| Copyright | (c) The University of Glasgow 2001 |
|---|---|
| License | BSD-style (see the file libraries/base/LICENSE) |
| Maintainer | [email protected] |
| Stability | stable |
| Portability | portable |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
The Prelude: a standard module. The Prelude is imported by default into all Haskell modules unless either there is an explicit import statement for it, or the NoImplicitPrelude extension is enabled.
(&&) :: Bool -> Bool -> Bool infixr 3 Source
Boolean "and"
(||) :: Bool -> Bool -> Bool infixr 2 Source
Boolean "or"
Boolean "not"
otherwise is defined as the value True. It helps to make guards more readable. eg.
f x | x < 0 = ...
| otherwise = ...
The Maybe type encapsulates an optional value. A value of type Maybe a either contains a value of type a (represented as Just a), or it is empty (represented as Nothing). Using Maybe is a good way to deal with errors or exceptional cases without resorting to drastic measures such as error.
The Maybe type is also a monad. It is a simple kind of error monad, where all errors are represented by Nothing. A richer error monad can be built using the Either type.
| Monad Maybe | |
| Functor Maybe | |
| MonadFix Maybe | |
| MonadFail Maybe | |
| Applicative Maybe | |
| Foldable Maybe | |
| Traversable Maybe | |
| Generic1 Maybe | |
| MonadPlus Maybe | |
| Alternative Maybe | |
| MonadZip Maybe | |
| Show1 Maybe | |
| Read1 Maybe | |
| Ord1 Maybe | |
| Eq1 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) | |
| Generic (Maybe a) | |
| Semigroup a => Semigroup (Maybe a) | |
| Monoid a => Monoid (Maybe a) | Lift a semigroup into |
| type Rep1 Maybe | |
| type Rep (Maybe a) | |
| type (==) (Maybe k) a b | |
maybe :: b -> (a -> b) -> Maybe a -> b Source
The maybe function takes a default value, a function, and a Maybe value. If the Maybe value is Nothing, the function returns the default value. Otherwise, it applies the function to the value inside the Just and returns the result.
Basic usage:
>>>maybe False odd (Just 3)True
>>>maybe False odd NothingFalse
Read an integer from a string using readMaybe. If we succeed, return twice the integer; that is, apply (*2) to it. If instead we fail to parse an integer, return 0 by default:
>>>import Text.Read ( readMaybe )>>>maybe 0 (*2) (readMaybe "5")10>>>maybe 0 (*2) (readMaybe "")0
Apply show to a Maybe Int. If we have Just n, we want to show the underlying Int n. But if we have Nothing, we return the empty string instead of (for example) "Nothing":
>>>maybe "" show (Just 5)"5">>>maybe "" show Nothing""
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").
The type Either String Int is the type of values which can be either a String or an Int. The Left constructor can be used only on Strings, and the Right constructor can be used only on Ints:
>>>let s = Left "foo" :: Either String Int>>>sLeft "foo">>>let n = Right 3 :: Either String Int>>>nRight 3>>>:type ss :: Either String Int>>>:type nn :: Either String Int
The fmap from our Functor instance will ignore Left values, but will apply the supplied function to values contained in a Right:
>>>let s = Left "foo" :: Either String Int>>>let n = Right 3 :: Either String Int>>>fmap (*2) sLeft "foo">>>fmap (*2) nRight 6
The Monad instance for Either allows us to chain together multiple actions which may fail, and fail overall if any of the individual steps failed. First we'll write a function that can either parse an Int from a Char, or fail.
>>>import Data.Char ( digitToInt, isDigit )>>>:{let parseEither :: Char -> Either String Int parseEither c | isDigit c = Right (digitToInt c) | otherwise = Left "parse error">>>:}
The following should work, since both '1' and '2' can be parsed as Ints.
>>>:{let parseMultiple :: Either String Int parseMultiple = do x <- parseEither '1' y <- parseEither '2' return (x + y)>>>:}
>>>parseMultipleRight 3
But the following should fail overall, since the first operation where we attempt to parse 'm' as an Int will fail:
>>>:{let parseMultiple :: Either String Int parseMultiple = do x <- parseEither 'm' y <- parseEither '2' return (x + y)>>>:}
>>>parseMultipleLeft "parse error"
| Bifunctor Either | |
| Show2 Either | |
| Read2 Either | |
| Ord2 Either | |
| Eq2 Either | |
| Monad (Either e) | |
| Functor (Either a) | |
| MonadFix (Either e) | |
| Applicative (Either e) | |
| Foldable (Either a) | |
| Traversable (Either a) | |
| Generic1 (Either a) | |
| Show a => Show1 (Either a) | |
| Read a => Read1 (Either a) | |
| Ord a => Ord1 (Either a) | |
| Eq a => Eq1 (Either a) | |
| (Eq a, Eq b) => Eq (Either a b) | |
| (Data a, Data b) => Data (Either a b) | |
| (Ord a, Ord b) => Ord (Either a b) | |
| (Read a, Read b) => Read (Either a b) | |
| (Show a, Show b) => Show (Either a b) | |
| Generic (Either a b) | |
| Semigroup (Either a b) | |
| type Rep1 (Either a) | |
| type Rep (Either a b) | |
| type (==) (Either k k1) a b | |
either :: (a -> c) -> (b -> c) -> Either a b -> c Source
Case analysis for the Either type. If the value is Left a, apply the first function to a; if it is Right b, apply the second function to b.
We create two values of type Either String Int, one using the Left constructor and another using the Right constructor. Then we apply "either" the length function (if we have a String) or the "times-two" function (if we have an Int):
>>>let s = Left "foo" :: Either String Int>>>let n = Right 3 :: Either String Int>>>either length (*2) s3>>>either length (*2) n6
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 characters), 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 toEnum and fromEnum from the Enum class respectively (or equivalently ord and chr).
| Bounded Char | |
| Enum Char | |
| Eq Char | |
| Data Char | |
| Ord Char | |
| Read Char | |
| Show Char | |
| Ix Char | |
| Storable Char | |
| IsChar Char | |
| PrintfArg Char | |
| Functor (URec Char) | |
| Foldable (URec Char) | |
| Traversable (URec Char) | |
| Generic1 (URec Char) | |
| Eq (URec Char p) | |
| Ord (URec Char p) | |
| Show (URec Char p) | |
| Generic (URec Char p) | |
| data URec Char | Used for marking occurrences of |
| type Rep1 (URec Char) | |
| type Rep (URec Char p) | |
A String is a list of characters. String constants in Haskell are values of type String.
Extract the first component of a pair.
Extract the second component of a pair.
curry :: ((a, b) -> c) -> a -> b -> c Source
curry converts an uncurried function to a curried function.
uncurry :: (a -> b -> c) -> (a, b) -> c Source
uncurry converts a curried function to a function on pairs.
