base-4.7.0.0: Basic libraries

Copyright | (c) The University of Glasgow 2001
License | BSD-style (see the file libraries/base/LICENSE)
Maintainer | libraries@haskell.org
Stability | stable
Portability | portable
Safe Haskell | Trustworthy
Language | Haskell2010

Prelude

Contents

- Standard types, classes and related functions
  - Basic data types
    - Tuples
  - Basic type classes
  - Numbers
    - Numeric types
    - Numeric type classes
    - Numeric functions
  - Monads and functors
  - Miscellaneous functions
- List operations
  - Reducing lists (folds)
    - Special folds
  - Building lists
    - Scans
    - Infinite lists
  - Sublists
  - Searching lists
  - Zipping and unzipping lists
  - Functions on strings
- Converting to and from `String`
  - Converting to `String`
  - Converting from `String`
- Basic Input and output
  - Simple I/O operations
    - Output functions
    - Input functions
    - Files
  - Exception handling in the I/O monad

Description

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.

Synopsis

- data Bool :: *
  - = False
  - | True
- (&&) :: Bool -> Bool -> Bool
- (||) :: Bool -> Bool -> Bool
- not :: Bool -> Bool
- otherwise :: Bool
- data Maybe a
  - = Nothing
  - | Just a
- maybe :: b -> (a -> b) -> Maybe a -> b
- data Either a b
  - = Left a
  - | Right b
- either :: (a -> c) -> (b -> c) -> Either a b -> c
- data Ordering :: *
  - = LT
  - | EQ
  - | GT
- data Char :: *
- type String = [Char]
- fst :: (a, b) -> a
- snd :: (a, b) -> b
- curry :: ((a, b) -> c) -> a -> b -> c
- uncurry :: (a -> b -> c) -> (a, b) -> c
- class Eq a where
  - (==) :: a -> a -> Bool
  - (/=) :: a -> a -> Bool
- class Eq a => Ord a where
  - compare :: a -> a -> Ordering
  - (<) :: a -> a -> Bool
  - (>=) :: a -> a -> Bool
  - (>) :: a -> a -> Bool
  - (<=) :: a -> a -> Bool
  - max :: a -> a -> a
  - min :: a -> a -> a
- class Enum a where
  - succ :: a -> a
  - pred :: a -> a
  - toEnum :: Int -> a
  - fromEnum :: a -> Int
  - enumFrom :: a -> [a]
  - enumFromThen :: a -> a -> [a]
  - enumFromTo :: a -> a -> [a]
  - enumFromThenTo :: a -> a -> a -> [a]
- class Bounded a where
  - minBound, maxBound :: a
- data Int :: *
- data Integer :: *
- data Float :: *
- data Double :: *
- type Rational = Ratio Integer
- class Num a where
  - (+), (*), (-) :: a -> a -> a
  - negate :: a -> a
  - abs :: a -> a
  - signum :: a -> a
  - fromInteger :: Integer -> a
- class (Num a, Ord a) => Real a where
  - toRational :: a -> Rational
- class (Real a, Enum a) => Integral a where
  - quot :: a -> a -> a
  - rem :: a -> a -> a
  - div :: a -> a -> a
  - mod :: a -> a -> a
  - quotRem :: a -> a -> (a, a)
  - divMod :: a -> a -> (a, a)
  - toInteger :: a -> Integer
- class Num a => Fractional a where
  - (/) :: a -> a -> a
  - recip :: a -> a
  - fromRational :: Rational -> a
- class Fractional a => Floating a where
  - pi :: a
  - exp, sqrt, log :: a -> a
  - (**), logBase :: a -> a -> a
  - sin, tan, cos :: a -> a
  - asin, atan, acos :: a -> a
  - sinh, tanh, cosh :: a -> a
  - asinh, atanh, acosh :: a -> a
- class (Real a, Fractional a) => RealFrac a where
  - properFraction :: Integral b => a -> (b, a)
  - truncate :: Integral b => a -> b
  - round :: Integral b => a -> b
  - ceiling :: Integral b => a -> b
  - floor :: Integral b => a -> b
- class (RealFrac a, Floating a) => RealFloat a where
  - floatRadix :: a -> Integer
  - floatDigits :: a -> Int
  - floatRange :: a -> (Int, Int)
  - decodeFloat :: a -> (Integer, Int)
  - encodeFloat :: Integer -> Int -> a
  - exponent :: a -> Int
  - significand :: a -> a
  - scaleFloat :: Int -> a -> a
  - isNaN :: a -> Bool
  - isInfinite :: a -> Bool
  - isDenormalized :: a -> Bool
  - isNegativeZero :: a -> Bool
  - isIEEE :: a -> Bool
  - atan2 :: a -> a -> a
- subtract :: Num a => a -> a -> a
- even :: Integral a => a -> Bool
- odd :: Integral a => a -> Bool
- gcd :: Integral a => a -> a -> a
- lcm :: Integral a => a -> a -> a
- (^) :: (Num a, Integral b) => a -> b -> a
- (^^) :: (Fractional a, Integral b) => a -> b -> a
- fromIntegral :: (Integral a, Num b) => a -> b
- realToFrac :: (Real a, Fractional b) => a -> b
- class Monad m where
  - (>>=) :: forall a b. m a -> (a -> m b) -> m b
  - (>>) :: forall a b. m a -> m b -> m b
  - return :: a -> m a
  - fail :: String -> m a
- class Functor f where
  - fmap :: (a -> b) -> f a -> f b
- mapM :: Monad m => (a -> m b) -> [a] -> m [b]
- mapM_ :: Monad m => (a -> m b) -> [a] -> m ()
- sequence :: Monad m => [m a] -> m [a]
- sequence_ :: Monad m => [m a] -> m ()
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- id :: a -> a
- const :: a -> b -> a
- (.) :: (b -> c) -> (a -> b) -> a -> c
- flip :: (a -> b -> c) -> b -> a -> c
- ($) :: (a -> b) -> a -> b
- until :: (a -> Bool) -> (a -> a) -> a -> a
- asTypeOf :: a -> a -> a
- error :: [Char] -> a
- undefined :: a
- seq :: a -> b -> b
- ($!) :: (a -> b) -> a -> b
- map :: (a -> b) -> [a] -> [b]
- (++) :: [a] -> [a] -> [a]
- filter :: (a -> Bool) -> [a] -> [a]
- head :: [a] -> a
- last :: [a] -> a
- tail :: [a] -> [a]
- init :: [a] -> [a]
- null :: [a] -> Bool
- length :: [a] -> Int
- (!!) :: [a] -> Int -> a
- reverse :: [a] -> [a]
- foldl :: (b -> a -> b) -> b -> [a] -> b
- foldl1 :: (a -> a -> a) -> [a] -> a
- foldr :: (a -> b -> b) -> b -> [a] -> b
- foldr1 :: (a -> a -> a) -> [a] -> a
- and :: [Bool] -> Bool
- or :: [Bool] -> Bool
- any :: (a -> Bool) -> [a] -> Bool
- all :: (a -> Bool) -> [a] -> Bool
- sum :: Num a => [a] -> a
- product :: Num a => [a] -> a
- concat :: [[a]] -> [a]
- concatMap :: (a -> [b]) -> [a] -> [b]
- maximum :: Ord a => [a] -> a
- minimum :: Ord a => [a] -> a
- scanl :: (b -> a -> b) -> b -> [a] -> [b]
- scanl1 :: (a -> a -> a) -> [a] -> [a]
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanr1 :: (a -> a -> a) -> [a] -> [a]
- iterate :: (a -> a) -> a -> [a]
- repeat :: a -> [a]
- replicate :: Int -> a -> [a]
- cycle :: [a] -> [a]
- take :: Int -> [a] -> [a]
- drop :: Int -> [a] -> [a]
- splitAt :: Int -> [a] -> ([a], [a])
- takeWhile :: (a -> Bool) -> [a] -> [a]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- span :: (a -> Bool) -> [a] -> ([a], [a])
- break :: (a -> Bool) -> [a] -> ([a], [a])
- elem :: Eq a => a -> [a] -> Bool
- notElem :: Eq a => a -> [a] -> Bool
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- zip :: [a] -> [b] -> [(a, b)]
- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
- unzip :: [(a, b)] -> ([a], [b])
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- lines :: String -> [String]
- words :: String -> [String]
- unlines :: [String] -> String
- unwords :: [String] -> String
- type ShowS = String -> String
- class Show a where
  - showsPrec :: Int -> a -> ShowS
  - show :: a -> String
  - showList :: [a] -> ShowS
- shows :: Show a => a -> ShowS
- showChar :: Char -> ShowS
- showString :: String -> ShowS
- showParen :: Bool -> ShowS -> ShowS
- type ReadS a = String -> [(a, String)]
- class Read a where
  - readsPrec :: Int -> ReadS a
  - readList :: ReadS [a]
- reads :: Read a => ReadS a
- readParen :: Bool -> ReadS a -> ReadS a
- read :: Read a => String -> a
- lex :: ReadS String
- data IO a :: * -> *
- putChar :: Char -> IO ()
- putStr :: String -> IO ()
- putStrLn :: String -> IO ()
- print :: Show a => a -> IO ()
- getChar :: IO Char
- getLine :: IO String
- getContents :: IO String
- interact :: (String -> String) -> IO ()
- type FilePath = String
- readFile :: FilePath -> IO String
- writeFile :: FilePath -> String -> IO ()
- appendFile :: FilePath -> String -> IO ()
- readIO :: Read a => String -> IO a
- readLn :: Read a => IO a
- type IOError = IOException
- ioError :: IOError -> IO a
- userError :: String -> IOError

