Prelude.Listless

list-extras-0.2.2: Common not-so-common functions for lists

Prelude.Listless

Portability	portable
Stability	stable
Maintainer	wren@community.haskell.org

Description

This module provides the Prelude but removing all the list functions. This is helpful for modules that overload those function names to work for other types.

Be sure to disable the implicit importing of the prelude when you import this one (by passing -fno-implicit-prelude for GHC, or by explicitly importing the prelude with an empty import list for most implementations).

Synopsis

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

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

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

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

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

data Bool

class Bounded a where

data Char

data Double

data Either a b

= Left 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 Eq a where

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

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

type FilePath = String

data Float

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 Num a => Fractional a where

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

recip :: a -> a

fromRational :: Rational -> a

class Functor f where

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

data IO a

type IOError = IOException

data Int

data Integer

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

data Maybe a

| Just a

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 (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 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

data Ordering

= LT

| EQ

| GT

type Rational = Ratio Integer

class Read a where

readsPrec :: Int -> ReadS a

readList :: ReadS [a]

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

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

toRational :: a -> Rational

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

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 Show a where

showsPrec :: Int -> a -> ShowS

show :: a -> String

showList :: [a] -> ShowS

type ShowS = String -> String

type String = [Char]

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

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

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

asTypeOf :: a -> a -> a

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

const :: a -> b -> a

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

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

error :: [Char] -> a

even :: Integral a => a -> Bool

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

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

fst :: (a, b) -> a

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

getChar :: IO Char

getContents :: IO String

getLine :: IO String

id :: a -> a

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

ioError :: IOError -> IO a

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

lex :: ReadS String

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

not :: Bool -> Bool

odd :: Integral a => a -> Bool

otherwise :: Bool

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

putChar :: Char -> IO ()

putStr :: String -> IO ()

putStrLn :: String -> IO ()

read :: Read a => String -> a

readFile :: FilePath -> IO String

readIO :: Read a => String -> IO a

readLn :: Read a => IO a

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

reads :: Read a => ReadS a

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

seq :: a -> b -> b

showChar :: Char -> ShowS

showParen :: Bool -> ShowS -> ShowS

showString :: String -> ShowS

shows :: Show a => a -> ShowS

snd :: (a, b) -> b

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

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

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

userError :: String -> IOError

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

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

Documentation

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

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

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

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.

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

Boolean "and"

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

Function composition.

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

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

data Bool

Constructors

False
True

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Instances

Bounded Bool
Enum Bool
Eq Bool
Ord Bool
Read Bool
Show Bool

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 :: a

maxBound :: a

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Instances

Bounded Bool
Bounded Char
Bounded Int
Bounded Ordering
Bounded ()
(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)

data Char

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Instances

Bounded Char
Enum Char
Eq Char
Ord Char
Read Char
Show Char

data Double

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.

show/hide

Instances

Enum Double
Eq Double
Floating Double
Fractional Double
Num Double
Ord Double
Read Double
Real Double
RealFloat Double
RealFrac Double
Show Double

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

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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)

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

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].

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Instances

Enum Bool
Enum Char
Enum Double
Enum Float
Enum Int
Enum Integer
Enum Ordering
Enum ()
Integral a => Enum (Ratio a)

class Eq a where

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

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

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Instances

Eq Bool
Eq Char
Eq Double
Eq Float
Eq Int
Eq Integer
Eq Ordering
Eq ()
Eq AsyncException
Eq ArrayException
Eq ExitCode
Eq IOErrorType
Eq IOException
Eq a => Eq [a]
Integral a => Eq (Ratio a)
Eq a => Eq (Maybe a)
(Eq a, Eq b) => Eq (Either a b)
(Eq a, Eq b) => Eq (a, b)
(Eq a, Eq b, Eq c) => Eq (a, b, c)
(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)

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.

data Float

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.

show/hide

Instances

Enum Float
Eq Float
Floating Float
Fractional Float
Num Float
Ord Float
Read Float
Real Float
RealFloat Float
RealFrac Float
Show Float

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

Methods

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

show/hide

Instances

Floating Double
Floating Float

class Num a => Fractional a where

Fractional numbers, supporting real division.

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

Methods

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

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.

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Instances

Fractional Double
Fractional Float
Integral a => Fractional (Ratio a)

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, Data.Maybe.Maybe and System.IO.IO defined in the Prelude satisfy these laws.

Methods

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

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Instances

Functor []
Functor IO
Functor ReadP
Functor Maybe

data IO a

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.

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Instances

Monad IO
Functor IO

type IOError = IOException

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.

data Int

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.

show/hide

Instances

Bounded Int
Enum Int
Eq Int
Integral Int
Num Int
Ord Int
Read Int
Real Int
Show Int

data Integer

Arbitrary-precision integers.

show/hide

Instances

Enum Integer
Eq Integer
Integral Integer
Num Integer
Ord Integer
Read Integer
Real Integer
Show Integer

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

Integral numbers, supporting integer division.

Minimal complete definition: quotRem and toInteger

Methods

quot :: a -> a -> a

integer division truncated toward zero

rem :: a -> a -> a

integer remainder, satisfying

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

div :: a -> a -> a

integer division truncated toward negative infinity

mod :: a -> a -> a

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

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Instances

Integral Int
Integral Integer

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 Data.Either.Either type.

Constructors

Nothing
Just a

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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)

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, Data.Maybe.Maybe and System.IO.IO defined in the Prelude satisfy these laws.

Methods

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

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

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

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.

