v:-36-)` x). However, [$](Prelude.html#v:-36-) 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](Prelude.html#v:map)` (`[$](Prelude.html#v:-36-)` 0) xs, or `[zipWith](Data-List.html#t:zipWith)` (`[$](Prelude.html#v:-36-)`) fs xs.

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

`[until](Prelude.html#v:until)` p f yields the result of applying f until p holds.

asTypeOf :: a -> a -> aSource

[asTypeOf](Prelude.html#v:asTypeOf) is a type-restricted version of [const](Prelude.html#v:const). It is usually used as an infix operator, and its typing forces its first argument (which is usually overloaded) to have the same type as the second.

undefined :: aSource

A special case of [error](Prelude.html#v:error). It is expected that compilers will recognize this and insert error messages which are more appropriate to the context in which [undefined](Prelude.html#v:undefined) appears.

seq :: a -> b -> b[Source](/packages/archive///doc/html/src/GHC-Prim.html#seq)

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

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

Strict (call-by-value) application, defined in terms of [seq](Prelude.html#v:seq).

List operations

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

[map](Prelude.html#v: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](Prelude.html#v: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] -> aSource

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

last :: [a] -> aSource

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.

length :: [a] -> Int Source

O(n). [length](Prelude.html#v:length) returns the length of a finite list as an [Int](Prelude.html#t:Int). It is an instance of the more general [genericLength](Data-List.html#t:genericLength), the result type of which may be any kind of number.

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

List index (subscript) operator, starting from 0. It is an instance of the more general [genericIndex](Data-List.html#t:genericIndex), which takes an index of any integral type.

reverse :: [a] -> [a]Source

[reverse](Prelude.html#v:reverse) xs returns the elements of xs in reverse order.xs must be finite.

Reducing lists (folds)

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

[foldl](Prelude.html#v: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] -> aSource

[foldl1](Prelude.html#v:foldl1) is a variant of [foldl](Prelude.html#v:foldl) that has no starting value argument, and thus must be applied to non-empty lists.

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

[foldr](Prelude.html#v: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] -> aSource

[foldr1](Prelude.html#v:foldr1) is a variant of [foldr](Prelude.html#v:foldr) that has no starting value argument, and thus must be applied to non-empty lists.

Special folds

and :: [Bool] -> Bool Source

[and](Prelude.html#v:and) returns the conjunction of a Boolean list. For the result to be[True](Prelude.html#v:True), the list must be finite; [False](Prelude.html#v:False), however, results from a [False](Prelude.html#v:False) value at a finite index of a finite or infinite list.

or :: [Bool] -> Bool Source

[or](Prelude.html#v:or) returns the disjunction of a Boolean list. For the result to be[False](Prelude.html#v:False), the list must be finite; [True](Prelude.html#v:True), however, results from a [True](Prelude.html#v: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](Prelude.html#v:any) determines if any element of the list satisfies the predicate. For the result to be[False](Prelude.html#v:False), the list must be finite; [True](Prelude.html#v:True), however, results from a [True](Prelude.html#v: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](Prelude.html#v:all) determines if all elements of the list satisfy the predicate. For the result to be[True](Prelude.html#v:True), the list must be finite; [False](Prelude.html#v:False), however, results from a [False](Prelude.html#v:False) value for the predicate applied to an element at a finite index of a finite or infinite list.

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

The [sum](Prelude.html#v:sum) function computes the sum of a finite list of numbers.

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

Map a function over a list and concatenate the results.

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

[maximum](Prelude.html#v: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](Data-List.html#v:maximumBy), which allows the programmer to supply their own comparison function.

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

[minimum](Prelude.html#v: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](Data-List.html#v:minimumBy), which allows the programmer to supply their own comparison function.

Building lists

Scans

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

[scanl](Prelude.html#v:scanl) is similar to [foldl](Prelude.html#v: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](Prelude.html#v:scanl1) is a variant of [scanl](Prelude.html#v:scanl) that has no starting value argument:

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

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

[scanr](Prelude.html#v:scanr) is the right-to-left dual of [scanl](Prelude.html#v:scanl). Note that

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

Infinite lists

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

[iterate](Prelude.html#v:iterate) f x returns an infinite list of repeated applications of f to x:

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

cycle :: [a] -> [a]Source

[cycle](Prelude.html#v: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](Prelude.html#v:take) n, applied to a list xs, returns the prefix of xs of length n, or xs itself if n > `[length](Prelude.html#v: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](Data-List.html#t:genericTake), in which n may be of any integral type.