# Standard types, classes and related functions

## Basic data types

data Bool :: * Source

Constructors

False |
True |

Instances

Bounded Bool |
Enum Bool |
Eq Bool |
Data Bool |
Ord Bool |
Read Bool |
Show Bool |
Ix Bool |
Generic Bool |
Typeable Bool |
FiniteBits Bool |
Bits Bool |
Storable Bool |
Typeable * Bool |
type Rep Bool |
type (==) Bool a b |

(&&) :: Bool -> Bool -> Bool infixr 3 Source

Boolean "and"

(||) :: Bool -> Bool -> Bool infixr 2 Source

Boolean "or"

not :: Bool -> Bool Source

Boolean "not"

otherwise :: Bool

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

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

data Maybe a

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

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

Constructors

Nothing |
Just a |

Instances

Alternative Maybe |
Monad Maybe |
Functor Maybe |
MonadFix Maybe |
MonadPlus Maybe |
Applicative Maybe |
Foldable Maybe |
Traversable Maybe |
Generic1 Maybe |
Typeable1 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) |
Monoid a => Monoid (Maybe a) | Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `e*e = e` and `e*s = s = s*e` for all `s ∈ S`." Since there is no "Semigroup" typeclass providing just `mappend`, we use `Monoid` instead.
Typeable (* -> *) Maybe |
type Rep1 Maybe |
type Rep (Maybe a) |
type (==) (Maybe k) a b |

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

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

data Either a b

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

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

Constructors

Left a |
Right b |

Instances

Monad (Either e) |
Functor (Either a) |
MonadFix (Either e) |
Applicative (Either e) |
Foldable (Either a) |
Traversable (Either a) |
Generic1 (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) |
Typeable (* -> * -> *) Either |
type Rep1 (Either a) |
type Rep (Either a b) |
type (==) (Either k k1) a b |

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

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

data Ordering :: * Source

Constructors

LT |
EQ |
GT |

Instances

Bounded Ordering |
Enum Ordering |
Eq Ordering |
Data Ordering |
Ord Ordering |
Read Ordering |
Show Ordering |
Ix Ordering |
Generic Ordering |
Typeable Ordering |
Monoid Ordering |
Typeable * Ordering |
type Rep Ordering |
type (==) Ordering a b |

data Char :: * Source

The character type `Char` is an enumeration whose values represent Unicode (or equivalently ISO/IEC 10646) characters (see http://www.unicode.org/ for details). This set extends the ISO 8859-1 (Latin-1) character set (the first 256 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`).

