base-4.3.1.0: Basic libraries

Portabilityportable
Stabilitystable
Maintainer[email protected]

Prelude

Contents

Description

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

Synopsis

Standard types, classes and related functions

Basic data types

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

Boolean "and"

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

Boolean "or"

not :: Bool -> BoolSource

Boolean "not"

otherwise :: BoolSource

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

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

data Maybe a Source

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

The Maybe type is also a monad. It is a simple kind of error monad, where all errors are represented by Nothing. A richer error monad can be built using the Data.Either.Either type.

Constructors

Nothing 
Just a 

Instances

Monad Maybe 
Functor Maybe 
Typeable1 Maybe 
MonadFix Maybe 
MonadPlus Maybe 
Applicative Maybe 
Foldable Maybe 
Traversable Maybe 
Alternative Maybe 
Eq a => Eq (Maybe a) 
Data a => Data (Maybe a) 
Ord a => Ord (Maybe a) 
Read a => Read (Maybe a) 
Show a => Show (Maybe a) 
Monoid a => Monoid (Maybe a)

Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s  S." Since there is no "Semigroup" typeclass providing just mappend, we use Monoid instead.

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

The maybe function takes a default value, a function, and a Maybe value. If the Maybe value is Nothing, the function returns the default value. Otherwise, it applies the function to the value inside the Just and returns the result.

data Either a b Source

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

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

Constructors

Left a 
Right b 

Instances

Typeable2 Either 
Monad (Either e) 
Functor (Either a) 
MonadFix (Either e) 
Applicative (Either e) 
(Eq a, Eq b) => Eq (Either a b) 
(Data a, Data b) => Data (Either a b) 
(Ord a, Ord b) => Ord (Either a b) 
(Read a, Read b) => Read (Either a b) 
(Show a, Show b) => Show (Either a b) 

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

Case analysis for the Either type. If the value is Left a, apply the first function to a; if it is Right b, apply the second function to b.

data Char Source

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

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

type String = [Char]Source

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

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 converts an uncurried function to a curried function.

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

uncurry converts a curried function to a function on pairs.

Basic type classes

class Eq a whereSource

The Eq class defines equality (==) and inequality (/=). All the basic datatypes exported by the Prelude are instances of Eq, and Eq may be derived for any datatype whose constituents are also instances of Eq.

Minimal complete definition: either == or /=.

Methods

(==) :: a -> a -> BoolSource

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

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 IOMode 
Eq SeekMode 
Eq IODeviceType 
Eq CUIntMax 
Eq CIntMax 
Eq CUIntPtr 
Eq CIntPtr 
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 Any 
Eq All 
Eq GeneralCategory 
Eq Inserts 
Eq HashData 
Eq KeyPr 
Eq Key 
Eq Finalizers 
Eq IntPtr 
Eq WordPtr 
Eq BufferState 
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 ControlMessage 
Eq Event 
Eq EventType 
Eq EPollFd 
Eq Unique 
Eq State 
Eq TimeoutKey 
Eq FdKey 
Eq HandlePosn 
Eq Fixity 
Eq ConstrRep 
Eq DataRep 
Eq Constr

Equality of constructors

Eq SpecConstrAnnotation 
Eq Unique 
Eq Timeout 
Eq Version 
Eq Exception 
Eq Event 
Eq a => Eq [a] 
Integral a => Eq (Ratio a) 
Eq (StablePtr a) 
Eq (Ptr a) 
Eq (FunPtr a) 
Eq a => Eq ([::] a) 
Eq a => Eq (Maybe a) 
Eq (MVar a) 
Eq (IORef a) 
Eq 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 (ForeignPtr a) 
Eq (TVar a) 
Eq a => Eq (IntMap a) 
Eq a => Eq (LTree a) 
Eq a => Eq (PSQ a) 
Eq a => Eq (Elem a) 
Eq a => Eq (Down a) 
Eq (SampleVar a) 
RealFloat a => Eq (Complex a) 
Eq (Fixed a) 
Eq (StableName a) 
(Eq a, Eq b) => Eq (Either a b) 
(Eq a, Eq b) => Eq (a, b) 
(Ix i, Eq e) => Eq (Array i e) 
Eq (IOArray i e) 
Eq (STRef s a) 
(Eq a, Eq b, Eq c) => Eq (a, b, c) 
Eq (STArray s i e) 
(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) 
(Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) 
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) 
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) 
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) 
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) 
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) 
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) 
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) 
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) 
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) 
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) 

class Eq a => Ord a whereSource

The Ord class is used for totally ordered datatypes.