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

[drop](Prelude.html#v:drop) n xs returns the suffix of xs after the first n elements, or [] if n > `[length](Prelude.html#v: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](Data-List.html#t:genericDrop), in which n may be of any integral type.

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

[splitAt](Prelude.html#v: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](Prelude.html#v:take)` n xs, `[drop](Prelude.html#v:drop)` n xs) when n is not _|_ (splitAt _|_ xs = _|_).[splitAt](Prelude.html#v:splitAt) is an instance of the more general [genericSplitAt](Data-List.html#t:genericSplitAt), in which n may be of any integral type.

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

[takeWhile](Prelude.html#v: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](Prelude.html#v:dropWhile) p xs returns the suffix remaining after [takeWhile](Prelude.html#v: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](Prelude.html#v: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](Prelude.html#v:span) p xs is equivalent to (`[takeWhile](Prelude.html#v:takeWhile)` p xs, `[dropWhile](Prelude.html#v:dropWhile)` p xs)

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

[break](Prelude.html#v: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](Prelude.html#v:break) p is equivalent to `[span](Prelude.html#v:span)` (`[not](Prelude.html#v:not)` . p).

Searching lists

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

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

Zipping and unzipping lists

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

[zip](Prelude.html#v: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](Prelude.html#v:zip3) takes three lists and returns a list of triples, analogous to[zip](Prelude.html#v:zip).

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

[zipWith](Prelude.html#v:zipWith) generalises [zip](Prelude.html#v:zip) by zipping with the function given as the first argument, instead of a tupling function. For example, `[zipWith](Prelude.html#v: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](Prelude.html#v: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](Prelude.html#v:zipWith).

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

[unzip](Prelude.html#v: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](Prelude.html#v:unzip3) function takes a list of triples and returns three lists, analogous to [unzip](Prelude.html#v:unzip).

Functions on strings

lines :: String -> [String]Source

[lines](Prelude.html#v:lines) breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.

Converting to and from `String`

Converting to `String`

type ShowS = String -> String Source

The shows functions return a function that prepends the output [String](Prelude.html#t:String) to an existing [String](Prelude.html#t:String). This allows constant-time concatenation of results using function composition.

class Show a whereSource

Conversion of values to readable [String](Prelude.html#t:String)s.

Minimal complete definition: [showsPrec](Prelude.html#v:showsPrec) or [show](Prelude.html#v:show).

Derived instances of [Show](Prelude.html#t:Show) have the following properties, which are compatible with derived instances of [Read](Text-Read.html#t:Read):

The result of [show](Prelude.html#v: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](Prelude.html#v: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](Prelude.html#v: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](Prelude.html#t: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](Prelude.html#v:show)` (Leaf 1 :^: Leaf 2 :^: Leaf 3) produces the string"Leaf 1 :^: (Leaf 2 :^: Leaf 3)".

Methods

showsPrecSource

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](Prelude.html#t:String).

[showsPrec](Prelude.html#v:showsPrec) should satisfy the law

showsPrec d x r ++ s == showsPrec d x (r ++ s)

Derived instances of [Read](Text-Read.html#t:Read) and [Show](Prelude.html#t:Show) satisfy the following:

(x,"") is an element of(`[readsPrec](Text-Read.html#t:readsPrec)` d (`[showsPrec](Prelude.html#v:showsPrec)` d x "")).

That is, [readsPrec](Text-Read.html#t:readsPrec) parses the string produced by[showsPrec](Prelude.html#v:showsPrec), and delivers the value that [showsPrec](Prelude.html#v:showsPrec) started with.

show :: a -> String Source

A specialised variant of [showsPrec](Prelude.html#v:showsPrec), using precedence context zero, and returning an ordinary [String](Prelude.html#t:String).