Instances

Bounded Char |
Enum Char |
Eq Char |
Data Char |
Ord Char |
Read Char |
Show Char |
Ix Char |
Generic Char |
Typeable Char |
Storable Char |
IsChar Char |
PrintfArg Char |
Typeable * Char |
IsString [Char] |
type Rep Char |

type String = [Char]

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

### Tuples

fst :: (a, b) -> a

Extract the first component of a pair.

snd :: (a, b) -> b

Extract the second component of a pair.

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

`curry` converts an uncurried function to a curried function.

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

`uncurry` converts a curried function to a function on pairs.

## Basic type classes

class Eq a where Source

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 `/=`.

Minimal complete definition

(==) | (/=)

Methods

(==) :: a -> a -> Bool infix 4 Source

(/=) :: a -> a -> Bool infix 4 Source

Instances

Eq Bool |
Eq Char |
Eq Double |
Eq Float |
Eq Int |
Eq Int8 |
Eq Int16 |
Eq Int32 |
Eq Int64 |
Eq Integer |
Eq Ordering |
Eq Word |
Eq Word8 |
Eq Word16 |
Eq Word32 |
Eq Word64 |
Eq () |
Eq Number |
Eq Lexeme |
Eq Fingerprint |
Eq TyCon |
Eq TypeRep |
Eq Associativity |
Eq Fixity |
Eq Arity |
Eq Any |
Eq All |
Eq ArithException |
Eq ErrorCall |
Eq IOException |
Eq MaskingState |
Eq CUIntMax |
Eq CIntMax |
Eq CUIntPtr |
Eq CIntPtr |
Eq CSUSeconds |
Eq CUSeconds |
Eq CTime |
Eq CClock |
Eq CSigAtomic |
Eq CWchar |
Eq CSize |
Eq CPtrdiff |
Eq CDouble |
Eq CFloat |
Eq CULLong |
Eq CLLong |
Eq CULong |
Eq CLong |
Eq CUInt |
Eq CInt |
Eq CUShort |
Eq CShort |
Eq CUChar |
Eq CSChar |
Eq CChar |
Eq GeneralCategory |
Eq IntPtr |
Eq WordPtr |
Eq BufferState |
Eq CodingProgress |
Eq SeekMode |
Eq IODeviceType |
Eq NewlineMode |
Eq Newline |
Eq BufferMode |
Eq Handle |
Eq IOErrorType |
Eq ExitCode |
Eq ArrayException |
Eq AsyncException |
Eq Errno |
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 ThreadStatus |
Eq BlockReason |
Eq ThreadId |
Eq IOMode |
Eq Event |
Eq FdKey |
Eq TimeoutKey |
Eq HandlePosn |
Eq TyCon |
Eq TypeRep |
Eq TypeRepKey |
Eq SomeSymbol |
Eq SomeNat |
Eq Version |
Eq Fixity |
Eq ConstrRep |
Eq DataRep |
Eq Constr | Equality of constructors
Eq Unique |
Eq SpecConstrAnnotation |
Eq a => Eq [a] |
Eq a => Eq (Ratio a) |
Eq (StablePtr a) |
Eq (Ptr a) |
Eq (FunPtr a) |
Eq (U1 p) |
Eq p => Eq (Par1 p) |
Eq a => Eq (Maybe a) |
Eq a => Eq (Down 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 (IORef a) |
Eq (MVar a) |
Eq (ForeignPtr a) |
Eq (TVar a) |
Eq (Chan a) |
Eq a => Eq (ZipList a) |
Eq a => Eq (Complex a) |
Eq (Fixed a) |
Eq (StableName a) |
(Eq a, Eq b) => Eq (Either a b) |
Eq (f p) => Eq (Rec1 f p) |
(Eq a, Eq b) => Eq (a, b) |
Eq (STRef s a) |
Eq (Proxy k s) |
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 p) => Eq (M1 i c f p) |
(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) |
(Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |

class Eq a => Ord a where Source

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.

Minimal complete definition

compare | (<=)

