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base-4.4.0.0: Basic libraries

Portabilityportable
Stabilitystable
Maintainerlibraries@haskell.org

Prelude

Contents

Description

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

Synopsis

Standard types, classes and related functions

Basic data types

dataBoolSource

Constructors

False 
True 

Instances

BoundedBool 
EnumBool 
EqBool 
DataBool 
OrdBool 
ReadBool 
ShowBool 
IxBool 
TypeableBool 
GenericBool 
StorableBool 

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

Boolean "and"

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

Boolean "or"

not ::Bool ->BoolSource

Boolean "not"

otherwise ::BoolSource

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

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

dataMaybe aSource

TheMaybe type encapsulates an optional value. A value of typeMaybe a either contains a value of typea (represented asJust a), or it is empty (represented asNothing). UsingMaybe is a good way to deal with errors or exceptional cases without resorting to drastic measures such aserror.

TheMaybe type is also a monad. It is a simple kind of error monad, where all errors are represented byNothing. A richer error monad can be built using theData.Either.Either type.

Constructors

Nothing 
Just a 

Instances

MonadMaybe 
FunctorMaybe 
Typeable1Maybe 
MonadFixMaybe 
MonadPlusMaybe 
ApplicativeMaybe 
FoldableMaybe 
TraversableMaybe 
AlternativeMaybe 
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) 
Generic (Maybe a) 
Monoid a =>Monoid (Maybe a)

Lift a semigroup intoMaybe forming aMonoid according tohttp://en.wikipedia.org/wiki/Monoid: "Any semigroupS may be turned into a monoid simply by adjoining an elemente not inS and defininge*e = e ande*s = s = s*e for alls  S." Since there is no "Semigroup" typeclass providing justmappend, we useMonoid instead.

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

Themaybe function takes a default value, a function, and aMaybe value. If theMaybe value isNothing, the function returns the default value. Otherwise, it applies the function to the value inside theJust and returns the result.

dataEither a bSource

TheEither type represents values with two possibilities: a value oftypeEither a b is eitherLeft a orRight b.

TheEither type is sometimes used to represent a value which iseither correct or an error; by convention, theLeft constructor isused to hold an error value and theRight constructor is used tohold a correct value (mnemonic: "right" also means "correct").

Constructors

Left a 
Right b 

Instances

Typeable2Either 
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) 
Generic (Either a b) 

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

Case analysis for theEither type. If the value isLeft a, apply the first function toa; if it isRight b, apply the second function tob.

dataOrderingSource

Constructors

LT 
EQ 
GT 

Instances

BoundedOrdering 
EnumOrdering 
EqOrdering 
DataOrdering 
OrdOrdering 
ReadOrdering 
ShowOrdering 
IxOrdering 
TypeableOrdering 
GenericOrdering 
MonoidOrdering 

dataCharSource

The character typeChar is an enumeration whose values representUnicode (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 charachers), which is itself an extension of the ASCIIcharacter set (the first 128 characters).A character literal in Haskell has typeChar.

To convert aChar to or from the correspondingInt value definedby Unicode, usePrelude.toEnum andPrelude.fromEnum from thePrelude.Enum class respectively (or equivalentlyord andchr).

Instances

BoundedChar 
EnumChar 
EqChar 
DataChar 
OrdChar 
ReadChar 
ShowChar 
IxChar 
TypeableChar 
GenericChar 
StorableChar 
IsCharChar 
PrintfArgChar 
IsString [Char] 

typeString = [Char]Source

AString is a list of characters. String constants in Haskell are values of typeString.

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

classEq awhereSource

TheEq class defines equality (==) and inequality (/=). All the basic datatypes exported by thePrelude are instances ofEq, andEq may be derived for any datatype whose constituents are also instances ofEq.

Minimal complete definition: either== or/=.