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

Minimal complete definition: either compare or <=. Using compare can be more efficient for complex types.

Methods

compare :: a -> a -> OrderingSource

(<) :: a -> a -> BoolSource

(>=) :: a -> a -> BoolSource

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

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

max :: a -> a -> aSource

min :: a -> a -> aSource

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 ArithException 
Ord IOMode 
Ord SeekMode 
Ord CUIntMax 
Ord CIntMax 
Ord CUIntPtr 
Ord CIntPtr 
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 Any 
Ord All 
Ord GeneralCategory 
Ord IntPtr 
Ord WordPtr 
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 Unique 
Ord Version 
Ord a => Ord [a] 
Integral a => Ord (Ratio a) 
Ord (Ptr a) 
Ord (FunPtr a) 
Ord a => Ord ([::] a) 
Ord a => Ord (Maybe a) 
Ord 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 (ForeignPtr a) 
Ord a => Ord (Down a) 
Ord (Fixed a) 
(Ord a, Ord b) => Ord (Either a b) 
(Ord a, Ord b) => Ord (a, b) 
(Ix i, Ord e) => Ord (Array i e) 
(Ord a, Ord b, Ord c) => Ord (a, b, c) 
(Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) 
(Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) 
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) 
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) 
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h) 
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i) 
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j) 
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k) 
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l) 
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m) 
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n) 
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) 

class Enum a whereSource

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

Methods

succ :: a -> aSource

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

pred :: a -> aSource

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

toEnum :: Int -> aSource

Convert from an Int.

fromEnum :: a -> IntSource

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 whereSource

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.

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 Any 
Bounded All 
Bounded GeneralCategory 
Bounded IntPtr 
Bounded WordPtr 
Bounded Fd 
Bounded CRLim 
Bounded CTcflag 
Bounded CUid 
Bounded CNlink 
Bounded CGid 
Bounded CSsize 
Bounded CPid 
Bounded COff 
Bounded CMode 
Bounded CIno 
Bounded a => Bounded (Product a) 
Bounded a => Bounded (Sum a) 
Bounded a => Bounded (Dual a) 
(Bounded a, Bounded b) => Bounded (a, b) 
(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) 
(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) 

Numbers

Numeric types

data Int Source

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

data Float Source

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

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 IntegerSource

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

Numeric type classes

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

Basic numeric class.

Minimal complete definition: all except negate or (-)

Methods

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

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

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

negate :: a -> aSource

Unary negation.

abs :: a -> aSource

Absolute value.

signum :: a -> aSource

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 -> aSource

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 whereSource

Integral numbers, supporting integer division.

Minimal complete definition: quotRem and toInteger

Methods

quot :: a -> a -> aSource

integer division truncated toward zero

rem :: a -> a -> aSource

integer remainder, satisfying

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

div :: a -> a -> aSource

integer division truncated toward negative infinity

mod :: a -> a -> aSource

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 -> IntegerSource

conversion to Integer

class Num a => Fractional a whereSource

Fractional numbers, supporting real division.

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

Methods

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

fractional division

recip :: a -> aSource

reciprocal fraction

fromRational :: Rational -> aSource

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 whereSource

Trigonometric and hyperbolic functions and related functions.

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

Methods

pi :: aSource

exp :: a -> aSource

sqrt :: a -> aSource

log :: a -> aSource

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

logBase :: a -> a -> aSource

sin :: a -> aSource

tan :: a -> aSource

cos :: a -> aSource

asin :: a -> aSource

atan :: a -> aSource

acos :: a -> aSource

sinh :: a -> aSource

tanh :: a -> aSource

cosh :: a -> aSource

asinh :: a -> aSource

atanh :: a -> aSource

acosh :: a -> aSource

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

Extracting components of fractions.