Methods

compare :: a -> a -> Ordering Source

(<) :: a -> a -> Bool infix 4 Source

(>=) :: a -> a -> Bool infix 4 Source

(>) :: a -> a -> Bool infix 4 Source

(<=) :: a -> a -> Bool infix 4 Source

max :: a -> a -> a Source

min :: a -> a -> a Source

Instances

Ord Bool |
Ord Char |
Ord Double |
Ord Float |
Ord Int |
Ord Int8 |
Ord Int16 |
Ord Int32 |
Ord Int64 |
Ord Integer |
Ord Ordering |
Ord Word |
Ord Word8 |
Ord Word16 |
Ord Word32 |
Ord Word64 |
Ord () |
Ord Fingerprint |
Ord TyCon |
Ord TypeRep |
Ord Associativity |
Ord Fixity |
Ord Arity |
Ord Any |
Ord All |
Ord ArithException |
Ord ErrorCall |
Ord CUIntMax |
Ord CIntMax |
Ord CUIntPtr |
Ord CIntPtr |
Ord CSUSeconds |
Ord CUSeconds |
Ord CTime |
Ord CClock |
Ord CSigAtomic |
Ord CWchar |
Ord CSize |
Ord CPtrdiff |
Ord CDouble |
Ord CFloat |
Ord CULLong |
Ord CLLong |
Ord CULong |
Ord CLong |
Ord CUInt |
Ord CInt |
Ord CUShort |
Ord CShort |
Ord CUChar |
Ord CSChar |
Ord CChar |
Ord GeneralCategory |
Ord IntPtr |
Ord WordPtr |
Ord SeekMode |
Ord NewlineMode |
Ord Newline |
Ord BufferMode |
Ord ExitCode |
Ord ArrayException |
Ord AsyncException |
Ord Fd |
Ord CRLim |
Ord CTcflag |
Ord CSpeed |
Ord CCc |
Ord CUid |
Ord CNlink |
Ord CGid |
Ord CSsize |
Ord CPid |
Ord COff |
Ord CMode |
Ord CIno |
Ord CDev |
Ord ThreadStatus |
Ord BlockReason |
Ord ThreadId |
Ord IOMode |
Ord TyCon |
Ord TypeRep |
Ord TypeRepKey |
Ord SomeSymbol |
Ord SomeNat |
Ord Version |
Ord Unique |
Ord a => Ord [a] |
Integral a => Ord (Ratio a) |
Ord (Ptr a) |
Ord (FunPtr a) |
Ord (U1 p) |
Ord p => Ord (Par1 p) |
Ord a => Ord (Maybe a) |
Ord a => Ord (Down 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 (ZipList a) |
Ord (Fixed a) |
(Ord a, Ord b) => Ord (Either a b) |
Ord (f p) => Ord (Rec1 f p) |
(Ord a, Ord b) => Ord (a, b) |
Ord (Proxy k s) |
Ord c => Ord (K1 i c p) |
(Ord (f p), Ord (g p)) => Ord ((:+:) f g p) |
(Ord (f p), Ord (g p)) => Ord ((:*:) f g p) |
Ord (f (g p)) => Ord ((:.:) f g p) |
(Ord a, Ord b, Ord c) => Ord (a, b, c) |
Ord ((:~:) k a b) |
Ord (Coercion k a b) |
Ord (f p) => Ord (M1 i c f p) |
(Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) |
(Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |

class Enum a where

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:

- The calls ``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

Minimal complete definition

toEnum, fromEnum

Methods

succ :: a -> a

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

pred :: a -> a

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

toEnum :: Int -> a

Convert from an `Int`.

fromEnum :: a -> 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`.

enumFrom :: a -> [a]

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

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

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

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

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

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

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

Instances

Enum Bool |
Enum Char |
Enum Double |
Enum Float |
Enum Int |
Enum Int8 |
Enum Int16 |
Enum Int32 |
Enum Int64 |
Enum Integer |
Enum Ordering |
Enum Word |
Enum Word8 |
Enum Word16 |
Enum Word32 |
Enum Word64 |
Enum () |
Enum CUIntMax |
Enum CIntMax |
Enum CUIntPtr |
Enum CIntPtr |
Enum CSUSeconds |
Enum CUSeconds |
Enum CTime |
Enum CClock |
Enum CSigAtomic |
Enum CWchar |
Enum CSize |
Enum CPtrdiff |
Enum CDouble |
Enum CFloat |
Enum CULLong |
Enum CLLong |
Enum CULong |
Enum CLong |
Enum CUInt |
Enum CInt |
Enum CUShort |
Enum CShort |
Enum CUChar |
Enum CSChar |
Enum CChar |
Enum GeneralCategory |
Enum IntPtr |
Enum WordPtr |
Enum SeekMode |
Enum Fd |
Enum CRLim |
Enum CTcflag |
Enum CSpeed |
Enum CCc |
Enum CUid |
Enum CNlink |
Enum CGid |
Enum CSsize |
Enum CPid |
Enum COff |
Enum CMode |
Enum CIno |
Enum CDev |
Enum IOMode |
Integral a => Enum (Ratio a) |
Enum (Fixed a) |
Enum (Proxy k s) |
(~) k a b => Enum ((:~:) k a b) |
Coercible k a b => Enum (Coercion k a b) |

class Bounded a where

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

The `Bounded` class may be derived for any enumeration type; `minBound` is the first constructor listed in the `data` declaration and `maxBound` is the last. `Bounded` may also be derived for single-constructor datatypes whose constituent types are in `Bounded`.

Methods

minBound, maxBound :: a

Instances

Bounded Bool |
Bounded Char |
Bounded Int |
Bounded Int8 |
Bounded Int16 |
Bounded Int32 |
Bounded Int64 |
Bounded Ordering |
Bounded Word |
Bounded Word8 |
Bounded Word16 |
Bounded Word32 |
Bounded Word64 |
Bounded () |
Bounded Any |
Bounded All |
Bounded CUIntMax |
Bounded CIntMax |
Bounded CUIntPtr |
Bounded CIntPtr |
Bounded CSigAtomic |
Bounded CWchar |
Bounded CSize |
Bounded CPtrdiff |
Bounded CULLong |
Bounded CLLong |
Bounded CULong |
Bounded CLong |
Bounded CUInt |
Bounded CInt |
Bounded CUShort |
Bounded CShort |
Bounded CUChar |
Bounded CSChar |
Bounded CChar |
Bounded GeneralCategory |
Bounded IntPtr |
Bounded WordPtr |
Bounded Fd |
Bounded CRLim |
Bounded CTcflag |
Bounded CUid |
Bounded CNlink |
Bounded CGid |
Bounded CSsize |
Bounded CPid |
Bounded COff |
Bounded CMode |
Bounded CIno |
Bounded CDev |
Bounded a => Bounded (Product a) |
Bounded a => Bounded (Sum a) |
Bounded a => Bounded (Dual a) |
(Bounded a, Bounded b) => Bounded (a, b) |
Bounded (Proxy k s) |
(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) |
(~) k a b => Bounded ((:~:) k a b) |
Coercible k a b => Bounded (Coercion k a b) |
(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |