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 /=.
| 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 TypeRep | |
| Eq () | |
| Eq TyCon | |
| Eq BigNat | |
| Eq SrcLoc | |
| Eq GeneralCategory | |
| Eq Number | |
| Eq Lexeme | |
| Eq IOMode | |
| Eq SomeSymbol | |
| Eq SomeNat | |
| Eq Fingerprint | |
| Eq ArithException | |
| Eq ErrorCall | |
| Eq IOException | |
| Eq MaskingState | |
| Eq DecidedStrictness | |
| Eq SourceStrictness | |
| Eq SourceUnpackedness | |
| Eq Associativity | |
| Eq Fixity | |
| Eq Any | |
| Eq All | |
| Eq SeekMode | |
| Eq IODeviceType | |
| Eq CUIntMax | |
| Eq CIntMax | |
| Eq CUIntPtr | |
| Eq CIntPtr | |
| Eq CSUSeconds | |
| Eq CUSeconds | |
| Eq CTime | |
| Eq CClock | |
| Eq CSigAtomic | |
| Eq CWchar | |
| Eq CSize | |
| Eq CPtrdiff | |
| Eq CDouble | |
| Eq CFloat | |
| Eq CULLong | |
| Eq CLLong | |
| Eq CULong | |
| Eq CLong | |
| Eq CUInt | |
| Eq CInt | |
| Eq CUShort | |
| Eq CShort | |
| Eq CUChar | |
| Eq CSChar | |
| Eq CChar | |
| Eq IntPtr | |
| Eq WordPtr | |
| Eq BufferState | |
| Eq CodingProgress | |
| Eq NewlineMode | |
| Eq Newline | |
| Eq BufferMode | |
| Eq Handle | |
| Eq IOErrorType | |
| Eq ExitCode | |
| Eq ArrayException | |
| Eq AsyncException | |
| Eq Errno | |
| Eq ThreadStatus | |
| Eq BlockReason | |
| Eq ThreadId | |
| Eq Fd | |
| Eq CRLim | |
| Eq CTcflag | |
| Eq CSpeed | |
| Eq CCc | |
| Eq CUid | |
| Eq CNlink | |
| Eq CGid | |
| Eq CSsize | |
| Eq CPid | |
| Eq COff | |
| Eq CMode | |
| Eq CIno | |
| Eq CDev | |
| Eq Lifetime | |
| Eq Event | |
| Eq FdKey | |
| Eq TimeoutKey | |
| Eq HandlePosn | |
| Eq Unique | |
| Eq Version | |
| Eq Fixity | |
| Eq ConstrRep | |
| Eq DataRep | |
| Eq Constr | Equality of constructors |
| Eq Void | |
| Eq Natural | |
| Eq SpecConstrAnnotation | |
| Eq a => Eq [a] | |
| Eq a => Eq (Maybe a) | |
| Eq a => Eq (Ratio a) | |
| Eq (StablePtr a) | |
| Eq (Ptr a) | |
| Eq (FunPtr a) | |
| Eq (V1 p) | |
| Eq (U1 p) | |
| Eq p => Eq (Par1 p) | |
| Eq (MVar a) | |
| Eq a => Eq (Down 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 (ZipList a) | |
| Eq (Chan a) | |
| Eq (StableName a) | |
| Eq a => Eq (Complex a) | |
| Eq (Fixed a) | |
| Eq a => Eq (NonEmpty a) | |
| Eq a => Eq (Option a) | |
| Eq m => Eq (WrappedMonoid m) | |
| Eq a => Eq (Last a) | |
| Eq a => Eq (First a) | |
| Eq a => Eq (Max a) | |
| Eq a => Eq (Min a) | |
| Eq a => Eq (Identity a) | |
| (Eq a, Eq b) => Eq (Either a b) | |
| Eq (f p) => Eq (Rec1 f p) | |
| Eq (URec Char p) | |
| Eq (URec Double p) | |
| Eq (URec Float p) | |
| Eq (URec Int p) | |
| Eq (URec Word p) | |
| Eq (URec (Ptr ()) p) | |
| (Eq a, Eq b) => Eq (a, b) | |
| Eq (STRef s a) | |
| Eq (Proxy k s) | |
| Eq a => Eq (Arg a b) | |
| Eq c => Eq (K1 i c p) | |
| (Eq (f p), Eq (g p)) => Eq ((:+:) f g p) | |
| (Eq (f p), Eq (g p)) => Eq ((:*:) f g p) | |
| Eq (f (g p)) => Eq ((:.:) f g p) | |
| (Eq a, Eq b, Eq c) => Eq (a, b, c) | |
| Eq ((:~:) k a b) | |
| Eq (Coercion k a b) | |
| Eq (f a) => Eq (Alt k f a) | |
| Eq a => Eq (Const k a b) | |
| Eq (f p) => Eq (M1 i c f p) | |
| (Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) | |
| (Eq1 f, Eq1 g, Eq a) => Eq (Product * f g a) | |
| (Eq1 f, Eq1 g, Eq a) => Eq (Sum * f g a) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) | |
| (Eq1 f, Eq1 g, Eq a) => Eq (Compose * * f g a) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | |
class Eq a => Ord a where Source
The Ord class is used for totally ordered datatypes.
Instances of Ord can be derived for any user-defined datatype whose constituent types are in Ord. The declared order of the constructors in the data declaration determines the ordering in derived Ord instances. The Ordering datatype allows a single comparison to determine the precise ordering of two objects.
Minimal complete definition: either compare or <=. Using compare can be more efficient for complex types.
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:
succ maxBound and pred minBound should result in a runtime error.fromEnum and toEnum should give a runtime error if the result value is not representable in the result type. For example, toEnum 7 :: Bool is an error.enumFrom and enumFromThen should be defined with an implicit bound, thus: enumFrom x = enumFromTo x maxBound
enumFromThen x y = enumFromThenTo x y bound
where
bound | fromEnum y >= fromEnum x = maxBound
| otherwise = minBound
the successor of a value. For numeric types, succ adds 1.
the predecessor of a value. For numeric types, pred subtracts 1.
Convert from an Int.
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.
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].
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.