Methods

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

Instances

EqBool 
EqChar 
EqDouble 
EqFloat 
EqInt 
EqInt8 
EqInt16 
EqInt32 
EqInt64 
EqInteger 
EqOrdering 
EqWord 
EqWord8 
EqWord16 
EqWord32 
EqWord64 
Eq () 
EqArity 
EqFixity 
EqAssociativity 
EqTyCon 
EqTypeRep 
EqArithException 
EqIOException 
EqMaskingState 
EqLexeme 
EqFingerprint 
EqIOMode 
EqSeekMode 
EqIODeviceType 
EqCUIntMax 
EqCIntMax 
EqCUIntPtr 
EqCIntPtr 
EqCSUSeconds 
EqCUSeconds 
EqCTime 
EqCClock 
EqCSigAtomic 
EqCWchar 
EqCSize 
EqCPtrdiff 
EqCDouble 
EqCFloat 
EqCULLong 
EqCLLong 
EqCULong 
EqCLong 
EqCUInt 
EqCInt 
EqCUShort 
EqCShort 
EqCUChar 
EqCSChar 
EqCChar 
EqAny 
EqAll 
EqGeneralCategory 
EqTypeRepKey 
Eq Finalizers 
EqIntPtr 
EqWordPtr 
Eq Inserts 
Eq HashData 
EqBufferState 
EqCodingProgress 
EqNewlineMode 
EqNewline 
EqBufferMode 
EqHandle 
EqIOErrorType 
EqExitCode 
EqArrayException 
EqAsyncException 
EqErrno 
EqThreadStatus 
EqBlockReason 
EqThreadId 
EqFd 
EqCRLim 
EqCTcflag 
EqCSpeed 
EqCCc 
EqCUid 
EqCNlink 
EqCGid 
EqCSsize 
EqCPid 
EqCOff 
EqCMode 
EqCIno 
EqCDev 
Eq ControlMessage 
EqEvent 
Eq EventType 
Eq EPollFd 
Eq Unique 
Eq State 
EqTimeoutKey 
EqFdKey 
EqHandlePosn 
EqFixity 
EqConstrRep 
EqDataRep 
EqConstr

Equality of constructors

EqSpecConstrAnnotation 
EqUnique 
EqQSem 
EqQSemN 
Eq Timeout 
EqVersion 
EqException 
Eq Event 
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 (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 (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) 
(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) 

classEq a =>Ord awhereSource

TheOrd class is used for totally ordered datatypes.

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

Minimal complete definition: eithercompare or<=. Usingcompare can be more efficient for complex types.

Methods

compare :: a -> a ->OrderingSource

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

max,min :: a -> a -> aSource

Instances

OrdBool 
OrdChar 
OrdDouble 
OrdFloat 
OrdInt 
OrdInt8 
OrdInt16 
OrdInt32 
OrdInt64 
OrdInteger 
OrdOrdering 
OrdWord 
OrdWord8 
OrdWord16 
OrdWord32 
OrdWord64 
Ord () 
OrdArity 
OrdFixity 
OrdAssociativity 
OrdTyCon 
OrdTypeRep 
OrdArithException 
OrdFingerprint 
OrdIOMode 
OrdSeekMode 
OrdCUIntMax 
OrdCIntMax 
OrdCUIntPtr 
OrdCIntPtr 
OrdCSUSeconds 
OrdCUSeconds 
OrdCTime 
OrdCClock 
OrdCSigAtomic 
OrdCWchar 
OrdCSize 
OrdCPtrdiff 
OrdCDouble 
OrdCFloat 
OrdCULLong 
OrdCLLong 
OrdCULong 
OrdCLong 
OrdCUInt 
OrdCInt 
OrdCUShort 
OrdCShort 
OrdCUChar 
OrdCSChar 
OrdCChar 
OrdAny 
OrdAll 
OrdGeneralCategory 
OrdTypeRepKey 
OrdIntPtr 
OrdWordPtr 
OrdNewlineMode 
OrdNewline 
OrdBufferMode 
OrdExitCode 
OrdArrayException 
OrdAsyncException 
OrdThreadStatus 
OrdBlockReason 
OrdThreadId 
OrdFd 
OrdCRLim 
OrdCTcflag 
OrdCSpeed 
OrdCCc 
OrdCUid 
OrdCNlink 
OrdCGid 
OrdCSsize 
OrdCPid 
OrdCOff 
OrdCMode 
OrdCIno 
OrdCDev 
Ord Unique 
OrdUnique 
OrdVersion 
Ord a =>Ord [a] 
Integral a =>Ord (Ratio a) 
Ord (Ptr a) 
Ord (FunPtr 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) 

classEnum awhereSource

ClassEnum defines operations on sequentially ordered types.

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

Instances ofEnum may be derived for any enumeration type (types whose constructors have no fields). The nullary constructors are assumed to be numbered left-to-right byfromEnum from0 throughn-1. See Chapter 10 of theHaskell Report for more details.