## Numbers

### Numeric types

data Int :: * Source

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

Instances

Bounded Int |
Enum Int |
Eq Int |
Integral Int |
Data Int |
Num Int |
Ord Int |
Read Int |
Real Int |
Show Int |
Ix Int |
Generic Int |
Typeable Int |
FiniteBits Int |
Bits Int |
Storable Int |
PrintfArg Int |
Typeable * Int |
type Rep Int |

data Integer :: * Source

Arbitrary-precision integers.

Instances

Enum Integer |
Eq Integer |
Integral Integer |
Data Integer |
Num Integer |
Ord Integer |
Read Integer |
Real Integer |
Show Integer |
Ix Integer |
Typeable Integer |
Bits Integer |
PrintfArg Integer |
Typeable * Integer |

data Float :: * Source

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

Instances

Enum Float |
Eq Float |
Floating Float |
Fractional Float |
Data Float |
Num Float |
Ord Float |
Read Float |
Real Float |
RealFloat Float |
RealFrac Float |
Show Float |
Generic Float |
Typeable Float |
Storable Float |
PrintfArg Float |
Typeable * Float |
type Rep Float |

data Double :: * Source

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

Instances

Enum Double |
Eq Double |
Floating Double |
Fractional Double |
Data Double |
Num Double |
Ord Double |
Read Double |
Real Double |
RealFloat Double |
RealFrac Double |
Show Double |
Generic Double |
Typeable Double |
Storable Double |
PrintfArg Double |
Typeable * Double |
type Rep Double |

type Rational = Ratio Integer

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

### Numeric type classes

class Num a where

Basic numeric class.

Minimal complete definition: all except `negate` or `(-)`

Minimal complete definition

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

Methods

(+), (*), (-) :: a -> a -> a infixl 7 *infixl 6 +, -

negate :: a -> a

Unary negation.

abs :: a -> a

Absolute value.

signum :: a -> a

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

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`.

Instances

Num Double |
Num Float |
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 |
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) |

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

Methods

toRational :: a -> Rational

the rational equivalent of its real argument with full precision

Instances

Real Double |
Real Float |
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 |
Integral a => Real (Ratio a) |
HasResolution a => Real (Fixed a) |

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

Integral numbers, supporting integer division.

Minimal complete definition: `quotRem` and `toInteger`

Minimal complete definition

quotRem, toInteger

Methods

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

integer division truncated toward zero

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

integer remainder, satisfying

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

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

integer division truncated toward negative infinity

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

integer modulus, satisfying

    (x `div` y)*y + (x `mod` y) == x

quotRem :: a -> a -> (a, a)

simultaneous `quot` and `rem`

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

simultaneous `div` and `mod`

toInteger :: a -> Integer

conversion to `Integer`

Instances

Integral Int |
Integral Int8 |
Integral Int16 |
Integral Int32 |
Integral Int64 |
Integral Integer |
Integral Word |
Integral Word8 |
Integral Word16 |
Integral Word32 |
Integral Word64 |
Integral CUIntMax |
Integral CIntMax |
Integral CUIntPtr |
Integral CIntPtr |
Integral CSigAtomic |
Integral CWchar |
Integral CSize |
Integral CPtrdiff |
Integral CULLong |
Integral CLLong |
Integral CULong |
Integral CLong |
Integral CUInt |
Integral CInt |
Integral CUShort |
Integral CShort |
Integral CUChar |
Integral CSChar |
Integral CChar |
Integral IntPtr |
Integral WordPtr |
Integral Fd |
Integral CRLim |
Integral CTcflag |
Integral CUid |
Integral CNlink |
Integral CGid |
Integral CSsize |
Integral CPid |
Integral COff |
Integral CMode |
Integral CIno |
Integral CDev |

class Num a => Fractional a where

Fractional numbers, supporting real division.

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

Minimal complete definition

fromRational, (recip | (/))

Methods

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

fractional division

recip :: a -> a

reciprocal fraction

fromRational :: Rational -> a

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`.

Instances

Fractional Double |
Fractional Float |
Fractional CDouble |
Fractional CFloat |
Integral a => Fractional (Ratio a) |
RealFloat a => Fractional (Complex a) |
HasResolution a => Fractional (Fixed a) |

class Fractional a => Floating a where

Trigonometric and hyperbolic functions and related functions.

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

Minimal complete definition

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

Methods

pi :: a

exp, sqrt, log :: a -> a

(**), logBase :: a -> a -> a infixr 8

sin, tan, cos :: a -> a

asin, atan, acos :: a -> a

sinh, tanh, cosh :: a -> a

asinh, atanh, acosh :: a -> a

Instances

Floating Double |
Floating Float |
Floating CDouble |
Floating CFloat |
RealFloat a => Floating (Complex a) |

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

Extracting components of fractions.