A fixed-precision integer type with at least the range [-2^29 .. 2^29-1]. The exact range for a given implementation can be determined by using minBound and maxBound from the Bounded class.
| Bounded Int | |
| Enum Int | |
| Eq Int | |
| Integral Int | |
| Data Int | |
| Num Int | |
| Ord Int | |
| Read Int | |
| Real Int | |
| Show Int | |
| Ix Int | |
| FiniteBits Int | |
| Bits Int | |
| Storable Int | |
| PrintfArg Int | |
| Functor (URec Int) | |
| Foldable (URec Int) | |
| Traversable (URec Int) | |
| Generic1 (URec Int) | |
| Eq (URec Int p) | |
| Ord (URec Int p) | |
| Show (URec Int p) | |
| Generic (URec Int p) | |
| data URec Int | Used for marking occurrences of |
| type Rep1 (URec Int) | |
| type Rep (URec Int p) | |
Invariant: Jn# and Jp# are used iff value doesn't fit in S#
Useful properties resulting from the invariants:
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.
| Eq Float | |
| Floating Float | |
| Data Float | |
| Ord Float | |
| Read Float | |
| RealFloat Float | |
| Storable Float | |
| PrintfArg Float | |
| Functor (URec Float) | |
| Foldable (URec Float) | |
| Traversable (URec Float) | |
| Generic1 (URec Float) | |
| Eq (URec Float p) | |
| Ord (URec Float p) | |
| Show (URec Float p) | |
| Generic (URec Float p) | |
| data URec Float | Used for marking occurrences of |
| type Rep1 (URec Float) | |
| type Rep (URec Float p) | |
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.
| Eq Double | |
| Floating Double | |
| Data Double | |
| Ord Double | |
| Read Double | |
| RealFloat Double | |
| Storable Double | |
| PrintfArg Double | |
| Functor (URec Double) | |
| Foldable (URec Double) | |
| Traversable (URec Double) | |
| Generic1 (URec Double) | |
| Eq (URec Double p) | |
| Ord (URec Double p) | |
| Show (URec Double p) | |
| Generic (URec Double p) | |
| data URec Double | Used for marking occurrences of |
| type Rep1 (URec Double) | |
| type Rep (URec Double p) | |
type Rational = Ratio Integer Source
Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.
A Word is an unsigned integral type, with the same size as Int.
| Bounded Word | |
| Enum Word | |
| Eq Word | |
| Integral Word | |
| Data Word | |
| Num Word | |
| Ord Word | |
| Read Word | |
| Real Word | |
| Show Word | |
| Ix Word | |
| FiniteBits Word | |
| Bits Word | |
| Storable Word | |
| PrintfArg Word | |
| Functor (URec Word) | |
| Foldable (URec Word) | |
| Traversable (URec Word) | |
| Generic1 (URec Word) | |
| Eq (URec Word p) | |
| Ord (URec Word p) | |
| Show (URec Word p) | |
| Generic (URec Word p) | |
| data URec Word | Used for marking occurrences of |
| type Rep1 (URec Word) | |
| type Rep (URec Word p) | |
Basic numeric class.
(+), (-), (*) :: a -> a -> a infixl 7 *infixl 6 +, - Source
Unary negation.
Absolute value.
Sign of a number. The functions abs and signum should satisfy the law:
abs x * signum x == x
For real numbers, the signum is either -1 (negative), 0 (zero) or 1 (positive).
fromInteger :: Integer -> a Source
Conversion from an Integer. An integer literal represents the application of the function fromInteger to the appropriate value of type Integer, so such literals have type (Num a) => a.
| Num Int | |
| Num Int8 | |
| Num Int16 | |
| Num Int32 | |
| Num Int64 | |
| Num Integer | |
| Num Word | |
| Num Word8 | |
| Num Word16 | |
| Num Word32 | |
| Num Word64 | |
| Num CUIntMax | |
| Num CIntMax | |
| Num CUIntPtr | |
| Num CIntPtr | |
| Num CSUSeconds | |
| Num CUSeconds | |
| Num CTime | |
| Num CClock | |
| Num CSigAtomic | |
| Num CWchar | |
| Num CSize | |
| Num CPtrdiff | |
| Num CDouble | |
| Num CFloat | |
| Num CULLong | |
| Num CLLong | |
| Num CULong | |
| Num CLong | |
| Num CUInt | |
| Num CInt | |
| Num CUShort | |
| Num CShort | |
| Num CUChar | |
| Num CSChar | |
| Num CChar | |
| Num IntPtr | |
| Num WordPtr | |
| Num Fd | |
| Num CRLim | |
| Num CTcflag | |
| Num CSpeed | |
| Num CCc | |
| Num CUid | |
| Num CNlink | |
| Num CGid | |
| Num CSsize | |
| Num CPid | |
| Num COff | |
| Num CMode | |
| Num CIno | |
| Num CDev | |
| Num Natural | |
| Integral a => Num (Ratio a) | |
| Num a => Num (Product a) | |
| Num a => Num (Sum a) | |
| RealFloat a => Num (Complex a) | |
| HasResolution a => Num (Fixed a) | |
| Num a => Num (Max a) | |
| Num a => Num (Min a) | |
| Num a => Num (Identity a) | |
| Num (f a) => Num (Alt k f a) | |
| Num a => Num (Const k a b) | |
class (Num a, Ord a) => Real a where Source
toRational :: a -> Rational Source
the rational equivalent of its real argument with full precision
| Real Int | |
| Real Int8 | |
| Real Int16 | |
| Real Int32 | |
| Real Int64 | |
| Real Integer | |
| Real Word | |
| Real Word8 | |
| Real Word16 | |
| Real Word32 | |
| Real Word64 | |
| Real CUIntMax | |
| Real CIntMax | |
| Real CUIntPtr | |
| Real CIntPtr | |
| Real CSUSeconds | |
| Real CUSeconds | |
| Real CTime | |
| Real CClock | |
| Real CSigAtomic | |
| Real CWchar | |
| Real CSize | |
| Real CPtrdiff | |
| Real CDouble | |
| Real CFloat | |
| Real CULLong | |
| Real CLLong | |
| Real CULong | |
| Real CLong | |
| Real CUInt | |
| Real CInt | |
| Real CUShort | |
| Real CShort | |
| Real CUChar | |
| Real CSChar | |
| Real CChar | |
| Real IntPtr | |
| Real WordPtr | |
| Real Fd | |
| Real CRLim | |
| Real CTcflag | |
| Real CSpeed | |
| Real CCc | |
| Real CUid | |
| Real CNlink | |
| Real CGid | |
| Real CSsize | |
| Real CPid | |
| Real COff | |
| Real CMode | |
| Real CIno | |
| Real CDev | |
| Real Natural | |
| Integral a => Real (Ratio a) | |
| HasResolution a => Real (Fixed a) | |
| Real a => Real (Identity a) | |
| Real a => Real (Const k a b) | |
class (Real a, Enum a) => Integral a where Source
Integral numbers, supporting integer division.
quot :: a -> a -> a infixl 7 Source
integer division truncated toward zero
rem :: a -> a -> a infixl 7 Source
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
div :: a -> a -> a infixl 7 Source
integer division truncated toward negative infinity
mod :: a -> a -> a infixl 7 Source
integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
quotRem :: a -> a -> (a, a) Source
divMod :: a -> a -> (a, a) Source
toInteger :: a -> Integer Source
conversion to Integer
class Num a => Fractional a where Source
Fractional numbers, supporting real division.
fromRational, (recip | (/))
(/) :: a -> a -> a infixl 7 Source
fractional division
reciprocal fraction
fromRational :: Rational -> a Source
Conversion from a Rational (that is Ratio Integer). A floating literal stands for an application of fromRational to a value of type Rational, so such literals have type (Fractional a) => a.
| Fractional CDouble | |
| Fractional CFloat | |
| Integral a => Fractional (Ratio a) | |
| RealFloat a => Fractional (Complex a) | |
| HasResolution a => Fractional (Fixed a) | |
| Fractional a => Fractional (Identity a) | |
| Fractional a => Fractional (Const k a b) | |
class Fractional a => Floating a where Source
Trigonometric and hyperbolic functions and related functions.
pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh
exp, log, sqrt :: a -> a Source
(**), logBase :: a -> a -> a infixr 8 Source
sin, cos, tan :: a -> a Source
asin, acos, atan :: a -> a Source
class (Real a, Fractional a) => RealFrac a where Source
Extracting components of fractions.