For any type that is an instance of classBounded as well asEnum, 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 anInt.

fromEnum :: a ->IntSource

Convert to anInt. It is implementation-dependent whatfromEnum returns when applied to a value that is too large to fit in anInt.

enumFrom :: a -> [a]Source

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

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

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

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

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

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

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

Instances

EnumBool 
EnumChar 
EnumDouble 
EnumFloat 
EnumInt 
EnumInt8 
EnumInt16 
EnumInt32 
EnumInt64 
EnumInteger 
EnumOrdering 
EnumWord 
EnumWord8 
EnumWord16 
EnumWord32 
EnumWord64 
Enum () 
EnumIOMode 
EnumSeekMode 
EnumCUIntMax 
EnumCIntMax 
EnumCUIntPtr 
EnumCIntPtr 
EnumCSUSeconds 
EnumCUSeconds 
EnumCTime 
EnumCClock 
EnumCSigAtomic 
EnumCWchar 
EnumCSize 
EnumCPtrdiff 
EnumCDouble 
EnumCFloat 
EnumCULLong 
EnumCLLong 
EnumCULong 
EnumCLong 
EnumCUInt 
EnumCInt 
EnumCUShort 
EnumCShort 
EnumCUChar 
EnumCSChar 
EnumCChar 
EnumGeneralCategory 
EnumIntPtr 
EnumWordPtr 
EnumFd 
EnumCRLim 
EnumCTcflag 
EnumCSpeed 
EnumCCc 
EnumCUid 
EnumCNlink 
EnumCGid 
EnumCSsize 
EnumCPid 
EnumCOff 
EnumCMode 
EnumCIno 
EnumCDev 
Integral a =>Enum (Ratio a) 
Enum (Fixed a) 

classBounded awhereSource

TheBounded class is used to name the upper and lower limits of a type.Ord is not a superclass ofBounded since types that are not totally ordered may also have upper and lower bounds.

TheBounded class may be derived for any enumeration type;minBound is the first constructor listed in thedata declaration andmaxBound is the last.Bounded may also be derived for single-constructor datatypes whose constituent types are inBounded.

Methods

minBound,maxBound :: aSource

Instances

BoundedBool 
BoundedChar 
BoundedInt 
BoundedInt8 
BoundedInt16 
BoundedInt32 
BoundedInt64 
BoundedOrdering 
BoundedWord 
BoundedWord8 
BoundedWord16 
BoundedWord32 
BoundedWord64 
Bounded () 
BoundedCUIntMax 
BoundedCIntMax 
BoundedCUIntPtr 
BoundedCIntPtr 
BoundedCSigAtomic 
BoundedCWchar 
BoundedCSize 
BoundedCPtrdiff 
BoundedCULLong 
BoundedCLLong 
BoundedCULong 
BoundedCLong 
BoundedCUInt 
BoundedCInt 
BoundedCUShort 
BoundedCShort 
BoundedCUChar 
BoundedCSChar 
BoundedCChar 
BoundedAny 
BoundedAll 
BoundedGeneralCategory 
BoundedIntPtr 
BoundedWordPtr 
BoundedFd 
BoundedCRLim 
BoundedCTcflag 
BoundedCUid 
BoundedCNlink 
BoundedCGid 
BoundedCSsize 
BoundedCPid 
BoundedCOff 
BoundedCMode 
BoundedCIno 
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

dataIntSource

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 usingPrelude.minBound andPrelude.maxBound from thePrelude.Bounded class.

Instances

BoundedInt 
EnumInt 
EqInt 
IntegralInt 
DataInt 
NumInt 
OrdInt 
ReadInt 
RealInt 
ShowInt 
IxInt 
TypeableInt 
GenericInt 
BitsInt 
StorableInt 
PrintfArgInt 

dataIntegerSource

Arbitrary-precision integers.

Instances

EnumInteger 
EqInteger 
IntegralInteger 
DataInteger 
NumInteger 
OrdInteger 
ReadInteger 
RealInteger 
ShowInteger 
IxInteger 
TypeableInteger 
BitsInteger 
PrintfArgInteger 

dataFloatSource

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

Instances

EnumFloat 
EqFloat 
FloatingFloat 
FractionalFloat 
DataFloat 
NumFloat 
OrdFloat 
ReadFloat 
RealFloat 
RealFloatFloat 
RealFracFloat 
ShowFloat 
TypeableFloat 
GenericFloat 
StorableFloat 
PrintfArgFloat 

dataDoubleSource

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

Instances

EnumDouble 
EqDouble 
FloatingDouble 
FractionalDouble 
DataDouble 
NumDouble 
OrdDouble 
ReadDouble 
RealDouble 
RealFloatDouble 
RealFracDouble 
ShowDouble 
TypeableDouble 
GenericDouble 
StorableDouble 
PrintfArgDouble 

typeRational =RatioIntegerSource

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

Numeric type classes

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

Basic numeric class.