showList :: [a] -> ShowS Source

The method [showList](Prelude.html#v: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](Prelude.html#t:Show) instance of the [Char](Prelude.html#t:Char) type, where values of type [String](Prelude.html#t: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 Word8 | | | Show Word16 | | | Show Word32 | | | Show Word64 | | | Show () | | | Show TyCon | | | Show TypeRep | | | Show ArithException | | | Show ErrorCall | | | Show SomeException | | | Show IOException | | | Show MaskingState | | | Show Lexeme | | | Show IOMode | | | Show SeekMode | | | Show CUIntMax | | | Show CIntMax | | | Show CUIntPtr | | | Show CIntPtr | | | Show CSUSeconds | | | Show CUSeconds | | | Show CTime | | | Show CClock | | | Show CSigAtomic | | | Show CWchar | | | Show CSize | | | Show CPtrdiff | | | Show CDouble | | | Show CFloat | | | Show CULLong | | | Show CLLong | | | Show CULong | | | Show CLong | | | Show CUInt | | | Show CInt | | | Show CUShort | | | Show CShort | | | Show CUChar | | | Show CSChar | | | Show CChar | | | Show GeneralCategory | | | Show Associativity | | | Show Fixity | | | Show Arity | | | Show Dynamic | | | Show IntPtr | | | Show WordPtr | | | Show Any | | | Show All | | | Show CodingProgress | | | Show TextEncoding | | | Show NewlineMode | | | Show Newline | | | Show BufferMode | | | Show Handle | | | Show IOErrorType | | | Show ExitCode | | | Show ArrayException | | | Show AsyncException | | | Show AssertionFailed | | | Show Deadlock | | | Show BlockedIndefinitelyOnSTM | | | Show BlockedIndefinitelyOnMVar | | | Show CodingFailureMode | | | Show ThreadStatus | | | Show BlockReason | | | Show ThreadId | | | Show NestedAtomically | | | Show NonTermination | | | Show NoMethodError | | | Show RecUpdError | | | Show RecConError | | | Show RecSelError | | | Show PatternMatchFail | | | Show Fd | | | Show CRLim | | | Show CTcflag | | | Show CSpeed | | | Show CCc | | | Show CUid | | | Show CNlink | | | Show CGid | | | Show CSsize | | | Show CPid | | | Show COff | | | Show CMode | | | Show CIno | | | Show CDev | | | Show Event | | | Show FdKey | | | Show HandlePosn | | | Show Fixity | | | Show ConstrRep | | | Show DataRep | | | Show Constr | | | Show DataType | | | Show GCStats | | | Show Version | | | Show a => Show [a] | | | (Integral a, Show a) => Show (Ratio a) | | | Show (Ptr a) | | | Show (FunPtr a) | | | Show a => Show (Maybe a) | | | Show (ForeignPtr a) | | | Show (IsEven n) | | | Show (IsZero n) | | | 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) | | | Show 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) | | | (SingE k (Kind k) rep, Show rep) => Show (Sing k a) | | | (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) | |

Converting from `String`

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

A parser for a type a, represented as a function that takes a[String](Prelude.html#t:String) and returns a list of possible parses as (a,`[String](Prelude.html#t:String)`) pairs.

Note that this kind of backtracking parser is very inefficient; reading a large structure may be quite slow (cf [ReadP](Text-ParserCombinators-ReadP.html#t:ReadP)).

class Read a whereSource

Parsing of [String](Prelude.html#t:String)s, producing values.

Minimal complete definition: [readsPrec](Prelude.html#v:readsPrec) (or, for GHC only, [readPrec](Text-Read.html#v:readPrec))

Derived instances of [Read](Prelude.html#t:Read) make the following assumptions, which derived instances of [Show](Text-Show.html#t:Show) obey:

If the constructor is defined to be an infix operator, then the derived [Read](Prelude.html#t: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](Prelude.html#t: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](Prelude.html#t: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](Prelude.html#t: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

readsPrecSource

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](Prelude.html#t:Read) and [Show](Text-Show.html#t:Show) satisfy the following:

(x,"") is an element of(`[readsPrec](Prelude.html#v:readsPrec)` d (`[showsPrec](Text-Show.html#t:showsPrec)` d x "")).