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; andf is a fraction with the same type and sign as x, and with absolute value less than 1.The default definitions of the ceiling, floor, truncate and round functions are in terms of properFraction.
truncate :: Integral b => a -> b Source
truncate x returns the integer nearest x between zero and x
round :: Integral b => a -> b Source
round x returns the nearest integer to x; the even integer if x is equidistant between two integers
ceiling :: Integral b => a -> b Source
ceiling x returns the least integer not less than x
floor :: Integral b => a -> b Source
floor x returns the greatest integer not greater than x
class (RealFrac a, Floating a) => RealFloat a where Source
Efficient, machine-independent access to the components of a floating-point number.
floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE
floatRadix :: a -> Integer Source
a constant function, returning the radix of the representation (often 2)
floatDigits :: a -> Int Source
a constant function, returning the number of digits of floatRadix in the significand
floatRange :: a -> (Int, Int) Source
a constant function, returning the lowest and highest values the exponent may assume
decodeFloat :: a -> (Integer, Int) Source
The function decodeFloat applied to a real floating-point number returns the significand expressed as an Integer and an appropriately scaled exponent (an Int). If decodeFloat x yields (m,n), then x is equal in value to m*b^^n, where b is the floating-point radix, and furthermore, either m and n are both zero or else b^(d-1) <= abs m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0). If the type contains a negative zero, also decodeFloat (-0.0) = (0,0). The result of decodeFloat x is unspecified if either of isNaN x or isInfinite x is True.
encodeFloat :: Integer -> Int -> a Source
encodeFloat performs the inverse of decodeFloat in the sense that for finite x with the exception of -0.0, uncurry encodeFloat (decodeFloat x) = x. encodeFloat m n is one of the two closest representable floating-point numbers to m*b^^n (or ±Infinity if overflow occurs); usually the closer, but if m contains too many bits, the result may be rounded in the wrong direction.
exponent corresponds to the second component of decodeFloat. exponent 0 = 0 and for finite nonzero x, exponent x = snd (decodeFloat x) + floatDigits x. If x is a finite floating-point number, it is equal in value to significand x * b ^^ exponent x, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.
significand :: a -> a Source
The first component of decodeFloat, scaled to lie in the open interval (-1,1), either 0.0 or of absolute value >= 1/b, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.
scaleFloat :: Int -> a -> a Source
multiplies a floating-point number by an integer power of the radix
True if the argument is an IEEE "not-a-number" (NaN) value
isInfinite :: a -> Bool Source
True if the argument is an IEEE infinity or negative infinity
isDenormalized :: a -> Bool Source
True if the argument is too small to be represented in normalized format
isNegativeZero :: a -> Bool Source
True if the argument is an IEEE negative zero
True if the argument is an IEEE floating point number
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.
subtract :: Num a => a -> a -> a Source
Because - is treated specially in the Haskell grammar, (- e) is not a section, but an application of prefix negation. However, (subtract exp) is equivalent to the disallowed section.
even :: Integral a => a -> Bool Source
odd :: Integral a => a -> Bool Source
gcd :: Integral a => a -> a -> a Source
gcd x y is the non-negative factor of both x and y of which every common factor of x and y is also a factor; for example gcd 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, abs minBound < 0, the result may be negative if one of the arguments is minBound (and necessarily is if the other is 0 or minBound) for such types.
lcm :: Integral a => a -> a -> a Source
lcm x y is the smallest positive integer that both x and y divide.
(^) :: (Num a, Integral b) => a -> b -> a infixr 8 Source
raise a number to a non-negative integral power
(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 Source
raise a number to an integral power
fromIntegral :: (Integral a, Num b) => a -> b Source
general coercion from integral types
realToFrac :: (Real a, Fractional b) => a -> b Source
general coercion to fractional types
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:
mappend mempty x = x
mappend x mempty = x
mappend x (mappend y z) = mappend (mappend x y) z
mconcat = foldr mappend memptyThe method names refer to the monoid of lists under concatenation, but there are many other instances.
Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product.
Identity of mappend
An associative operation
Fold a list using the monoid. For most types, the default definition for mconcat will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.
| Monoid Ordering | |
| Monoid () | |
| Monoid Any | |
| Monoid All | |
| Monoid Lifetime |
|
| Monoid Event | |
| Monoid [a] | |
| Monoid a => Monoid (Maybe a) | Lift a semigroup into |
| Monoid a => Monoid (IO a) | |
| Monoid (Last a) | |
| Monoid (First a) | |
| Num a => Monoid (Product a) | |
| Num a => Monoid (Sum a) | |
| Monoid (Endo a) | |
| Monoid a => Monoid (Dual a) | |
| Semigroup a => Monoid (Option a) | |
| Monoid m => Monoid (WrappedMonoid m) | |
| (Ord a, Bounded a) => Monoid (Max a) | |
| (Ord a, Bounded a) => Monoid (Min a) | |
| Monoid a => Monoid (Identity a) | |
| Monoid b => Monoid (a -> b) | |
| (Monoid a, Monoid b) => Monoid (a, b) | |
| Monoid (Proxy k s) | |
| (Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | |
| Alternative f => Monoid (Alt * f a) | |
| Monoid a => Monoid (Const k a b) | |
| (Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | |
| (Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) | |
The Functor class is used for types that can be mapped over. Instances of Functor should satisfy the following laws:
fmap id == id fmap (f . g) == fmap f . fmap g
The instances of Functor for lists, Maybe and IO satisfy these laws.
fmap :: (a -> b) -> f a -> f b Source
(<$) :: a -> f b -> f a infixl 4 Source
Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 Source
An infix synonym for fmap.
The name of this operator is an allusion to $. Note the similarities between their types:
($) :: (a -> b) -> a -> b (<$>) :: Functor f => (a -> b) -> f a -> f b
Whereas $ is function application, <$> is function application lifted over a Functor.