Minimal complete definition: all exceptnegate or(-)

Methods

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

negate :: a -> aSource

Unary negation.

abs :: a -> aSource

Absolute value.

signum :: a -> aSource

Sign of a number. The functionsabs andsignum should satisfy the law:

 abs x * signum x == x

For real numbers, thesignum is either-1 (negative),0 (zero) or1 (positive).

fromInteger ::Integer -> aSource

Conversion from anInteger. An integer literal represents the application of the functionfromInteger to the appropriate value of typeInteger, so such literals have type(Num a) => a.

Instances

NumDouble 
NumFloat 
NumInt 
NumInt8 
NumInt16 
NumInt32 
NumInt64 
NumInteger 
NumWord 
NumWord8 
NumWord16 
NumWord32 
NumWord64 
NumCUIntMax 
NumCIntMax 
NumCUIntPtr 
NumCIntPtr 
NumCSUSeconds 
NumCUSeconds 
NumCTime 
NumCClock 
NumCSigAtomic 
NumCWchar 
NumCSize 
NumCPtrdiff 
NumCDouble 
NumCFloat 
NumCULLong 
NumCLLong 
NumCULong 
NumCLong 
NumCUInt 
NumCInt 
NumCUShort 
NumCShort 
NumCUChar 
NumCSChar 
NumCChar 
NumIntPtr 
NumWordPtr 
NumFd 
NumCRLim 
NumCTcflag 
NumCSpeed 
NumCCc 
NumCUid 
NumCNlink 
NumCGid 
NumCSsize 
NumCPid 
NumCOff 
NumCMode 
NumCIno 
NumCDev 
Num EventType 
Num Unique 
Num Event 
Integral a =>Num (Ratio a) 
RealFloat a =>Num (Complex a) 
HasResolution a =>Num (Fixed a) 

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

Methods

toRational :: a ->RationalSource

the rational equivalent of its real argument with full precision

Instances

RealDouble 
RealFloat 
RealInt 
RealInt8 
RealInt16 
RealInt32 
RealInt64 
RealInteger 
RealWord 
RealWord8 
RealWord16 
RealWord32 
RealWord64 
RealCUIntMax 
RealCIntMax 
RealCUIntPtr 
RealCIntPtr 
RealCSUSeconds 
RealCUSeconds 
RealCTime 
RealCClock 
RealCSigAtomic 
RealCWchar 
RealCSize 
RealCPtrdiff 
RealCDouble 
RealCFloat 
RealCULLong 
RealCLLong 
RealCULong 
RealCLong 
RealCUInt 
RealCInt 
RealCUShort 
RealCShort 
RealCUChar 
RealCSChar 
RealCChar 
RealIntPtr 
RealWordPtr 
RealFd 
RealCRLim 
RealCTcflag 
RealCSpeed 
RealCCc 
RealCUid 
RealCNlink 
RealCGid 
RealCSsize 
RealCPid 
RealCOff 
RealCMode 
RealCIno 
RealCDev 
Integral a =>Real (Ratio a) 
HasResolution a =>Real (Fixed a) 

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

Integral numbers, supporting integer division.

Minimal complete definition:quotRem andtoInteger

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

simultaneousquot andrem

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

simultaneousdiv andmod

toInteger :: a ->IntegerSource

conversion toInteger

Instances

IntegralInt 
IntegralInt8 
IntegralInt16 
IntegralInt32 
IntegralInt64 
IntegralInteger 
IntegralWord 
IntegralWord8 
IntegralWord16 
IntegralWord32 
IntegralWord64 
IntegralCUIntMax 
IntegralCIntMax 
IntegralCUIntPtr 
IntegralCIntPtr 
IntegralCSigAtomic 
IntegralCWchar 
IntegralCSize 
IntegralCPtrdiff 
IntegralCULLong 
IntegralCLLong 
IntegralCULong 
IntegralCLong 
IntegralCUInt 
IntegralCInt 
IntegralCUShort 
IntegralCShort 
IntegralCUChar 
IntegralCSChar 
IntegralCChar 
IntegralIntPtr 
IntegralWordPtr 
IntegralFd 
IntegralCRLim 
IntegralCTcflag 
IntegralCUid 
IntegralCNlink 
IntegralCGid 
IntegralCSsize 
IntegralCPid 
IntegralCOff 
IntegralCMode 
IntegralCIno 

classNum a =>Fractional awhereSource

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 aRational (that isRatioInteger). A floating literal stands for an application offromRational to a value of typeRational, so such literals have type(Fractional a) => a.

Instances

FractionalDouble 
FractionalFloat 
FractionalCDouble 
FractionalCFloat 
Integral a =>Fractional (Ratio a) 
RealFloat a =>Fractional (Complex a) 
HasResolution a =>Fractional (Fixed a) 

classFractional a =>Floating awhereSource

Trigonometric and hyperbolic functions and related functions.