Minimal complete definition: properFraction

Methods

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

The function properFraction takes a real fractional number x and returns a pair (n,f) such that x = n+f, and:

  • n is an integral number with the same sign as x; and
  • f is a fraction with the same type and sign as x, and with absolute value less than 1.

The default definitions of the ceiling, floor, truncate and round functions are in terms of properFraction.

truncate :: Integral b => a -> bSource

truncate x returns the integer nearest x between zero and x

round :: Integral b => a -> bSource

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

ceiling :: Integral b => a -> bSource

ceiling x returns the least integer not less than x

floor :: Integral b => a -> bSource

floor x returns the greatest integer not greater than x

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

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 -> IntegerSource

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

floatDigits :: a -> IntSource

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

floatRange :: a -> (Int, Int)Source

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

decodeFloat :: a -> (Integer, Int)Source

The function decodeFloat applied to a real floating-point number returns the significand expressed as an Integer and an appropriately scaled exponent (an Int). If decodeFloat x yields (m,n), then x is equal in value to m*b^^n, where b is the floating-point radix, and furthermore, either m and n are both zero or else b^(d-1) <= m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0).

encodeFloat :: Integer -> Int -> aSource

encodeFloat performs the inverse of decodeFloat

exponent :: a -> IntSource

the second component of decodeFloat.

significand :: a -> aSource

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

scaleFloat :: Int -> a -> aSource

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

isNaN :: a -> BoolSource

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

isInfinite :: a -> BoolSource

True if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> BoolSource

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

isNegativeZero :: a -> BoolSource

True if the argument is an IEEE negative zero

isIEEE :: a -> BoolSource

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 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 -> aSource

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 -> BoolSource

odd :: Integral a => a -> BoolSource

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

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 -> aSource

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

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

raise a number to a non-negative integral power

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

raise a number to an integral power

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

general coercion from integral types

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

general coercion to fractional types

Monads and functors

class Monad m whereSource

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

Minimal complete definition: >>= and return.

Instances of Monad should satisfy the following laws:

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

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

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

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

Methods

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

Instances

class Functor f whereSource

The Functor class is used for types that can be mapped over. Instances of Functor should satisfy the following laws:

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

The instances of Functor for lists, Data.Maybe.Maybe and System.IO.IO satisfy these laws.

Methods

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

Instances

Functor [] 
Functor IO 
Functor [::] 
Functor Maybe 
Functor ReadP 
Functor ReadPrec 
Functor STM 
Functor ZipList 
Functor Id 
Functor ((->) r) 
Functor (Either a) 
Functor ((,) a) 
Functor (ST s) 
Ix i => Functor (Array i) 
Monad m => Functor (WrappedMonad m) 
Functor (Const m) 
Functor (StateR s) 
Functor (StateL s) 
Functor (ST s) 
Arrow a => Functor (WrappedArrow a b) 

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

mapM f is equivalent to sequence . map f.

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

mapM_ f is equivalent to sequence_ . map f.

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

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

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

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

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

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

Miscellaneous functions

id :: a -> aSource

Identity function.

const :: a -> b -> aSource

Constant function.

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

Function composition.

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

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 $ x). However, $ has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:

     f $ g $ h x  =  f (g (h x))

It is also useful in higher-order situations, such as map ($ 0) xs, or Data.List.zipWith ($) fs xs.

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

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

asTypeOf :: a -> a -> aSource

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] -> aSource

error stops execution and displays an error message.

undefined :: aSource

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 -> bSource

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.

List operations

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

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

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

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

Append two lists, i.e.,

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

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

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

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

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

head :: [a] -> 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.

null :: [a] -> BoolSource

Test whether a list is empty.

length :: [a] -> IntSource

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

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

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

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

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

Reducing lists (folds)

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

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 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] -> bSource

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

Special folds

and :: [Bool] -> BoolSource

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] -> BoolSource

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] -> BoolSource

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] -> BoolSource

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] -> aSource

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

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

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] -> aSource

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] -> aSource

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

Building lists

Scans

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

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

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

Note that

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

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

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

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

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

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

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

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

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

Infinite lists

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

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

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

repeat :: a -> [a]Source

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

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

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

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

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

Sublists

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Searching lists

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

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] -> BoolSource

notElem is the negation of elem.