Convert from a Maybe Int to a Maybe String using show:
>>>show <$> NothingNothing>>>show <$> Just 3Just "3"
Convert from an Either Int Int to an Either Int String using show:
>>>show <$> Left 17Left 17>>>show <$> Right 17Right "17"
Double each element of a list:
>>>(*2) <$> [1,2,3][2,4,6]
Apply even to the second element of a pair:
>>>even <$> (2,2)(2,True)
class Functor f => Applicative f where Source
A functor with application, providing operations to
A minimal complete definition must include implementations of these functions satisfying the following laws:
pureid<*>v = v
pure(.)<*>u<*>v<*>w = u<*>(v<*>w)
puref<*>purex =pure(f x)
u<*>purey =pure($y)<*>u
The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:
As a consequence of these laws, the Functor instance for f will satisfy
If f is also a Monad, it should satisfy
(which implies that pure and <*> satisfy the applicative functor laws).
Lift a value.
(<*>) :: f (a -> b) -> f a -> f b infixl 4 Source
Sequential application.
(*>) :: f a -> f b -> f b infixl 4 Source
Sequence actions, discarding the value of the first argument.
(<*) :: f a -> f b -> f a infixl 4 Source
Sequence actions, discarding the value of the second argument.
class Applicative m => Monad m where Source
The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.
Instances of Monad should satisfy the following laws:
Furthermore, the Monad and Applicative operations should relate as follows:
The above laws imply:
and that pure and (<*>) satisfy the applicative functor laws.
The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.
(>>=) :: forall a b. m a -> (a -> m b) -> m b infixl 1 Source
Sequentially compose two actions, passing any value produced by the first as an argument to the second.
(>>) :: forall a b. m a -> m b -> m b infixl 1 Source
Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.
Inject a value into the monadic type.
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.
As part of the MonadFail proposal (MFP), this function is moved to its own class MonadFail (see Control.Monad.Fail for more details). The definition here will be removed in a future release.
| Monad [] | |
| Monad Maybe | |
| Monad IO | |
| Monad U1 | |
| Monad Par1 | |
| Monad ReadP | |
| Monad ReadPrec | |
| Monad Last | |
| Monad First | |
| Monad Product | |
| Monad Sum | |
| Monad Dual | |
| Monad STM | |
| Monad Complex | |
| Monad NonEmpty | |
| Monad Option | |
| Monad Last | |
| Monad First | |
| Monad Max | |
| Monad Min | |
| Monad Identity | |
| Monad ((->) r) | |
| Monad (Either e) | |
| Monad f => Monad (Rec1 f) | |
| Monoid a => Monad ((,) a) | |
| Monad (ST s) | |
| Monad (Proxy *) | |
| ArrowApply a => Monad (ArrowMonad a) | |
| Monad m => Monad (WrappedMonad m) | |
| Monad (ST s) | |
| (Monad f, Monad g) => Monad ((:*:) f g) | |
| Monad f => Monad (Alt * f) | |
| Monad f => Monad (M1 i c f) | |
| (Monad f, Monad g) => Monad (Product * f g) | |
mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m () Source
Map each element of a structure to a monadic action, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results see mapM.
As of base 4.8.0.0, mapM_ is just traverse_, specialized to Monad.
sequence_ :: (Foldable t, Monad m) => t (m a) -> m () Source
Evaluate each monadic action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see sequence.
As of base 4.8.0.0, sequence_ is just sequenceA_, specialized to Monad.
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 Source
Same as >>=, but with the arguments interchanged.
Data structures that can be folded.
For example, given a data type
data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
a suitable instance would be
instance Foldable Tree where foldMap f Empty = mempty foldMap f (Leaf x) = f x foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r
This is suitable even for abstract types, as the monoid is assumed to satisfy the monoid laws. Alternatively, one could define foldr:
instance Foldable Tree where foldr f z Empty = z foldr f z (Leaf x) = f x z foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l
Foldable instances are expected to satisfy the following laws:
foldr f z t = appEndo (foldMap (Endo . f) t ) z
foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z
fold = foldMap id
sum, product, maximum, and minimum should all be essentially equivalent to foldMap forms, such as
sum = getSum . foldMap Sum
but may be less defined.
If the type is also a Functor instance, it should satisfy
foldMap f = fold . fmap f
which implies that
foldMap f . fmap g = foldMap (f . g)
foldMap :: Monoid m => (a -> m) -> t a -> m Source
Map each element of the structure to a monoid, and combine the results.
foldr :: (a -> b -> b) -> b -> t a -> b Source
Right-associative fold of a structure.
In the case of lists, foldr, when 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)...)
Note that, since the head of the resulting expression is produced by an application of the operator to the first element of the list, foldr can produce a terminating expression from an infinite list.
For a general Foldable structure this should be semantically identical to,
foldr f z =foldrf z .toList
foldl :: (b -> a -> b) -> b -> t a -> b Source
Left-associative fold of a structure.
In the case of lists, foldl, when 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
Note that to produce the outermost application of the operator the entire input list must be traversed. This means that foldl' will diverge if given an infinite list.
Also note that if you want an efficient left-fold, you probably want to use foldl' instead of foldl. The reason for this is that latter does not force the "inner" results (e.g. z f x1 in the above example) before applying them to the operator (e.g. to (f x2)). This results in a thunk chain O(n) elements long, which then must be evaluated from the outside-in.
For a general Foldable structure this should be semantically identical to,
foldl f z =foldlf z .toList
foldr1 :: (a -> a -> a) -> t a -> a Source
A variant of foldr that has no base case, and thus may only be applied to non-empty structures.
foldr1f =foldr1f .toList
foldl1 :: (a -> a -> a) -> t a -> a Source
A variant of foldl that has no base case, and thus may only be applied to non-empty structures.
foldl1f =foldl1f .toList
Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.
Returns the size/length of a finite structure as an Int. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.
elem :: Eq a => a -> t a -> Bool infix 4 Source
Does the element occur in the structure?
maximum :: forall a. Ord a => t a -> a Source
The largest element of a non-empty structure.
minimum :: forall a. Ord a => t a -> a Source
The least element of a non-empty structure.
sum :: Num a => t a -> a Source
The sum function computes the sum of the numbers of a structure.
product :: Num a => t a -> a Source
The product function computes the product of the numbers of a structure.
| Foldable [] | |
| Foldable Maybe | |
| Foldable V1 | |
| Foldable U1 | |
| Foldable Par1 | |
| Foldable Last | |
| Foldable First | |
| Foldable Product | |
| Foldable Sum | |
| Foldable Dual | |
| Foldable ZipList | |
| Foldable Complex | |
| Foldable NonEmpty | |
| Foldable Option | |
| Foldable Last | |
| Foldable First | |
| Foldable Max | |
| Foldable Min | |
| Foldable Identity | |
| Foldable (Either a) | |
| Foldable f => Foldable (Rec1 f) | |
| Foldable (URec Char) | |
| Foldable (URec Double) | |
| Foldable (URec Float) | |
| Foldable (URec Int) | |
| Foldable (URec Word) | |
| Foldable (URec (Ptr ())) | |
| Foldable ((,) a) | |
| Foldable (Proxy *) | |
| Foldable (Arg a) | |
| Foldable (K1 i c) | |
| (Foldable f, Foldable g) => Foldable ((:+:) f g) | |
| (Foldable f, Foldable g) => Foldable ((:*:) f g) | |
| (Foldable f, Foldable g) => Foldable ((:.:) f g) | |
| Foldable (Const * m) | |
| Foldable f => Foldable (M1 i c f) | |
| (Foldable f, Foldable g) => Foldable (Product * f g) | |
| (Foldable f, Foldable g) => Foldable (Sum * f g) | |
| (Foldable f, Foldable g) => Foldable (Compose * * f g) | |
class (Functor t, Foldable t) => Traversable t where Source
Functors representing data structures that can be traversed from left to right.