That is, [readsPrec](Prelude.html#v:readsPrec) parses the string produced by[showsPrec](Text-Show.html#t:showsPrec), and delivers the value that[showsPrec](Text-Show.html#t:showsPrec) started with.

readList :: ReadS [a]Source

The method [readList](Prelude.html#v: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](Prelude.html#t:Read) instance of the [Char](Prelude.html#t:Char) type, where values of type [String](Prelude.html#t: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 Word8 | | | Read Word16 | | | Read Word32 | | | Read Word64 | | | Read () | | | Read Lexeme | | | Read IOMode | | | Read SeekMode | | | Read CUIntMax | | | Read CIntMax | | | Read CUIntPtr | | | Read CIntPtr | | | Read CSUSeconds | | | Read CUSeconds | | | Read CTime | | | Read CClock | | | Read CSigAtomic | | | Read CWchar | | | Read CSize | | | Read CPtrdiff | | | Read CDouble | | | Read CFloat | | | Read CULLong | | | Read CLLong | | | Read CULong | | | Read CLong | | | Read CUInt | | | Read CInt | | | Read CUShort | | | Read CShort | | | Read CUChar | | | Read CSChar | | | Read CChar | | | Read GeneralCategory | | | Read Associativity | | | Read Fixity | | | Read Arity | | | Read IntPtr | | | Read WordPtr | | | Read Any | | | Read All | | | Read NewlineMode | | | Read Newline | | | Read BufferMode | | | Read ExitCode | | | Read Fd | | | Read CRLim | | | Read CTcflag | | | Read CSpeed | | | Read CCc | | | Read CUid | | | Read CNlink | | | Read CGid | | | Read CSsize | | | Read CPid | | | Read COff | | | Read CMode | | | Read CIno | | | Read CDev | | | Read GCStats | | | Read Version | | | Read a => Read [a] | | | (Integral a, Read a) => Read (Ratio 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 => Read (Complex a) | | | HasResolution a => Read (Fixed a) | | | (Read a, Read b) => Read (Either a b) | | | (Read a, Read b) => Read (a, b) | | | (SingRep k a rep, Read rep, Eq rep) => Read (Sing k a) | | | (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) | |

read :: Read a => String -> aSource

The [read](Prelude.html#v:read) function reads input from a string, which must be completely consumed by the input process.

lex :: ReadS String Source

The [lex](Prelude.html#v: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](Prelude.html#v:lex) returns a single successful `lexeme' consisting of the empty string. (Thus`[lex](Prelude.html#v:lex)` "" = [("","")].) If there is no legal lexeme at the beginning of the input string, [lex](Prelude.html#v: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](/packages/archive///doc/html/src/GHC-Types.html#IO)

A value of type `[IO](Prelude.html#t: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 toMain.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](Prelude.html#t:IO) monad and called at some point, directly or indirectly, from Main.main.

[IO](Prelude.html#t:IO) is a monad, so [IO](Prelude.html#t:IO) actions can be combined using either the do-notation or the >> and >>= operations from the Monad class.

Simple I/O operations

Output functions

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

The [print](Prelude.html#v:print) function outputs a value of any printable type to the standard output device. Printable types are those that are instances of class [Show](Prelude.html#t:Show); [print](Prelude.html#v:print) converts values to strings for output using the [show](Prelude.html#v: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

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

The [interact](Prelude.html#v: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](Prelude.html#t: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.

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

The computation [appendFile](Prelude.html#v:appendFile) file str function appends the string str, to the file file.

Note that [writeFile](Prelude.html#v:writeFile) and [appendFile](Prelude.html#v:appendFile) write a literal string to a file. To write a value of any printable type, as with [print](Prelude.html#v:print), use the [show](Prelude.html#v:show) function to convert the value to a string first.

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

Exception handling in the I/O monad

type IOError = IOException Source

The Haskell 98 type for exceptions in the [IO](Prelude.html#t:IO) monad. Any I/O operation may raise an [IOError](Prelude.html#t: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.

Prelude (original) (raw)

Standard types, classes and related functions

Basic data types

Tuples

Basic type classes

Numbers

Numeric types

Numeric type classes

Numeric functions

Monads and functors

Miscellaneous functions

List operations

Reducing lists (folds)

Special folds

Building lists

Scans

Infinite lists

Sublists

Searching lists

Zipping and unzipping lists

Functions on strings

Converting to and from String

Converting to String

Converting from String

Basic Input and output

Simple I/O operations

Output functions

Input functions

Files

Exception handling in the I/O monad

Converting to and from `String`

Converting to `String`

Converting from `String`