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

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] -> StringSource

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

unwords :: [String] -> StringSource

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

Converting to and from String

Converting to String

type ShowS = String -> StringSource

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 whereSource

Conversion of values to readable Strings.

Minimal complete definition: showsPrec or show.

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

  • The result of show is a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used.
  • If the constructor is defined to be an infix operator, then showsPrec will produce infix applications of the constructor.
  • the representation will be enclosed in parentheses if the precedence of the top-level constructor in x is less than d (associativity is ignored). Thus, if d is 0 then the result is never surrounded in parentheses; if d is 11 it is always surrounded in parentheses, unless it is an atomic expression.
  • If the constructor is defined using record syntax, then show will produce the record-syntax form, with the fields given in the same order as the original declaration.

For example, given the declarations

 infixr 5 :^:
 data Tree a =  Leaf a  |  Tree a :^: Tree a

the derived instance of Show is equivalent to

 instance (Show a) => Show (Tree a) where

        showsPrec d (Leaf m) = showParen (d > app_prec) $
             showString "Leaf " . showsPrec (app_prec+1) m
          where app_prec = 10

        showsPrec d (u :^: v) = showParen (d > up_prec) $
             showsPrec (up_prec+1) u . 
             showString " :^: "      .
             showsPrec (up_prec+1) v
          where up_prec = 5

Note that right-associativity of :^: is ignored. For example,

  • show (Leaf 1 :^: Leaf 2 :^: Leaf 3) produces the string "Leaf 1 :^: (Leaf 2 :^: Leaf 3)".

Methods

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.

showsPrec should satisfy the law

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

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

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

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

show :: a -> StringSource

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

showList :: [a] -> ShowSSource

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 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 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 Any 
Show All 
Show GeneralCategory 
Show HashData 
Show Dynamic 
Show IntPtr 
Show WordPtr 
Show TextEncoding 
Show NewlineMode 
Show Newline 
Show BufferMode 
Show HandleType 
Show Handle 
Show IOErrorType 
Show ExitCode 
Show ArrayException 
Show AsyncException 
Show AssertionFailed 
Show Deadlock 
Show BlockedIndefinitelyOnSTM 
Show BlockedIndefinitelyOnMVar 
Show BlockedIndefinitely 
Show BlockedOnDeadMVar 
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 Control 
Show ControlMessage 
Show Timeout 
Show Event 
Show EventType 
Show Event 
Show EPollFd 
Show Unique 
Show State 
Show IOCallback 
Show FdKey 
Show FdData 
Show FD 
Show HandlePosn 
Show Fixity 
Show ConstrRep 
Show DataRep 
Show Constr 
Show DataType 
Show Timeout 
Show Version 
Show Exception 
Show Event 
Show PollFd 
Show a => Show [a] 
Integral a => Show (Ratio a) 
Show (Ptr a) 
Show (FunPtr a) 
Show a => Show ([::] a) 
Show a => Show (Maybe a) 
Show 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 (ForeignPtr a) 
Show a => Show (IntMap a) 
Show a => Show (Sequ a) 
Show a => Show (LTree a) 
Show a => Show (PSQ a) 
Show a => Show (Elem a) 
RealFloat a => Show (Complex a) 
HasResolution a => Show (Fixed a) 
Show (a -> b) 
(Show a, Show b) => Show (Either a b) 
(Show a, Show b) => Show (a, b) 
Show (ST s a) 
(Ix a, Show a, Show b) => Show (Array a b) 
(Show a, Show b, Show c) => Show (a, b, c) 
(Show a, Show b, Show c, Show d) => Show (a, b, c, d) 
(Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e) 
(Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f) 
(Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g) 
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h) => Show (a, b, c, d, e, f, g, h) 
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i) => Show (a, b, c, d, e, f, g, h, i) 
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j) => Show (a, b, c, d, e, f, g, h, i, j) 
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k) => Show (a, b, c, d, e, f, g, h, i, j, k) 
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l) => Show (a, b, c, d, e, f, g, h, i, j, k, l) 
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m) 
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n) 
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n, Show o) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) 

shows :: Show a => a -> ShowSSource

equivalent to showsPrec with a precedence of 0.

showChar :: Char -> ShowSSource

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

showString :: String -> ShowSSource

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

showParen :: Bool -> ShowS -> ShowSSource

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 whereSource

Parsing of Strings, producing values.