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

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

Instances

FloatingDouble 
FloatingFloat 
FloatingCDouble 
FloatingCFloat 
RealFloat a =>Floating (Complex a) 

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

Extracting components of fractions.

Minimal complete definition:properFraction

Methods

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

The functionproperFraction takes a real fractional numberx and returns a pair(n,f) such thatx = n+f, and:

  • n is an integral number with the same sign asx; and
  • f is a fraction with the same type and sign asx, and with absolute value less than1.

The default definitions of theceiling,floor,truncate andround functions are in terms ofproperFraction.

truncate ::Integral b => a -> bSource

truncate x returns the integer nearestx between zero andx

round ::Integral b => a -> bSource

round x returns the nearest integer tox; the even integer ifx is equidistant between two integers

ceiling ::Integral b => a -> bSource

ceiling x returns the least integer not less thanx

floor ::Integral b => a -> bSource

floor x returns the greatest integer not greater thanx

Instances

RealFracDouble 
RealFracFloat 
RealFracCDouble 
RealFracCFloat 
Integral a =>RealFrac (Ratio a) 
HasResolution a =>RealFrac (Fixed a) 

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

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

Minimal complete definition: all exceptexponent,significand,scaleFloat andatan2

Methods

floatRadix :: a ->IntegerSource

a constant function, returning the radix of the representation (often2)

floatDigits :: a ->IntSource

a constant function, returning the number of digits offloatRadix 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 functiondecodeFloat applied to a real floating-point number returns the significand expressed as anInteger and an appropriately scaled exponent (anInt). IfdecodeFloat x yields(m,n), thenx is equal in value tom*b^^n, whereb is the floating-point radix, and furthermore, eitherm andn are both zero or elseb^(d-1) <= m < b^d, whered is the value offloatDigits x. In particular,decodeFloat 0 = (0,0).

encodeFloat ::Integer ->Int -> aSource

encodeFloat performs the inverse ofdecodeFloat

exponent :: a ->IntSource

the second component ofdecodeFloat.

significand :: a -> aSource

the first component ofdecodeFloat, 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 floatingx andy,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, withy in a type that isRealFloat, should return the same value asatan y. A default definition ofatan2 is provided, but implementors can provide a more accurate implementation.

Instances

RealFloatDouble 
RealFloatFloat 
RealFloatCDouble 
RealFloatCFloat 

Numeric functions

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

the same asflip (-).

Because- is treated specially in the Haskell grammar,(-e) is not a section, but an application of prefix negation. However,(subtractexp) is equivalent to the disallowed section.

even,odd ::Integral a => a ->BoolSource

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

gcd x y is the non-negative factor of bothx andy of which every common factor ofx andy is also a factor; for examplegcd 4 2 = 2,gcd (-4) 6 = 2,gcd 0 4 =4.gcd 0 0 =0. (That is, the common divisor that is "greatest" in the divisibility preordering.)

Note: Since for signed fixed-width integer types,absminBound < 0, the result may be negative if one of the arguments isminBound (and necessarily is if the other is0 orminBound) for such types.

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

lcm x y is the smallest positive integer that bothx andy 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

classMonad mwhereSource

TheMonad class defines the basic operations over amonad,a concept from a branch of mathematics known ascategory theory.From the perspective of a Haskell programmer, however, it is best tothink of a monad as anabstract datatype of actions.Haskell'sdo expressions provide a convenient syntax for writingmonadic expressions.

Minimal complete definition:>>= andreturn.

Instances ofMonad should satisfy the following laws:

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

Instances of bothMonad andFunctor should additionally satisfy the law:

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

The instances ofMonad for lists,Data.Maybe.Maybe andSystem.IO.IOdefined in thePrelude 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 ado expression.

Instances

Monad [] 
MonadIO 
MonadMaybe 
MonadReadP 
Monad P 
MonadReadPrec 
MonadSTM 
Monad ((->) r) 
Monad (Either e) 
Monad (ST s) 
ArrowApply a =>Monad (ArrowMonad a) 
Monad (ST s) 

classFunctor fwhereSource

TheFunctor class is used for types that can be mapped over.Instances ofFunctor should satisfy the following laws:

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

The instances ofFunctor for lists,Data.Maybe.Maybe andSystem.IO.IOsatisfy these laws.

