Prelude

haskell2010-1.0.0.0: Compatibility with Haskell 2010

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 Haskell 2010 Prelude: a standard module imported by default into all Haskell modules. For more documentation, see the Haskell 2010 Report http://www.haskell.org/onlinereport/.

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 :: a
  - maxBound :: a
- data Int
- data Integer
- data Float
- data Double
- type Rational = Ratio Integer
- class (Eq a, Show a) => Num a where
  - (+) :: a -> a -> a
  - (*) :: a -> a -> a
  - (-) :: 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 :: a -> a
  - sqrt :: a -> a
  - log :: a -> a
  - (**) :: a -> a -> a
  - logBase :: a -> a -> a
  - sin :: a -> a
  - tan :: a -> a
  - cos :: a -> a
  - asin :: a -> a
  - atan :: a -> a
  - acos :: a -> a
  - sinh :: a -> a
  - tanh :: a -> a
  - cosh :: a -> a
  - asinh :: a -> a
  - atanh :: a -> a
  - 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
  - (>>=) :: m a -> (a -> m b) -> m 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 :: (a -> b -> a) -> a -> [b] -> a
- 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 :: (a -> b -> a) -> a -> [b] -> [a]
- 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
- catch :: IO a -> (IOError -> IO a) -> IO a

# Standard types, classes and related functions

## Basic data types

data Bool Source

Constructors

False |
True |

Instances

Bounded Bool |
Enum Bool |
Eq Bool |
Ord Bool |
Read Bool |
Show Bool |
Ix Bool |
Storable Bool |

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

Boolean "and"

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

Boolean "or"

not :: Bool -> Bool Source

Boolean "not"

otherwise :: Bool Source

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

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

data Maybe a Source

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

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

Constructors

Nothing |
Just a |

Instances

Monad Maybe |
Functor Maybe |
MonadPlus Maybe |
Eq a => Eq (Maybe a) |
Ord a => Ord (Maybe a) |
Read a => Read (Maybe a) |
Show a => Show (Maybe a) |

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

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

data Either a b Source

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

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

Constructors

Left a |
Right b |

Instances

Typeable2 Either |
(Eq a, Eq b) => Eq (Either a b) |
(Ord a, Ord b) => Ord (Either a b) |
(Read a, Read b) => Read (Either a b) |
(Show a, Show b) => Show (Either a b) |

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

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

data Ordering Source

Constructors

LT |
EQ |
GT |

Instances

Bounded Ordering |
Enum Ordering |
Eq Ordering |
Ord Ordering |
Read Ordering |
Show Ordering |
Ix Ordering |

data Char Source

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

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

Instances

Bounded Char |
Enum Char |
Eq Char |
Ord Char |
Read Char |
Show Char |
Ix Char |
Storable Char |

type String = [Char]Source

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

### Tuples

fst :: (a, b) -> aSource

Extract the first component of a pair.

snd :: (a, b) -> bSource

Extract the second component of a pair.

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

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

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

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

## Basic type classes

class Eq a 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 `/=`.

Methods

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

(/=) :: a -> a -> Bool 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 Handle |
Eq Finalizers |
Eq HandlePosn |
Eq Errno |
Eq AsyncException |
Eq ArrayException |
Eq ExitCode |
Eq IOErrorType |
Eq BufferMode |
Eq Newline |
Eq NewlineMode |
Eq WordPtr |
Eq IntPtr |
Eq GeneralCategory |
Eq CChar |
Eq CSChar |
Eq CUChar |
Eq CShort |
Eq CUShort |
Eq CInt |
Eq CUInt |
Eq CLong |
Eq CULong |
Eq CLLong |
Eq CULLong |
Eq CFloat |
Eq CDouble |
Eq CPtrdiff |
Eq CSize |
Eq CWchar |
Eq CSigAtomic |
Eq CClock |
Eq CTime |
Eq CIntPtr |
Eq CUIntPtr |
Eq CIntMax |
Eq CUIntMax |
Eq IODeviceType |
Eq SeekMode |
Eq IOMode |
Eq MaskingState |
Eq IOException |
Eq a => Eq [a] |
Integral a => Eq (Ratio a) |
Eq (StablePtr a) |
Eq (Ptr a) |
Eq (FunPtr a) |
Eq (ForeignPtr a) |
RealFloat a => Eq (Complex a) |
Eq a => Eq (Maybe a) |
(Eq a, Eq b) => Eq (Either a b) |
(Eq a, Eq b) => Eq (a, b) |
(Ix i, Eq e) => Eq (Array i e) |
(Eq a, Eq b, Eq c) => Eq (a, b, c) |
Eq (STArray s i e) |
(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) |
(Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |

class Eq a => Ord a 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.