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

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

  • If the constructor is defined to be an infix operator, then the derived Read instance will parse only infix applications of the constructor (not the prefix form).
  • Associativity is not used to reduce the occurrence of parentheses, although precedence may be.
  • If the constructor is defined using record syntax, the derived Read will parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration.
  • The derived Read instance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.

For example, given the declarations

 infixr 5 :^:
 data Tree a =  Leaf a  |  Tree a :^: Tree a

the derived instance of Read in Haskell 98 is equivalent to

 instance (Read a) => Read (Tree a) where

         readsPrec d r =  readParen (d > app_prec)
                          (\r -> [(Leaf m,t) |
                                  ("Leaf",s) <- lex r,
                                  (m,t) <- readsPrec (app_prec+1) s]) r

                       ++ readParen (d > up_prec)
                          (\r -> [(u:^:v,w) |
                                  (u,s) <- readsPrec (up_prec+1) r,
                                  (":^:",t) <- lex s,
                                  (v,w) <- readsPrec (up_prec+1) t]) r

           where app_prec = 10
                 up_prec = 5

Note that right-associativity of :^: is unused.

The derived instance in GHC is equivalent to

 instance (Read a) => Read (Tree a) where

         readPrec = parens $ (prec app_prec $ do
                                  Ident "Leaf" <- lexP
                                  m <- step readPrec
                                  return (Leaf m))

                      +++ (prec up_prec $ do
                                  u <- step readPrec
                                  Symbol ":^:" <- lexP
                                  v <- step readPrec
                                  return (u :^: v))

           where app_prec = 10
                 up_prec = 5

         readListPrec = readListPrecDefault

Methods

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 and Text.Show.Show satisfy the following:

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

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

readList :: ReadS [a]Source

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

Instances

Read 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 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 Any 
Read All 
Read GeneralCategory 
Read IntPtr 
Read WordPtr 
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 Version 
Read a => Read [a] 
(Integral a, Read a) => Read (Ratio a) 
Read a => Read ([::] a) 
Read a => Read (Maybe a) 
Read a => Read (Last a) 
Read a => Read (First a) 
Read a => Read (Product a) 
Read a => Read (Sum a) 
Read a => Read (Dual a) 
(Read a, RealFloat a) => Read (Complex a) 
(Read a, Read b) => Read (Either a b) 
(Read a, Read b) => Read (a, b) 
(Ix a, Read a, Read b) => Read (Array a b) 
(Read a, Read b, Read c) => Read (a, b, c) 
(Read a, Read b, Read c, Read d) => Read (a, b, c, d) 
(Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) 
(Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) 
(Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) 
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h) 
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i) 
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j) 
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k) 
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l) 
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) 
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) 
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) 

reads :: Read a => ReadS aSource

equivalent to readsPrec with a precedence of 0.

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

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 -> aSource

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

lex :: ReadS StringSource

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

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

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

Basic Input and output

data IO a Source

A value of type IO a is a computation which, when performed, does some I/O before returning a value of type a.

There is really only one way to "perform" an I/O action: bind it to Main.main in your program. When your program is run, the I/O will be performed. It isn't possible to perform I/O from an arbitrary function, unless that function is itself in the IO monad and called at some point, directly or indirectly, from Main.main.

IO is a monad, so IO actions can be combined using either the do-notation or the >> and >>= operations from the Monad class.

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 CharSource

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

getLine :: IO StringSource

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

getContents :: IO StringSource

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 = StringSource

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 StringSource

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 aSource

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 aSource

The readLn function combines getLine and readIO.

Exception handling in the I/O monad

type IOError = IOExceptionSource

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

In Haskell 98, this is an opaque type.

ioError :: IOError -> IO aSource

Raise an IOError in the IO monad.

userError :: String -> IOErrorSource

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 aSource

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

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

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

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

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