Methods

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

Instances

Functor [] 
FunctorIO 
FunctorMaybe 
FunctorReadP 
FunctorReadPrec 
FunctorSTM 
FunctorZipList 
Functor Id 
Functor ((->) r) 
Functor (Either a) 
Functor ((,) a) 
Functor (ST s) 
Ix i =>Functor (Array i) 
Functor (ST s) 
Monad m =>Functor (WrappedMonad m) 
Functor (Const m) 
Functor (StateR s) 
Functor (StateL s) 
Arrow a =>Functor (WrappedArrow a b) 

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

mapM f is equivalent tosequence .map f.

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

mapM_ f is equivalent tosequence_ .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 off.

($) :: (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 asmap ($ 0) xs, orData.List.zipWith ($) fs xs.

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

until p f yields the result of applyingf untilp holds.

asTypeOf :: a -> a -> aSource

asTypeOf is a type-restricted version ofconst. 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 oferror. It is expected that compilers will recognize this and insert error messages which are more appropriate to the context in whichundefined 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 ofseq.

List operations

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

mapf xs is the list obtained by applyingf to each element ofxs, 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 anInt. It is an instance of the more generalData.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 generalData.List.genericIndex, which takes an index of any integral type.

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

reversexs returns the elements ofxs 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 offoldl 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 offoldr 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 beTrue, the list must be finite;False, however, results from aFalse 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 beFalse, the list must be finite;True, however, results from aTrue 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 beFalse, the list must be finite;True, however, results from aTrue 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 beTrue, the list must be finite;False, however, results from aFalse value for the predicate applied to an element at a finite index of a finite or infinite list.

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

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

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

Theproduct 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 ofmaximumBy, 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 ofminimumBy, which allows the programmer to supply their own comparison function.

Building lists

Scans

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

scanl is similar tofoldl, 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 ofscanl 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 ofscanl. Note that

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

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

scanr1 is a variant ofscanr that has no starting value argument.

Infinite lists

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

iteratef x returns an infinite list of repeated applications off tox:

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

repeat :: a -> [a]Source

repeatx is an infinite list, withx the value of every element.

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

replicaten x is a list of lengthn withx the value of every element. It is an instance of the more generalData.List.genericReplicate, in whichn 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

taken, applied to a listxs, returns the prefix ofxs of lengthn, orxs itself ifn >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 generalData.List.genericTake, in whichn may be of any integral type.

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

dropn xs returns the suffix ofxs after the firstn elements, or[] ifn >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 generalData.List.genericDrop, in whichn may be of any integral type.

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

splitAtn xs returns a tuple where first element isxs prefix of lengthn 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) whenn is not_|_ (splitAt _|_ xs = _|_).splitAt is an instance of the more generalData.List.genericSplitAt, in whichn may be of any integral type.

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

takeWhile, applied to a predicatep and a listxs, returns the longest prefix (possibly empty) ofxs of elements that satisfyp:

 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

dropWhilep xs returns the suffix remaining aftertakeWhilep 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 predicatep and a listxs, returns a tuple where first element is longest prefix (possibly empty) ofxs of elements that satisfyp 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])

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

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

break, applied to a predicatep and a listxs, returns a tuple where first element is longest prefix (possibly empty) ofxs of elements thatdo not satisfyp 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],[])

breakp is equivalent tospan (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 beFalse, the list must be finite;True, however, results from an element equal tox found at a finite index of a finite or infinite list.

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

notElem is the negation ofelem.

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

lookupkey 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 tozip.

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

zipWith generaliseszip 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

ThezipWith3 function takes a function which combines three elements, as well as three lists and returns a list of their point-wise combination, analogous tozipWith.

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

Theunzip3 function takes a list of triples and returns three lists, analogous tounzip.

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 tolines. It joins lines, after appending a terminating newline to each.

unwords :: [String] ->StringSource

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

Converting to and fromString

Converting toString

typeShowS =String ->StringSource

Theshows functions return a function that prepends the outputString to an existingString. This allows constant-time concatenation of results using function composition.

classShow awhereSource

Conversion of values to readableStrings.

Minimal complete definition:showsPrec orshow.

Derived instances ofShow have the following properties, which are compatible with derived instances ofText.Read.Read:

  • The result ofshow 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, thenshowsPrec will produce infix applications of the constructor.
  • the representation will be enclosed in parentheses if the precedence of the top-level constructor inx is less thand (associativity is ignored). Thus, ifd is0 then the result is never surrounded in parentheses; ifd is11 it is always surrounded in parentheses, unless it is an atomic expression.
  • If the constructor is defined using record syntax, thenshow 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 ofShow 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 from0 to11). Function application has precedence10.