Methods

compare :: a -> a -> Ordering Source

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

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

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

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

max :: a -> a -> aSource

min :: a -> a -> aSource

Instances

Ord Bool |
Ord Char |
Ord Double |
Ord Float |
Ord Int |
Ord Int8 |
Ord Int16 |
Ord Int32 |
Ord Int64 |
Ord Integer |
Ord Ordering |
Ord Word |
Ord Word8 |
Ord Word16 |
Ord Word32 |
Ord Word64 |
Ord () |
Ord AsyncException |
Ord ArrayException |
Ord ExitCode |
Ord BufferMode |
Ord Newline |
Ord NewlineMode |
Ord WordPtr |
Ord IntPtr |
Ord GeneralCategory |
Ord CChar |
Ord CSChar |
Ord CUChar |
Ord CShort |
Ord CUShort |
Ord CInt |
Ord CUInt |
Ord CLong |
Ord CULong |
Ord CLLong |
Ord CULLong |
Ord CFloat |
Ord CDouble |
Ord CPtrdiff |
Ord CSize |
Ord CWchar |
Ord CSigAtomic |
Ord CClock |
Ord CTime |
Ord CIntPtr |
Ord CUIntPtr |
Ord CIntMax |
Ord CUIntMax |
Ord SeekMode |
Ord IOMode |
Ord a => Ord [a] |
Integral a => Ord (Ratio a) |
Ord (Ptr a) |
Ord (FunPtr a) |
Ord (ForeignPtr a) |
Ord a => Ord (Maybe a) |
(Ord a, Ord b) => Ord (Either a b) |
(Ord a, Ord b) => Ord (a, b) |
(Ix i, Ord e) => Ord (Array i e) |
(Ord a, Ord b, Ord c) => Ord (a, b, c) |
(Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) |
(Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n) |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |

class Enum a where Source

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

Methods

succ :: a -> aSource

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

pred :: a -> aSource

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

toEnum :: Int -> aSource

Convert from an `Int`.

fromEnum :: a -> Int Source

Convert to an `Int`. It is implementation-dependent what `fromEnum` returns when applied to a value that is too large to fit in an `Int`.

enumFrom :: a -> [a]Source

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

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

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

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

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

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

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

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 WordPtr |
Enum IntPtr |
Enum GeneralCategory |
Enum CChar |
Enum CSChar |
Enum CUChar |
Enum CShort |
Enum CUShort |
Enum CInt |
Enum CUInt |
Enum CLong |
Enum CULong |
Enum CLLong |
Enum CULLong |
Enum CFloat |
Enum CDouble |
Enum CPtrdiff |
Enum CSize |
Enum CWchar |
Enum CSigAtomic |
Enum CClock |
Enum CTime |
Enum CIntPtr |
Enum CUIntPtr |
Enum CIntMax |
Enum CUIntMax |
Enum SeekMode |
Enum IOMode |
Integral a => Enum (Ratio a) |

class Bounded a where Source

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 :: aSource

maxBound :: aSource

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 WordPtr |
Bounded IntPtr |
Bounded GeneralCategory |
Bounded CChar |
Bounded CSChar |
Bounded CUChar |
Bounded CShort |
Bounded CUShort |
Bounded CInt |
Bounded CUInt |
Bounded CLong |
Bounded CULong |
Bounded CLLong |
Bounded CULLong |
Bounded CPtrdiff |
Bounded CSize |
Bounded CWchar |
Bounded CSigAtomic |
Bounded CIntPtr |
Bounded CUIntPtr |
Bounded CIntMax |
Bounded CUIntMax |
(Bounded a, Bounded b) => Bounded (a, b) |
(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) |
(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n) |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |

## Numbers

### Numeric types

data Int Source

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

Instances

Bounded Int |
Enum Int |
Eq Int |
Integral Int |
Num Int |
Ord Int |
Read Int |
Real Int |
Show Int |
Ix Int |
Storable Int |
Bits Int |

data Integer

Instances

Enum Integer |
Eq Integer |
Integral Integer |
Num Integer |
Ord Integer |
Read Integer |
Real Integer |
Show Integer |
Ix Integer |
Bits 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 |
Num Float |
Ord Float |
Read Float |
Real Float |
RealFloat Float |
RealFrac Float |
Show Float |
Storable 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 |
Num Double |
Ord Double |
Read Double |
Real Double |
RealFloat Double |
RealFrac Double |
Show Double |
Storable Double |

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.

### Numeric type classes

class (Eq a, Show a) => Num a where Source

Basic numeric class.