A definition of traverse must satisfy the following laws:
t . traverse f = traverse (t . f) for every applicative transformation t
traverse Identity = Identitytraverse (Compose . fmap g . f) = Compose . fmap (traverse g) . traverse fA definition of sequenceA must satisfy the following laws:
t . sequenceA = sequenceA . fmap t for every applicative transformation t
sequenceA . fmap Identity = IdentitysequenceA . fmap Compose = Compose . fmap sequenceA . sequenceAwhere an applicative transformation is a function
t :: (Applicative f, Applicative g) => f a -> g a
preserving the Applicative operations, i.e.
and the identity functor Identity and composition of functors Compose are defined as
newtype Identity a = Identity a
instance Functor Identity where
fmap f (Identity x) = Identity (f x)
instance Applicative Identity where
pure x = Identity x
Identity f <*> Identity x = Identity (f x)
newtype Compose f g a = Compose (f (g a))
instance (Functor f, Functor g) => Functor (Compose f g) where
fmap f (Compose x) = Compose (fmap (fmap f) x)
instance (Applicative f, Applicative g) => Applicative (Compose f g) where
pure x = Compose (pure (pure x))
Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)
(The naturality law is implied by parametricity.)
Instances are similar to Functor, e.g. given a data type
data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
a suitable instance would be
instance Traversable Tree where traverse f Empty = pure Empty traverse f (Leaf x) = Leaf <$> f x traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r
This is suitable even for abstract types, as the laws for <*> imply a form of associativity.
The superclass instances should satisfy the following:
Functor instance, fmap should be equivalent to traversal with the identity applicative functor (fmapDefault).Foldable instance, foldMap should be equivalent to traversal with a constant applicative functor (foldMapDefault).traverse :: Applicative f => (a -> f b) -> t a -> f (t b) Source
Map each element of a structure to an action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see traverse_.
sequenceA :: Applicative f => t (f a) -> f (t a) Source
Evaluate each action in the structure from left to right, and and collect the results. For a version that ignores the results see sequenceA_.
mapM :: Monad m => (a -> m b) -> t a -> m (t b) Source
Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see mapM_.
sequence :: Monad m => t (m a) -> m (t a) Source
Evaluate each monadic action in the structure from left to right, and collect the results. For a version that ignores the results see sequence_.
Identity function.
const x is a unary function which evaluates to x for all inputs.
For instance,
>>>map (const 42) [0..3][42,42,42,42]
(.) :: (b -> c) -> (a -> b) -> a -> c infixr 9 Source
Function composition.
flip :: (a -> b -> c) -> b -> a -> c Source
flip f takes its (first) two arguments in the reverse order of f.
($) :: (a -> b) -> a -> b infixr 0 Source
Application operator. This operator is redundant, since ordinary application (f x) means the same as (f $ x). However, $ has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:
f $ g $ h x = f (g (h x))
It is also useful in higher-order situations, such as map ($ 0) xs, or zipWith ($) fs xs.
until :: (a -> Bool) -> (a -> a) -> a -> a Source
until p f yields the result of applying f until p holds.
asTypeOf :: a -> a -> a Source
asTypeOf is a type-restricted version of const. It is usually used as an infix operator, and its typing forces its first argument (which is usually overloaded) to have the same type as the second.
error :: forall r. forall a. HasCallStack => [Char] -> a Source
error stops execution and displays an error message.
errorWithoutStackTrace :: forall r. forall a. [Char] -> a Source
A variant of error that does not produce a stack trace.
Since: 4.9.0.0
undefined :: forall r. forall a. HasCallStack => a Source
A special case of error. It is expected that compilers will recognize this and insert error messages which are more appropriate to the context in which undefined appears.
The value of seq a b is bottom if a is bottom, and otherwise equal to b. seq is usually introduced to improve performance by avoiding unneeded laziness.
A note on evaluation order: the expression seq a b does not guarantee that a will be evaluated before b. The only guarantee given by seq is that the both a and b will be evaluated before seq returns a value. In particular, this means that b may be evaluated before a. If you need to guarantee a specific order of evaluation, you must use the function pseq from the "parallel" package.
($!) :: (a -> b) -> a -> b infixr 0 Source
Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.
map :: (a -> b) -> [a] -> [b] Source
map f xs is the list obtained by applying f to each element of xs, i.e.,
map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn] map f [x1, x2, ...] == [f x1, f x2, ...]
(++) :: [a] -> [a] -> [a] infixr 5 Source
Append two lists, i.e.,
[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn] [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]
If the first list is not finite, the result is the first list.
filter :: (a -> Bool) -> [a] -> [a] Source
filter, applied to a predicate and a list, returns the list of those elements that satisfy the predicate; i.e.,
filter p xs = [ x | x <- xs, p x]
Extract the first element of a list, which must be non-empty.
Extract the last element of a list, which must be finite and non-empty.
Extract the elements after the head of a list, which must be non-empty.
Return all the elements of a list except the last one. The list must be non-empty.
null :: Foldable t => t a -> Bool Source
Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.
length :: Foldable t => t a -> Int Source
Returns the size/length of a finite structure as an Int. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.