-> a

the value to be converted to aString

->ShowS 

Convert a value to a readableString.

showsPrec should satisfy the law

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

Derived instances ofText.Read.Read andShow satisfy the following:

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

That is,Text.Read.readsPrec parses the string produced byshowsPrec, and delivers the value thatshowsPrec started with.

show :: a ->StringSource

A specialised variant ofshowsPrec, using precedence context zero, and returning an ordinaryString.

showList :: [a] ->ShowSSource

The methodshowList is provided to allow the programmer to give a specialised way of showing lists of values. For example, this is used by the predefinedShow instance of theChar type, where values of typeString should be shown in double quotes, rather than between square brackets.

Instances

ShowBool 
ShowChar 
ShowDouble 
ShowFloat 
ShowInt 
ShowInt8 
ShowInt16 
ShowInt32 
ShowInt64 
ShowInteger 
ShowOrdering 
ShowWord 
ShowWord8 
ShowWord16 
ShowWord32 
ShowWord64 
Show () 
ShowArity 
ShowFixity 
ShowAssociativity 
ShowTyCon 
ShowTypeRep 
ShowArithException 
ShowErrorCall 
ShowSomeException 
ShowIOException 
ShowMaskingState 
ShowLexeme 
ShowIOMode 
ShowSeekMode 
ShowCUIntMax 
ShowCIntMax 
ShowCUIntPtr 
ShowCIntPtr 
ShowCSUSeconds 
ShowCUSeconds 
ShowCTime 
ShowCClock 
ShowCSigAtomic 
ShowCWchar 
ShowCSize 
ShowCPtrdiff 
ShowCDouble 
ShowCFloat 
ShowCULLong 
ShowCLLong 
ShowCULong 
ShowCLong 
ShowCUInt 
ShowCInt 
ShowCUShort 
ShowCShort 
ShowCUChar 
ShowCSChar 
ShowCChar 
ShowAny 
ShowAll 
ShowGeneralCategory 
ShowDynamic 
ShowIntPtr 
ShowWordPtr 
Show HashData 
ShowCodingProgress 
ShowTextEncoding 
ShowNewlineMode 
ShowNewline 
ShowBufferMode 
Show HandleType 
ShowHandle 
ShowIOErrorType 
ShowExitCode 
ShowArrayException 
ShowAsyncException 
ShowAssertionFailed 
ShowDeadlock 
ShowBlockedIndefinitelyOnSTM 
ShowBlockedIndefinitelyOnMVar 
ShowCodingFailureMode 
ShowThreadStatus 
ShowBlockReason 
ShowThreadId 
ShowNestedAtomically 
ShowNonTermination 
ShowNoMethodError 
ShowRecUpdError 
ShowRecConError 
ShowRecSelError 
ShowPatternMatchFail 
ShowFd 
ShowCRLim 
ShowCTcflag 
ShowCSpeed 
ShowCCc 
ShowCUid 
ShowCNlink 
ShowCGid 
ShowCSsize 
ShowCPid 
ShowCOff 
ShowCMode 
ShowCIno 
ShowCDev 
Show Control 
Show ControlMessage 
Show Timeout 
ShowEvent 
Show EventType 
Show Event 
Show EPollFd 
Show Unique 
Show State 
ShowFdKey 
Show FD 
ShowHandlePosn 
ShowFixity 
ShowConstrRep 
ShowDataRep 
ShowConstr 
ShowDataType 
Show BlockedIndefinitely 
Show BlockedOnDeadMVar 
Show Timeout 
ShowVersion 
ShowException 
Show Event 
Show PollFd 
Show a =>Show [a] 
Integral a =>Show (Ratio a) 
Show (Ptr a) 
Show (FunPtr 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) 
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) 
(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 toshowsPrec with a precedence of 0.

showChar ::Char ->ShowSSource

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

showString ::String ->ShowSSource

utility function converting aString 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 theBool parameter isTrue.

Converting fromString

typeReadS a =String -> [(a,String)]Source

A parser for a typea, represented as a function that takes aString 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 (cfReadP).

classRead awhereSource

Parsing ofStrings, producing values.

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

Derived instances ofRead make the following assumptions, which derived instances ofText.Show.Show obey:

  • If the constructor is defined to be an infix operator, then the derivedRead 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 derivedRead will parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration.
  • The derivedRead 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 ofRead 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 from0 to11). Function application has precedence10.

->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 ofRead andText.Show.Show satisfy the following:

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

That is,readsPrec parses the string produced byText.Show.showsPrec, and delivers the value thatText.Show.showsPrec started with.

readList ::ReadS [a]Source

The methodreadList is provided to allow the programmer to give a specialised way of parsing lists of values. For example, this is used by the predefinedRead instance of theChar type, where values of typeString should be are expected to use double quotes, rather than square brackets.