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

Methods

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

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

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

negate :: a -> aSource

Unary negation.

abs :: a -> aSource

Absolute value.

signum :: a -> aSource

Sign of a number. The functions `abs` and `signum` should satisfy the law:

     abs x * signum x == x

For real numbers, the `signum` is either `-1` (negative), `0` (zero) or `1` (positive).

fromInteger :: Integer -> aSource

Conversion from an `Integer`. An integer literal represents the application of the function `fromInteger` to the appropriate value of type `Integer`, so such literals have type `(`Num` a) => a`.

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 WordPtr |
Num IntPtr |
Num CChar |
Num CSChar |
Num CUChar |
Num CShort |
Num CUShort |
Num CInt |
Num CUInt |
Num CLong |
Num CULong |
Num CLLong |
Num CULLong |
Num CFloat |
Num CDouble |
Num CPtrdiff |
Num CSize |
Num CWchar |
Num CSigAtomic |
Num CClock |
Num CTime |
Num CIntPtr |
Num CUIntPtr |
Num CIntMax |
Num CUIntMax |
Integral a => Num (Ratio a) |
RealFloat a => Num (Complex a) |

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

Methods

toRational :: a -> Rational Source

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 WordPtr |
Real IntPtr |
Real CChar |
Real CSChar |
Real CUChar |
Real CShort |
Real CUShort |
Real CInt |
Real CUInt |
Real CLong |
Real CULong |
Real CLLong |
Real CULLong |
Real CFloat |
Real CDouble |
Real CPtrdiff |
Real CSize |
Real CWchar |
Real CSigAtomic |
Real CClock |
Real CTime |
Real CIntPtr |
Real CUIntPtr |
Real CIntMax |
Real CUIntMax |
Integral a => Real (Ratio a) |

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

Integral numbers, supporting integer division.

Minimal complete definition: `quotRem` and `toInteger`

Methods

quot :: a -> a -> aSource

integer division truncated toward zero

rem :: a -> a -> aSource

integer remainder, satisfying

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

div :: a -> a -> aSource

integer division truncated toward negative infinity

mod :: a -> a -> aSource

integer modulus, satisfying

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

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

simultaneous `quot` and `rem`

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

simultaneous `div` and `mod`

toInteger :: a -> Integer Source

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 WordPtr |
Integral IntPtr |
Integral CChar |
Integral CSChar |
Integral CUChar |
Integral CShort |
Integral CUShort |
Integral CInt |
Integral CUInt |
Integral CLong |
Integral CULong |
Integral CLLong |
Integral CULLong |
Integral CPtrdiff |
Integral CSize |
Integral CWchar |
Integral CSigAtomic |
Integral CIntPtr |
Integral CUIntPtr |
Integral CIntMax |
Integral CUIntMax |

class Num a => Fractional a where Source

Fractional numbers, supporting real division.

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

Methods

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

fractional division

recip :: a -> aSource

reciprocal fraction

fromRational :: Rational -> aSource

Conversion from a `Rational` (that is ``Ratio` `Integer``). A floating literal stands for an application of `fromRational` to a value of type `Rational`, so such literals have type `(`Fractional` a) => a`.

Instances

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

class Fractional a => Floating a where Source

Trigonometric and hyperbolic functions and related functions.

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

Methods

pi :: aSource

exp :: a -> aSource

sqrt :: a -> aSource

log :: a -> aSource

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

logBase :: a -> a -> aSource

sin :: a -> aSource

tan :: a -> aSource

cos :: a -> aSource

asin :: a -> aSource

atan :: a -> aSource

acos :: a -> aSource

sinh :: a -> aSource

tanh :: a -> aSource

cosh :: a -> aSource

asinh :: a -> aSource

atanh :: a -> aSource

acosh :: a -> aSource

Instances

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

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

Extracting components of fractions.

Minimal complete definition: `properFraction`

Methods

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

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

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

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

truncate :: Integral b => a -> bSource

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

round :: Integral b => a -> bSource

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

ceiling :: Integral b => a -> bSource

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

floor :: Integral b => a -> bSource

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

Instances

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

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

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

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

Methods

floatRadix :: a -> 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) <= m < b^d`, where `d` is the value of ``floatDigits` x`. In particular, ``decodeFloat` 0 = (0,0)`.

encodeFloat :: Integer -> Int -> aSource

`encodeFloat` performs the inverse of `decodeFloat`

exponent :: a -> Int Source

the second component of `decodeFloat`.

significand :: a -> aSource

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

scaleFloat :: Int -> a -> aSource

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

isNaN :: a -> Bool Source

`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

isIEEE :: a -> Bool Source

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

atan2 :: a -> a -> aSource

a version of arctangent taking two real floating-point arguments. For real floating `x` and `y`, ``atan2` y x` computes the angle (from the positive x-axis) of the vector from the origin to the point `(x,y)`. ``atan2` y x` returns a value in the range [`-pi`, `pi`]. It follows the Common Lisp semantics for the origin when signed zeroes are supported. ``atan2` y 1`, with `y` in a type that is `RealFloat`, should return the same value as ``atan` y`. A default definition of `atan2` is provided, but implementors can provide a more accurate implementation.