(!!) :: [a] -> Int -> a infixl 9 Source
List index (subscript) operator, starting from 0. It is an instance of the more general genericIndex, which takes an index of any integral type.
reverse xs returns the elements of xs in reverse order. xs must be finite.
and :: Foldable t => t Bool -> Bool Source
and returns the conjunction of a container of Bools. For the result to be True, the container must be finite; False, however, results from a False value finitely far from the left end.
or :: Foldable t => t Bool -> Bool Source
or returns the disjunction of a container of Bools. For the result to be False, the container must be finite; True, however, results from a True value finitely far from the left end.
any :: Foldable t => (a -> Bool) -> t a -> Bool Source
Determines whether any element of the structure satisfies the predicate.
all :: Foldable t => (a -> Bool) -> t a -> Bool Source
Determines whether all elements of the structure satisfy the predicate.
concat :: Foldable t => t [a] -> [a] Source
The concatenation of all the elements of a container of lists.
concatMap :: Foldable t => (a -> [b]) -> t a -> [b] Source
Map a function over all the elements of a container and concatenate the resulting lists.
scanl :: (b -> a -> b) -> b -> [a] -> [b] Source
scanl is similar to foldl, but returns a list of successive reduced values from the left:
scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]
Note that
last (scanl f z xs) == foldl f z xs.
scanl1 :: (a -> a -> a) -> [a] -> [a] Source
scanl1 is a variant of scanl that has no starting value argument:
scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
scanr :: (a -> b -> b) -> b -> [a] -> [b] Source
scanr is the right-to-left dual of scanl. Note that
head (scanr f z xs) == foldr f z xs.
scanr1 :: (a -> a -> a) -> [a] -> [a] Source
scanr1 is a variant of scanr that has no starting value argument.
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 x is an infinite list, with x the value of every element.
replicate :: Int -> a -> [a] Source
replicate n x is a list of length n with x the value of every element. It is an instance of the more general genericReplicate, in which n may be of any integral type.
cycle ties a finite list into a circular one, or equivalently, the infinite repetition of the original list. It is the identity on infinite lists.
take :: Int -> [a] -> [a] Source
take n, applied to a list xs, returns the prefix of xs of length n, or xs itself if n > length xs:
take 5 "Hello World!" == "Hello" take 3 [1,2,3,4,5] == [1,2,3] take 3 [1,2] == [1,2] take 3 [] == [] take (-1) [1,2] == [] take 0 [1,2] == []
It is an instance of the more general genericTake, in which n may be of any integral type.
drop :: Int -> [a] -> [a] Source
drop n xs returns the suffix of xs after the first n elements, or [] if n > length xs:
drop 6 "Hello World!" == "World!" drop 3 [1,2,3,4,5] == [4,5] drop 3 [1,2] == [] drop 3 [] == [] drop (-1) [1,2] == [1,2] drop 0 [1,2] == [1,2]
It is an instance of the more general genericDrop, in which n may be of any integral type.
splitAt :: Int -> [a] -> ([a], [a]) Source
splitAt n xs returns a tuple where first element is xs prefix of length n and second element is the remainder of the list:
splitAt 6 "Hello World!" == ("Hello ","World!")
splitAt 3 [1,2,3,4,5] == ([1,2,3],[4,5])
splitAt 1 [1,2,3] == ([1],[2,3])
splitAt 3 [1,2,3] == ([1,2,3],[])
splitAt 4 [1,2,3] == ([1,2,3],[])
splitAt 0 [1,2,3] == ([],[1,2,3])
splitAt (-1) [1,2,3] == ([],[1,2,3])
It is equivalent to (take n xs, drop n xs) when n is not _|_ (splitAt _|_ xs = _|_). splitAt is an instance of the more general genericSplitAt, in which n may be of any integral type.
takeWhile :: (a -> Bool) -> [a] -> [a] Source
takeWhile, applied to a predicate p and a list xs, returns the longest prefix (possibly empty) of xs of elements that satisfy p:
takeWhile (< 3) [1,2,3,4,1,2,3,4] == [1,2] takeWhile (< 9) [1,2,3] == [1,2,3] takeWhile (< 0) [1,2,3] == []
dropWhile :: (a -> Bool) -> [a] -> [a] Source
dropWhile p xs returns the suffix remaining after takeWhile p xs:
dropWhile (< 3) [1,2,3,4,5,1,2,3] == [3,4,5,1,2,3] dropWhile (< 9) [1,2,3] == [] dropWhile (< 0) [1,2,3] == [1,2,3]
span :: (a -> Bool) -> [a] -> ([a], [a]) Source
span, applied to a predicate p and a list xs, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that satisfy p and second element is the remainder of the list:
span (< 3) [1,2,3,4,1,2,3,4] == ([1,2],[3,4,1,2,3,4]) span (< 9) [1,2,3] == ([1,2,3],[]) span (< 0) [1,2,3] == ([],[1,2,3])
span p xs is equivalent to (takeWhile p xs, dropWhile p xs)
break :: (a -> Bool) -> [a] -> ([a], [a]) Source
break, applied to a predicate p and a list xs, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that do not satisfy p and second element is the remainder of the list:
break (> 3) [1,2,3,4,1,2,3,4] == ([1,2,3],[4,1,2,3,4]) break (< 9) [1,2,3] == ([],[1,2,3]) break (> 9) [1,2,3] == ([1,2,3],[])
break p is equivalent to span (not . p).
notElem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 Source
notElem is the negation of elem.
lookup :: Eq a => a -> [(a, b)] -> Maybe b Source
lookup key assocs looks up a key in an association list.
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.
zip is right-lazy:
zip [] _|_ = []
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.
zipWith is right-lazy:
zipWith f [] _|_ = []
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.
lines :: String -> [String] Source
lines breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.
Note that after splitting the string at newline characters, the last part of the string is considered a line even if it doesn't end with a newline. For example,
lines "" == [] lines "\n" == [""] lines "one" == ["one"] lines "one\n" == ["one"] lines "one\n\n" == ["one",""] lines "one\ntwo" == ["one","two"] lines "one\ntwo\n" == ["one","two"]
Thus lines s contains at least as many elements as newlines in s.
words :: String -> [String] Source
words breaks a string up into a list of words, which were delimited by white space.
unlines :: [String] -> String Source
unlines is an inverse operation to lines. It joins lines, after appending a terminating newline to each.
unwords :: [String] -> String Source
unwords is an inverse operation to words. It joins words with separating spaces.
String
type ShowS = String -> String Source
The shows functions return a function that prepends the output String to an existing String. This allows constant-time concatenation of results using function composition.
Conversion of values to readable Strings.
Derived instances of Show have the following properties, which are compatible with derived instances of Read:
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.showsPrec will produce infix applications of the constructor.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.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)".showsPrec :: Int -> a -> ShowS Source
Convert a value to a readable String.
showsPrec should satisfy the law
showsPrec d x r ++ s == showsPrec d x (r ++ s)
Derived instances of Read and Show satisfy the following:
That is, readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with.
A specialised variant of showsPrec, using precedence context zero, and returning an ordinary String.
showList :: [a] -> ShowS Source
The method showList is provided to allow the programmer to give a specialised way of showing lists of values. For example, this is used by the predefined Show instance of the Char type, where values of type String should be shown in double quotes, rather than between square brackets.
shows :: Show a => a -> ShowS Source
equivalent to showsPrec with a precedence of 0.
showChar :: Char -> ShowS Source
utility function converting a Char to a show function that simply prepends the character unchanged.
showString :: String -> ShowS Source
utility function converting a String to a show function that simply prepends the string unchanged.
showParen :: Bool -> ShowS -> ShowS Source
utility function that surrounds the inner show function with parentheses when the Bool parameter is True.