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Instances

Monad []
Monad IO
Monad P
Monad ReadP
Monad Maybe

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

Basic numeric class.

Minimal complete definition: all except negate or (-)

Methods

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

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

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

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.

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Instances

Num Double
Num Float
Num Int
Num Integer
Integral a => Num (Ratio a)

class Eq a => Ord a where

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

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

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

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

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

max :: a -> a -> a

min :: a -> a -> a

show/hide

Instances

Ord Bool
Ord Char
Ord Double
Ord Float
Ord Int
Ord Integer
Ord Ordering
Ord ()
Ord AsyncException
Ord ArrayException
Ord ExitCode
Ord a => Ord [a]
Integral a => Ord (Ratio a)
Ord a => Ord (Maybe a)
(Ord a, Ord b) => Ord (Either a b)
(Ord a, Ord b) => Ord (a, b)
(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)

data Ordering

Constructors

LT
EQ
GT

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Instances

Bounded Ordering
Enum Ordering
Eq Ordering
Ord Ordering
Read Ordering
Show Ordering

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.

class Read a where

Parsing of Strings, producing values.

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

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

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

For example, given the declarations

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

the derived instance of Read in Haskell 98 is equivalent to

instance (Read a) => Read (Tree a) where readsPrec d r = readParen (d > app_prec) (\r -> [(Leaf m,t) | ("Leaf",s) <- lex r, (m,t) <- readsPrec (app_prec+1) s]) r ++ readParen (d > up_prec) (\r -> [(u:^:v,w) | (u,s) <- readsPrec (up_prec+1) r, (":^:",t) <- lex s, (v,w) <- readsPrec (up_prec+1) t]) r where app_prec = 10 up_prec = 5

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

The derived instance in GHC is equivalent to

instance (Read a) => Read (Tree a) where readPrec = parens $ (prec app_prec $ do Ident "Leaf" <- lexP m <- step readPrec return (Leaf m)) +++ (prec up_prec $ do u <- step readPrec Symbol ":^:" <- lexP v <- step readPrec return (u :^: v)) where app_prec = 10 up_prec = 5 readListPrec = readListPrecDefault

Methods

readsPrec

:: 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]

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.

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Instances

Read Bool
Read Char
Read Double
Read Float
Read Int
Read Integer
Read Ordering
Read ()
Read ExitCode
Read Lexeme
Read a => Read [a]
(Integral a, Read a) => Read (Ratio 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)

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

Methods

toRational :: a -> Rational

the rational equivalent of its real argument with full precision

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Instances

Real Double
Real Float
Real Int
Real Integer
Integral a => Real (Ratio 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

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) <= m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0).

encodeFloat :: Integer -> Int -> a

encodeFloat performs the inverse of decodeFloat

exponent :: a -> Int

the second component of decodeFloat.

significand :: a -> a

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

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.

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Instances

RealFloat Double
RealFloat Float

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

Extracting components of fractions.

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

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Instances

RealFrac Double
RealFrac Float
Integral a => RealFrac (Ratio a)

class Show a where

Conversion of values to readable Strings.

Minimal complete definition: showsPrec or show.

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

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

For example, given the declarations

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

the derived instance of Show is equivalent to

instance (Show a) => Show (Tree a) where showsPrec d (Leaf m) = showParen (d > app_prec) $ showString "Leaf " . showsPrec (app_prec+1) m where app_prec = 10 showsPrec d (u :^: v) = showParen (d > up_prec) $ showsPrec (up_prec+1) u . showString " :^: " . showsPrec (up_prec+1) v where up_prec = 5

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

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

Methods

showsPrec

:: 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

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.

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Instances

Show Bool
Show Char
Show Double
Show Float
Show Int
Show Integer
Show Ordering
Show ()
Show BlockedIndefinitelyOnMVar
Show BlockedIndefinitelyOnSTM
Show Deadlock
Show AssertionFailed
Show AsyncException
Show ArrayException
Show ExitCode
Show IOErrorType
Show IOException
Show a => Show [a]
Integral a => Show (Ratio a)
Show a => Show (Maybe a)
(Show a, Show b) => Show (Either a b)
(Show a, Show b) => Show (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)

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.

type String = [Char]

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

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

raise a number to a non-negative integral power

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

raise a number to an integral power

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]])

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.

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

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

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

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

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

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

const :: a -> b -> a

Constant function.

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

curry converts an uncurried function to a curried function.

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.

error :: [Char] -> a

error stops execution and displays an error message.

even :: Integral a => a -> Bool

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

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

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

general coercion from integral types

fst :: (a, b) -> a

Extract the first component of a pair.

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

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.

getChar :: IO Char

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

getLine :: IO String

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

id :: a -> a

Identity function.

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.

ioError :: IOError -> IO a

Raise an IOError in the IO monad.

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

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

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

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.

not :: Bool -> Bool

Boolean "not"

odd :: Integral a => a -> Bool

otherwise :: Bool

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

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

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]])

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.

read :: Read a => String -> a

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

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.

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.

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.

reads :: Read a => ReadS a

equivalent to readsPrec with a precedence of 0.

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

general coercion to fractional types

seq :: a -> b -> b

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

showChar :: Char -> ShowS

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

showParen :: Bool -> ShowS -> ShowS

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

showString :: String -> ShowS

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

shows :: Show a => a -> ShowS

equivalent to showsPrec with a precedence of 0.

snd :: (a, b) -> b

Extract the second component of a pair.

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.

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

uncurry converts a curried function to a function on pairs.

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.

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

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

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)

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

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

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

Boolean "or"

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