Instances

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

### Numeric functions

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

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

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

even :: Integral a => a -> Bool Source

odd :: Integral a => a -> Bool Source

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

``gcd` x y` is the greatest (positive) integer that divides both `x` and `y`; for example ``gcd` (-3) 6` = `3`, ``gcd` (-3) (-6)` = `3`, ``gcd` 0 4` = `4`. ``gcd` 0 0` raises a runtime error.

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

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

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

raise a number to a non-negative integral power

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

raise a number to an integral power

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

general coercion from integral types

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

general coercion to fractional types

## Monads and functors

class Monad m 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.

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

Instances of `Monad` should satisfy the following laws:

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

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

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

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

Methods

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

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

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

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

return :: a -> m aSource

Inject a value into the monadic type.

fail :: String -> m aSource

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

Instances

Monad [] |
Monad IO |
Monad P |
Monad ReadP |
Monad Maybe |

class Functor f where Source

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

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

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

Methods

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

Instances

Functor [] |
Functor IO |
Functor ReadP |
Functor Maybe |
Ix i => Functor (Array i) |

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

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

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

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

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

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

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

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

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

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

## Miscellaneous functions

id :: a -> aSource

Identity function.

const :: a -> b -> aSource

Constant function.

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

Function composition.

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

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

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

Application operator. This operator is redundant, since ordinary application `(f x)` means the same as `(f `$` x)`. However, `$` has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:

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

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

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

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

asTypeOf :: a -> a -> aSource

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

error :: [Char] -> aSource

`error` stops execution and displays an error message.

undefined :: aSource

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

seq :: a -> b -> bSource

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

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

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

# List operations

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

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

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

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

Append two lists, i.e.,

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

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

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

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

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

head :: [a] -> aSource

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

last :: [a] -> aSource

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

tail :: [a] -> [a]Source

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

init :: [a] -> [a]Source

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

null :: [a] -> Bool Source

Test whether a list is empty.

length :: [a] -> Int Source

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

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

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

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

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

## Reducing lists (folds)

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

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

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

The list must be finite.

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

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

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

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

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

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

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

### Special folds

and :: [Bool] -> Bool Source

`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 Source

`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 Source

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 Source

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

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

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

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

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

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

Concatenate a list of lists.

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

Map a function over a list and concatenate the results.

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

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

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

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

## Building lists

### Scans

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

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

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

Note that

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

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

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

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

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

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

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

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

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

### Infinite lists

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

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

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

repeat :: a -> [a]Source

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

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

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

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

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

## Sublists

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

## Searching lists

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

`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 Source

`notElem` is the negation of `elem`.

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

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

## Zipping and unzipping lists

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

`zip` takes two lists and returns a list of corresponding pairs. If one input list is short, excess elements of the longer list are discarded.

zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]Source

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

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

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

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

The `zipWith3` function takes a function which combines three elements, as well as three lists and returns a list of their point-wise combination, analogous to `zipWith`.

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

`unzip` transforms a list of pairs into a list of first components and a list of second components.

unzip3 :: [(a, b, c)] -> ([a], [b], [c])Source

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

## Functions on strings

lines :: String -> [String]Source

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

words :: String -> [String]Source

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

unlines :: [String] -> 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.

# Converting to and from `String`

## Converting to `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.

class Show a where Source

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 `Text.Read.Read`:

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

For example, given the declarations

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

the derived instance of `Show` is equivalent to

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

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

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

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

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

Methods

showsPrec Source

Arguments

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

Convert a value to a readable `String`.

`showsPrec` should satisfy the law

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

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

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

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

show :: a -> String Source

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.