Minimal complete definition: `properFraction`

Minimal complete definition

properFraction

Methods

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

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

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

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

truncate :: Integral b => a -> b

``truncate` x` returns the integer nearest `x` between zero and `x`

round :: Integral b => a -> b

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

ceiling :: Integral b => a -> b

``ceiling` x` returns the least integer not less than `x`

floor :: Integral b => a -> b

``floor` x` returns the greatest integer not greater than `x`

Instances

RealFrac Double |
RealFrac Float |
RealFrac CDouble |
RealFrac CFloat |
Integral a => RealFrac (Ratio a) |
HasResolution a => RealFrac (Fixed a) |

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

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

Minimal complete definition: all except `exponent`, `significand`, `scaleFloat` and `atan2`

Minimal complete definition

floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE

Methods

floatRadix :: a -> Integer

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

floatDigits :: a -> Int

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

floatRange :: a -> (Int, Int)

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

decodeFloat :: a -> (Integer, Int)

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

`encodeFloat` performs the inverse of `decodeFloat` in the sense that for finite `x` with the exception of `-0.0`, ``uncurry` `encodeFloat` (`decodeFloat` x) = x`. ``encodeFloat` m n` is one of the two closest representable floating-point numbers to `m*b^^n` (or `±Infinity` if overflow occurs); usually the closer, but if `m` contains too many bits, the result may be rounded in the wrong direction.

exponent :: a -> Int

`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

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

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

isNaN :: a -> Bool

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

isInfinite :: a -> Bool

`True` if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> Bool

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

isNegativeZero :: a -> Bool

`True` if the argument is an IEEE negative zero

isIEEE :: a -> Bool

`True` if the argument is an IEEE floating point number

atan2 :: a -> a -> a

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.

Instances

RealFloat Double |
RealFloat Float |
RealFloat CDouble |
RealFloat CFloat |

### Numeric functions

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

the same as ``flip` (`-`)`.

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

even :: Integral a => a -> Bool

odd :: Integral a => a -> Bool

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

``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

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

(^) :: (Num a, Integral b) => a -> b -> a infixr 8

raise a number to a non-negative integral power

(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8

raise a number to an integral power

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

general coercion from integral types

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

general coercion to fractional types

## Monads and functors

class Monad m where

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

Minimal complete definition: `>>=` and `return`.

Instances of `Monad` should satisfy the following laws:

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

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

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

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

Minimal complete definition

(>>=), return

Methods

(>>=) :: forall a b. m a -> (a -> m b) -> m b infixl 1

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

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

return :: a -> m a

Inject a value into the monadic type.

fail :: String -> m a

Fail with a message. This operation is not part of the mathematical definition of a monad, but is invoked on pattern-match failure in a `do` expression.

Instances

Monad [] |
Monad IO |
Monad Maybe |
Monad ReadP |
Monad ReadPrec |
Monad STM |
Monad ((->) r) |
Monad (Either e) |
Monad (ST s) |
Monad (Proxy *) |
ArrowApply a => Monad (ArrowMonad a) |
Monad (ST s) |
Monad m => Monad (WrappedMonad m) |

class Functor f where

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

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

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

Methods

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

Instances

Functor [] |
Functor IO |
Functor Maybe |
Functor ReadP |
Functor ReadPrec |
Functor STM |
Functor Handler |
Functor ZipList |
Functor ArgDescr |
Functor OptDescr |
Functor ArgOrder |
Functor ((->) r) |
Functor (Either a) |
Functor ((,) a) |
Functor (ST s) |
Functor (Proxy *) |
Arrow a => Functor (ArrowMonad a) |
Functor (ST s) |
Monad m => Functor (WrappedMonad m) |
Functor (Const m) |
Arrow a => Functor (WrappedArrow a b) |

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

``mapM` f` is equivalent to ``sequence` . `map` f`.

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

``mapM_` f` is equivalent to ``sequence_` . `map` f`.

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

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

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

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

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1

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

## Miscellaneous functions

id :: a -> a

Identity function.

const :: a -> b -> a

Constant function.

(.) :: (b -> c) -> (a -> b) -> a -> c infixr 9

Function composition.

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

``flip` f` takes its (first) two arguments in the reverse order of `f`.

($) :: (a -> b) -> a -> b infixr 0

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

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

asTypeOf :: a -> a -> a

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

error :: [Char] -> a

`error` stops execution and displays an error message.

undefined :: a

A special case of `error`. It is expected that compilers will recognize this and insert error messages which are more appropriate to the context in which `undefined` appears.

seq :: a -> b -> b Source

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

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

Strict (call-by-value) application, defined in terms of `seq`.

# List operations

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

`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

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]

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

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

head :: [a] -> a

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

last :: [a] -> a

Extract the last element of a list, which must be finite and non-empty.

tail :: [a] -> [a]

Extract the elements after the head of a list, which must be non-empty.

init :: [a] -> [a]

Return all the elements of a list except the last one. The list must be non-empty.

null :: [a] -> Bool

Test whether a list is empty.

length :: [a] -> Int

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

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

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

reverse :: [a] -> [a]

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

## Reducing lists (folds)

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

`foldl`, applied to a binary operator, a starting value (typically the left-identity of the operator), and a list, reduces the list using the binary operator, from left to right:

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

The list must be finite.

foldl1 :: (a -> a -> a) -> [a] -> a

`foldl1` is a variant of `foldl` that has no starting value argument, and thus must be applied to non-empty lists.

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

`foldr`, applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left:

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

foldr1 :: (a -> a -> a) -> [a] -> a

`foldr1` is a variant of `foldr` that has no starting value argument, and thus must be applied to non-empty lists.

### Special folds

and :: [Bool] -> Bool

`and` returns the conjunction of a Boolean list. For the result to be `True`, the list must be finite; `False`, however, results from a `False` value at a finite index of a finite or infinite list.

or :: [Bool] -> Bool

`or` returns the disjunction of a Boolean list. For the result to be `False`, the list must be finite; `True`, however, results from a `True` value at a finite index of a finite or infinite list.

any :: (a -> Bool) -> [a] -> Bool

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

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

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

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

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

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

The `product` function computes the product of a finite list of numbers.

concat :: [[a]] -> [a]

Concatenate a list of lists.