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).
Parsing of Strings, producing values.
Derived instances of Read make the following assumptions, which derived instances of Show obey:
Read instance will parse only infix applications of the constructor (not the prefix form).Read will parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration.Read instance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Read in Haskell 2010 is equivalent to
instance (Read a) => Read (Tree a) where
readsPrec d r = readParen (d > app_prec)
(\r -> [(Leaf m,t) |
("Leaf",s) <- lex r,
(m,t) <- readsPrec (app_prec+1) s]) r
++ readParen (d > up_prec)
(\r -> [(u:^:v,w) |
(u,s) <- readsPrec (up_prec+1) r,
(":^:",t) <- lex s,
(v,w) <- readsPrec (up_prec+1) t]) r
where app_prec = 10
up_prec = 5
Note that right-associativity of :^: is unused.
The derived instance in GHC is equivalent to
instance (Read a) => Read (Tree a) where
readPrec = parens $ (prec app_prec $ do
Ident "Leaf" <- lexP
m <- step readPrec
return (Leaf m))
+++ (prec up_prec $ do
u <- step readPrec
Symbol ":^:" <- lexP
v <- step readPrec
return (u :^: v))
where app_prec = 10
up_prec = 5
readListPrec = readListPrecDefault
readsPrec :: Int -> ReadS a Source
attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.
Derived instances of Read and Show satisfy the following:
That is, readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with.
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.
| 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 GeneralCategory | |
| Read Lexeme | |
| Read IOMode | |
| Read SomeSymbol | |
| Read SomeNat | |
| Read DecidedStrictness | |
| Read SourceStrictness | |
| Read SourceUnpackedness | |
| Read Associativity | |
| Read Fixity | |
| Read Any | |
| Read All | |
| Read SeekMode | |
| Read CUIntMax | |
| Read CIntMax | |
| Read CUIntPtr | |
| Read CIntPtr | |
| Read CSUSeconds | |
| Read CUSeconds | |
| Read CTime | |
| Read CClock | |
| Read CSigAtomic | |
| Read CWchar | |
| Read CSize | |
| Read CPtrdiff | |
| Read CDouble | |
| Read CFloat | |
| Read CULLong | |
| Read CLLong | |
| Read CULong | |
| Read CLong | |
| Read CUInt | |
| Read CInt | |
| Read CUShort | |
| Read CShort | |
| Read CUChar | |
| Read CSChar | |
| Read CChar | |
| Read 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 GCStats | |
| Read Version | |
| Read Void | Reading a |
| Read Natural | |
| Read a => Read [a] | |
| Read a => Read (Maybe a) | |
| (Integral a, Read a) => Read (Ratio a) | |
| Read (V1 p) | |
| Read (U1 p) | |
| Read p => Read (Par1 p) | |
| Read a => Read (Down 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 (ZipList a) | |
| Read a => Read (Complex a) | |
| HasResolution a => Read (Fixed a) | |
| Read a => Read (NonEmpty a) | |
| Read a => Read (Option a) | |
| Read m => Read (WrappedMonoid m) | |
| Read a => Read (Last a) | |
| Read a => Read (First a) | |
| Read a => Read (Max a) | |
| Read a => Read (Min a) | |
| Read a => Read (Identity a) | This instance would be equivalent to the derived instances of the |
| (Read a, Read b) => Read (Either a b) | |
| Read (f p) => Read (Rec1 f p) | |
| (Read a, Read b) => Read (a, b) | |
| Read (Proxy k s) | |
| (Read a, Read b) => Read (Arg a b) | |
| Read c => Read (K1 i c p) | |
| (Read (f p), Read (g p)) => Read ((:+:) f g p) | |
| (Read (f p), Read (g p)) => Read ((:*:) f g p) | |
| Read (f (g p)) => Read ((:.:) f g p) | |
| (Read a, Read b, Read c) => Read (a, b, c) | |
| (~) k a b => Read ((:~:) k a b) | |
| Coercible k a b => Read (Coercion k a b) | |
| Read (f a) => Read (Alt k f a) | |
| Read a => Read (Const k a b) | This instance would be equivalent to the derived instances of the |
| Read (f p) => Read (M1 i c f p) | |
| (Read a, Read b, Read c, Read d) => Read (a, b, c, d) | |
| (Read1 f, Read1 g, Read a) => Read (Product * f g a) | |
| (Read1 f, Read1 g, Read a) => Read (Sum * f g a) | |
| (Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) | |
| (Read1 f, Read1 g, Read a) => Read (Compose * * f g a) | |
| (Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | |
reads :: Read a => ReadS a Source
equivalent to readsPrec with a precedence of 0.
readParen :: Bool -> ReadS a -> ReadS a Source
readParen True p parses what p parses, but surrounded with parentheses.
readParen False p parses what p parses, but optionally surrounded with parentheses.
read :: Read a => String -> a Source
The read function reads input from a string, which must be completely consumed by the input process.
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:
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.
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]])
Read a character from the standard input device (same as hGetChar stdin).
Read a line from the standard input device (same as hGetLine stdin).
getContents :: IO String Source
The getContents operation returns all user input as a single string, which is read lazily as it is needed (same as hGetContents stdin).
interact :: (String -> String) -> IO () Source
The interact function takes a function of type String->String as its argument. The entire input from the standard input device is passed to this function as its argument, and the resulting string is output on the standard output device.
File and directory names are values of type String, whose precise meaning is operating system dependent. Files can be opened, yielding a handle which can then be used to operate on the contents of that file.
readFile :: FilePath -> IO String Source
The readFile function reads a file and returns the contents of the file as a string. The file is read lazily, on demand, as with getContents.
writeFile :: FilePath -> String -> IO () Source
The computation writeFile file str function writes the string str, to the file file.
appendFile :: FilePath -> String -> IO () Source
The computation appendFile file str function appends the string str, to the file file.
Note that writeFile and appendFile write a literal string to a file. To write a value of any printable type, as with print, use the show function to convert the value to a string first.
main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])
readIO :: Read a => String -> IO a Source
The readIO function is similar to read except that it signals parse failure to the IO monad instead of terminating the program.
readLn :: Read a => IO a Source
The readLn function combines getLine and readIO.
type IOError = IOException Source
The Haskell 2010 type for exceptions in the IO monad. Any I/O operation may raise an IOError instead of returning a result. For a more general type of exception, including also those that arise in pure code, see Exception.
In Haskell 2010, this is an opaque type.
ioError :: IOError -> IO a Source
Raise an IOError in the IO monad.
userError :: String -> IOError Source
Construct an IOError value with a string describing the error. The fail method of the IO instance of the Monad class raises a userError, thus:
instance Monad IO where ... fail s = ioError (userError s)
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Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.0.1/docs/html/libraries/base-4.9.0.0/Prelude.html