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 Handle |
Show HandleType |
Show HandlePosn |
Show BlockedIndefinitelyOnMVar |
Show BlockedIndefinitelyOnSTM |
Show Deadlock |
Show AssertionFailed |
Show AsyncException |
Show ArrayException |
Show ExitCode |
Show IOErrorType |
Show BufferMode |
Show Newline |
Show NewlineMode |
Show WordPtr |
Show IntPtr |
Show GeneralCategory |
Show CChar |
Show CSChar |
Show CUChar |
Show CShort |
Show CUShort |
Show CInt |
Show CUInt |
Show CLong |
Show CULong |
Show CLLong |
Show CULLong |
Show CFloat |
Show CDouble |
Show CPtrdiff |
Show CSize |
Show CWchar |
Show CSigAtomic |
Show CClock |
Show CTime |
Show CIntPtr |
Show CUIntPtr |
Show CIntMax |
Show CUIntMax |
Show SeekMode |
Show IOMode |
Show MaskingState |
Show IOException |
Show a => Show [a] |
Integral a => Show (Ratio a) |
Show (Ptr a) |
Show (FunPtr a) |
Show (ForeignPtr a) |
RealFloat a => Show (Complex a) |
Show a => Show (Maybe a) |
(Show a, Show b) => Show (Either a b) |
(Show a, Show b) => Show (a, b) |
(Ix a, Show a, Show b) => Show (Array a b) |
(Show a, Show b, Show c) => Show (a, b, c) |
(Show a, Show b, Show c, Show d) => Show (a, b, c, d) |
(Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e) |
(Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f) |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g) |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h) => Show (a, b, c, d, e, f, g, h) |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i) => Show (a, b, c, d, e, f, g, h, i) |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j) => Show (a, b, c, d, e, f, g, h, i, j) |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k) => Show (a, b, c, d, e, f, g, h, i, j, k) |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l) => Show (a, b, c, d, e, f, g, h, i, j, k, l) |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m) |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n) |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n, Show o) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |

shows :: Show a => a -> 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`.

## Converting from `String`

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

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

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

class Read a where Source

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 `Text.Show.Show` obey:

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

For example, given the declarations

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

the derived instance of `Read` in Haskell 98 is equivalent to

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

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

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

               where app_prec = 10
                     up_prec = 5

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

The derived instance in GHC is equivalent to

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

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

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

               where app_prec = 10
                     up_prec = 5

             readListPrec = readListPrecDefault

Methods

readsPrec Source

Arguments

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

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

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

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

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

readList :: ReadS [a]Source

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

Instances

Read Bool |
Read Char |
Read Double |
Read Float |
Read Int |
Read Int8 |
Read Int16 |
Read Int32 |
Read Int64 |
Read Integer |
Read Ordering |
Read Word |
Read Word8 |
Read Word16 |
Read Word32 |
Read Word64 |
Read () |
Read ExitCode |
Read BufferMode |
Read Newline |
Read NewlineMode |
Read WordPtr |
Read IntPtr |
Read GeneralCategory |
Read CChar |
Read CSChar |
Read CUChar |
Read CShort |
Read CUShort |
Read CInt |
Read CUInt |
Read CLong |
Read CULong |
Read CLLong |
Read CULLong |
Read CFloat |
Read CDouble |
Read CPtrdiff |
Read CSize |
Read CWchar |
Read CSigAtomic |
Read CClock |
Read CTime |
Read CIntPtr |
Read CUIntPtr |
Read CIntMax |
Read CUIntMax |
Read SeekMode |
Read IOMode |
Read Lexeme |
Read a => Read [a] |
(Integral a, Read a) => Read (Ratio a) |
(Read a, RealFloat a) => Read (Complex a) |
Read a => Read (Maybe a) |
(Read a, Read b) => Read (Either a b) |
(Read a, Read b) => Read (a, b) |
(Ix a, Read a, Read b) => Read (Array a b) |
(Read a, Read b, Read c) => Read (a, b, c) |
(Read a, Read b, Read c, Read d) => Read (a, b, c, d) |
(Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) |
(Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h) |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i) |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j) |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k) |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l) |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |

reads :: Read a => ReadS aSource

equivalent to `readsPrec` with a precedence of 0.

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

``readParen` `True` p` parses what `p` parses, but surrounded with parentheses.

``readParen` `False` p` parses what `p` parses, but optionally surrounded with parentheses.

read :: Read a => String -> aSource

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

lex :: ReadS String Source

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 |

## Simple I/O operations

### Output functions

putChar :: Char -> IO ()Source

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

putStr :: String -> IO ()Source

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

putStrLn :: String -> IO ()Source

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

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

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

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

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

### Input functions

getChar :: IO Char Source

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

getLine :: IO String Source

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.

### Files

type FilePath = String Source

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 aSource

The `readIO` function is similar to `read` except that it signals parse failure to the `IO` monad instead of terminating the program.

readLn :: Read a => IO aSource

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

## Exception handling in the I/O monad

type IOError = IOException Source

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

In Haskell 98, this is an opaque type.

ioError :: IOError -> IO aSource

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

userError :: String -> 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)

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

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

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

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

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

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