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

Map a function over a list and concatenate the results.

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

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

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

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

## Building lists

### Scans

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

`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]

`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]

`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]

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

### Infinite lists

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

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

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

repeat :: a -> [a]

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

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

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

cycle :: [a] -> [a]

`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]

`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]

`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])

`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]

`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]

`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])

`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])

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

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

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

## Searching lists

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

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

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

`notElem` is the negation of `elem`.

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

`lookup` `key assocs` looks up a key in an association list.

## Zipping and unzipping lists

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

`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)]

`zip3` takes three lists and returns a list of triples, analogous to `zip`.

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

`zipWith` generalises `zip` by zipping with the function given as the first argument, instead of a tupling function. For example, ``zipWith` (+)` is applied to two lists to produce the list of corresponding sums.

zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]

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])

`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])

The `unzip3` function takes a list of triples and returns three lists, analogous to `unzip`.

## Functions on strings

lines :: String -> [String]

`lines` breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.

words :: String -> [String]

`words` breaks a string up into a list of words, which were delimited by white space.

unlines :: [String] -> String

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

unwords :: [String] -> String

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

# Converting to and from `String`

## Converting to `String`

type ShowS = String -> String

The `shows` functions return a function that prepends the output `String` to an existing `String`. This allows constant-time concatenation of results using function composition.

class Show a where

Conversion of values to readable `String`s.

Minimal complete definition: `showsPrec` or `show`.

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

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

For example, given the declarations

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

the derived instance of `Show` is equivalent to

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

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

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

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

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

Minimal complete definition

showsPrec | show

Methods

showsPrec

Arguments

:: Int | the operator precedence of the enclosing context (a number from `0` to `11`). Function application has precedence `10`.
-> a | the value to be converted to a `String`
-> ShowS |

Convert a value to a readable `String`.

`showsPrec` should satisfy the law

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

Derived instances of `Read` and `Show` satisfy the following:

- `(x,"")` is an element of `(`readsPrec` d (`showsPrec` d x ""))`.

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

show :: a -> String

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

showList :: [a] -> ShowS

The method `showList` is provided to allow the programmer to give a specialised way of showing lists of values. For example, this is used by the predefined `Show` instance of the `Char` type, where values of type `String` should be shown in double quotes, rather than between square brackets.

Instances

Show Bool |
Show Char |
Show Double |
Show Float |
Show Int |
Show Int8 |
Show Int16 |
Show Int32 |
Show Int64 |
Show Integer |
Show Ordering |
Show Word |
Show Word8 |
Show Word16 |
Show Word32 |
Show Word64 |
Show () |
Show SomeException |
Show Number |
Show Lexeme |
Show Fingerprint |
Show TyCon |
Show TypeRep |
Show Associativity |
Show Fixity |
Show Arity |
Show Any |
Show All |
Show ArithException |
Show ErrorCall |
Show IOException |
Show MaskingState |
Show Dynamic |
Show CUIntMax |
Show CIntMax |
Show CUIntPtr |
Show CIntPtr |
Show CSUSeconds |
Show CUSeconds |
Show CTime |
Show CClock |
Show CSigAtomic |
Show CWchar |
Show CSize |
Show CPtrdiff |
Show CDouble |
Show CFloat |
Show CULLong |
Show CLLong |
Show CULong |
Show CLong |
Show CUInt |
Show CInt |
Show CUShort |
Show CShort |
Show CUChar |
Show CSChar |
Show CChar |
Show GeneralCategory |
Show IntPtr |
Show WordPtr |
Show CodingProgress |
Show TextEncoding |
Show SeekMode |
Show NewlineMode |
Show Newline |
Show BufferMode |
Show Handle |
Show IOErrorType |
Show ExitCode |
Show ArrayException |
Show AsyncException |
Show SomeAsyncException |
Show AssertionFailed |
Show Deadlock |
Show BlockedIndefinitelyOnSTM |
Show BlockedIndefinitelyOnMVar |
Show Fd |
Show CRLim |
Show CTcflag |
Show CSpeed |
Show CCc |
Show CUid |
Show CNlink |
Show CGid |
Show CSsize |
Show CPid |
Show COff |
Show CMode |
Show CIno |
Show CDev |
Show CodingFailureMode |
Show ThreadStatus |
Show BlockReason |
Show ThreadId |
Show NestedAtomically |
Show NonTermination |
Show NoMethodError |
Show RecUpdError |
Show RecConError |
Show RecSelError |
Show PatternMatchFail |
Show IOMode |
Show Event |
Show FdKey |
Show HandlePosn |
Show TyCon |
Show TypeRep |
Show SomeSymbol |
Show SomeNat |
Show Version |
Show Fixity |
Show ConstrRep |
Show DataRep |
Show Constr |
Show DataType |
Show GCStats |
Show a => Show [a] |
(Integral a, Show a) => Show (Ratio a) |
Show (Ptr a) |
Show (FunPtr a) |
Show (U1 p) |
Show p => Show (Par1 p) |
Show a => Show (Maybe a) |
Show a => Show (Down 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 (ZipList a) |
Show a => Show (Complex a) |
HasResolution a => Show (Fixed a) |
Show (a -> b) |
(Show a, Show b) => Show (Either a b) |
Show (f p) => Show (Rec1 f p) |
(Show a, Show b) => Show (a, b) |
Show (ST s a) |
Show (Proxy k s) |
Show c => Show (K1 i c p) |
(Show (f p), Show (g p)) => Show ((:+:) f g p) |
(Show (f p), Show (g p)) => Show ((:*:) f g p) |
Show (f (g p)) => Show ((:.:) f g p) |
(Show a, Show b, Show c) => Show (a, b, c) |
Show ((:~:) k a b) |
Show (Coercion k a b) |
Show (f p) => Show (M1 i c f p) |
(Show a, Show b, Show c, Show d) => Show (a, b, c, d) |
(Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e) |
(Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f) |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g) |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h) => Show (a, b, c, d, e, f, g, h) |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i) => Show (a, b, c, d, e, f, g, h, i) |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j) => Show (a, b, c, d, e, f, g, h, i, j) |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k) => Show (a, b, c, d, e, f, g, h, i, j, k) |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l) => Show (a, b, c, d, e, f, g, h, i, j, k, l) |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m) |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n) |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n, Show o) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |

shows :: Show a => a -> ShowS

equivalent to `showsPrec` with a precedence of 0.