Instances

ReadBool 
ReadChar 
ReadDouble 
ReadFloat 
ReadInt 
ReadInt8 
ReadInt16 
ReadInt32 
ReadInt64 
ReadInteger 
ReadOrdering 
ReadWord 
ReadWord8 
ReadWord16 
ReadWord32 
ReadWord64 
Read () 
ReadArity 
ReadFixity 
ReadAssociativity 
ReadLexeme 
ReadIOMode 
ReadSeekMode 
ReadCUIntMax 
ReadCIntMax 
ReadCUIntPtr 
ReadCIntPtr 
ReadCSUSeconds 
ReadCUSeconds 
ReadCTime 
ReadCClock 
ReadCSigAtomic 
ReadCWchar 
ReadCSize 
ReadCPtrdiff 
ReadCDouble 
ReadCFloat 
ReadCULLong 
ReadCLLong 
ReadCULong 
ReadCLong 
ReadCUInt 
ReadCInt 
ReadCUShort 
ReadCShort 
ReadCUChar 
ReadCSChar 
ReadCChar 
ReadAny 
ReadAll 
ReadGeneralCategory 
ReadIntPtr 
ReadWordPtr 
ReadNewlineMode 
ReadNewline 
ReadBufferMode 
ReadExitCode 
ReadFd 
ReadCRLim 
ReadCTcflag 
ReadCSpeed 
ReadCCc 
ReadCUid 
ReadCNlink 
ReadCGid 
ReadCSsize 
ReadCPid 
ReadCOff 
ReadCMode 
ReadCIno 
ReadCDev 
ReadVersion 
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) 
(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 toreadsPrec with a precedence of 0.

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

readParenTrue p parses whatp parses, but surrounded with parentheses.

readParenFalse p parses whatp parses, but optionally surrounded with parentheses.

read ::Read a =>String -> aSource

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

lex ::ReadSStringSource

Thelex 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. (Thuslex "" = [("","")].) 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

dataIO aSource

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

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 willbe performed. It isn't possible to perform I/O from an arbitraryfunction, unless that function is itself in theIO monad and calledat some point, directly or indirectly, fromMain.main.

IO is a monad, soIO actions can be combined using either the do-notationor the>> and>>= operations from theMonad class.

Instances

MonadIO 
FunctorIO 
Typeable1IO 
MonadFixIO 
ApplicativeIO 
HPrintfType (IO a) 
PrintfType (IO a) 

Simple I/O operations

Output functions

putChar ::Char ->IO()Source

Write a character to the standard output device (same ashPutCharstdout).

putStr ::String ->IO()Source

Write a string to the standard output device (same ashPutStrstdout).

putStrLn ::String ->IO()Source

The same asputStr, but adds a newline character.

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

Theprint function outputs a value of any printable type to the standard output device. Printable types are those that are instances of classShow;print converts values to strings for output using theshow 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 ::IOCharSource

Read a character from the standard input device (same ashGetCharstdin).

getLine ::IOStringSource

Read a line from the standard input device (same ashGetLinestdin).

getContents ::IOStringSource

ThegetContents operation returns all user input as a single string, which is read lazily as it is needed (same ashGetContentsstdin).

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

Theinteract function takes a function of typeString->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

typeFilePath =StringSource

File and directory names are values of typeString, 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 ->IOStringSource

ThereadFile function reads a file and returns the contents of the file as a string. The file is read lazily, on demand, as withgetContents.

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

The computationwriteFilefile str function writes the stringstr, to the filefile.

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

The computationappendFilefile str function appends the stringstr, to the filefile.

Note thatwriteFile andappendFile write a literal string to a file. To write a value of any printable type, as withprint, use theshow 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

ThereadIO function is similar toread except that it signals parse failure to theIO monad instead of terminating the program.

readLn ::Read a =>IO aSource

ThereadLn function combinesgetLine andreadIO.

Exception handling in the I/O monad

typeIOError =IOExceptionSource

The Haskell 98 type for exceptions in theIO monad. Any I/O operation may raise anIOError instead of returning a result. For a more general type of exception, including also those that arise in pure code, seeControl.Exception.Exception.

In Haskell 98, this is an opaque type.

ioError ::IOError ->IO aSource

Raise anIOError in theIO monad.

userError ::String ->IOErrorSource

Construct anIOError value with a string describing the error. Thefail method of theIO instance of theMonad class raises auserError, thus:

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

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

Thecatch function is deprecated. Please use the new exceptions variant,Control.Exception.catch fromControl.Exception, instead.

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