showChar :: Char -> ShowS

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

showString :: String -> ShowS

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

showParen :: Bool -> ShowS -> ShowS

utility function that surrounds the inner show function with parentheses when the `Bool` parameter is `True`.

## Converting from `String`

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

A parser for a type `a`, represented as a function that takes a `String` and returns a list of possible parses as `(a,`String`)` pairs.

Note that this kind of backtracking parser is very inefficient; reading a large structure may be quite slow (cf `ReadP`).

class Read a where

Parsing of `String`s, producing values.

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

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

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

For example, given the declarations

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

the derived instance of `Read` in Haskell 2010 is equivalent to

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

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

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

              where app_prec = 10
                    up_prec = 5

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

The derived instance in GHC is equivalent to

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

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

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

              where app_prec = 10
                    up_prec = 5

            readListPrec = readListPrecDefault

Minimal complete definition

readsPrec | readPrec

Methods

readsPrec

Arguments

:: Int | the operator precedence of the enclosing context (a number from `0` to `11`). Function application has precedence `10`.
-> ReadS a |

attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.

Derived instances of `Read` and `Show` satisfy the following:

- `(x,"")` is an element of `(`readsPrec` d (`showsPrec` d x ""))`.

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

readList :: ReadS [a]

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

Instances

Read Bool |
Read Char |
Read Double |
Read Float |
Read Int |
Read Int8 |
Read Int16 |
Read Int32 |
Read Int64 |
Read Integer |
Read Ordering |
Read Word |
Read Word8 |
Read Word16 |
Read Word32 |
Read Word64 |
Read () |
Read Lexeme |
Read Associativity |
Read Fixity |
Read Arity |
Read Any |
Read All |
Read CUIntMax |
Read CIntMax |
Read CUIntPtr |
Read CIntPtr |
Read CSUSeconds |
Read CUSeconds |
Read CTime |
Read CClock |
Read CSigAtomic |
Read CWchar |
Read CSize |
Read CPtrdiff |
Read CDouble |
Read CFloat |
Read CULLong |
Read CLLong |
Read CULong |
Read CLong |
Read CUInt |
Read CInt |
Read CUShort |
Read CShort |
Read CUChar |
Read CSChar |
Read CChar |
Read GeneralCategory |
Read IntPtr |
Read WordPtr |
Read SeekMode |
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 IOMode |
Read SomeSymbol |
Read SomeNat |
Read Version |
Read GCStats |
Read a => Read [a] |
(Integral a, Read a) => Read (Ratio a) |
Read (U1 p) |
Read p => Read (Par1 p) |
Read a => Read (Maybe a) |
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 b) => Read (Either a b) |
Read (f p) => Read (Rec1 f p) |
(Read a, Read b) => Read (a, b) |
Read (Proxy k s) |
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 p) => Read (M1 i c f p) |
(Read a, Read b, Read c, Read d) => Read (a, b, c, d) |
(Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) |
(Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h) |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i) |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j) |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k) |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l) |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |

reads :: Read a => ReadS a

equivalent to `readsPrec` with a precedence of 0.

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

``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

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

lex :: ReadS String

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

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

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

# Basic Input and output

data IO a :: * -> * Source

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

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

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

Instances

Monad IO |
Functor IO |
MonadFix IO |
Applicative IO |
Typeable1 IO |
(~) * a () => HPrintfType (IO a) |
(~) * a () => PrintfType (IO a) |
Typeable (* -> *) IO |

## Simple I/O operations

### Output functions

putChar :: Char -> IO ()

Write a character to the standard output device (same as `hPutChar` `stdout`).

putStr :: String -> IO ()

Write a string to the standard output device (same as `hPutStr` `stdout`).

putStrLn :: String -> IO ()

The same as `putStr`, but adds a newline character.

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

The `print` function outputs a value of any printable type to the standard output device. Printable types are those that are instances of class `Show`; `print` converts values to strings for output using the `show` operation and adds a newline.

For example, a program to print the first 20 integers and their powers of 2 could be written as:

    main = print ([(n, 2^n) | n <- [0..19]])

### Input functions

getChar :: IO Char

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

getLine :: IO String

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

getContents :: IO String

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 ()

The `interact` function takes a function of type `String->String` as its argument. The entire input from the standard input device is passed to this function as its argument, and the resulting string is output on the standard output device.

### Files

type FilePath = String

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

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 ()

The computation `writeFile` `file str` function writes the string `str`, to the file `file`.

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

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

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

The `readLn` function combines `getLine` and `readIO`.

## Exception handling in the I/O monad

type IOError = IOException

The Haskell 2010 type for exceptions in the `IO` monad. Any I/O operation may raise an `IOError` instead of returning a result. For a more general type of exception, including also those that arise in pure code, see Control.Exception.Exception.

In Haskell 2010, this is an opaque type.

ioError :: IOError -> IO a

Raise an `IOError` in the `IO` monad.

userError :: String -> IOError

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)