In this appendix the entire Haskell prelude is given. It is organized into a root module and three sub-modules. Primitives that are not definable in Haskell , indicated by names starting with prim, are defined in a system dependent manner in module PreludeBuiltin and are not shown here. Instance declarations that simply bind primitives to class methods are omitted. Some of the more verbose instances with obvious functionality have been left out for the sake of brevity.
Declarations for special types such as Integer, (), or (->) are included in the Prelude for completeness even though the declaration may be incomplete or syntactically invalid.
module Prelude (
module PreludeList, module PreludeText, module PreludeIO,
Bool(False, True),
Maybe(Nothing, Just),
Either(Left, Right),
Ordering(LT, EQ, GT),
Char, String, Int, Integer, Float, Double, IO, Void,
Ratio, Rational,
-- List type: []((:), [])
-- Tuple types: (,), (,,), etc.
-- Trivial type: ()
-- Functions: (->)
Eq((==), (/=)),
Ord(compare, (<), (<=), (>=), (>), max, min),
Enum(toEnum, fromEnum, enumFrom, enumFromThen,
enumFromTo, enumFromThenTo),
Bounded(minBound, maxBound),
Eval(seq, strict),
Num((+), (-), (*), negate, abs, signum, fromInteger),
Real(toRational),
Integral(quot, rem, div, mod, quotRem, divMod, toInteger),
Fractional((/), recip, fromRational),
Floating(pi, exp, log, sqrt, (**), logBase, sin, cos, tan,
asin, acos, atan, sinh, cosh, tanh, asinh, acosh, atanh),
RealFrac(properFraction, truncate, round, ceiling, floor),
RealFloat(floatRadix, floatDigits, floatRange, decodeFloat,
encodeFloat, exponent, significand, scaleFloat, isNaN,
isInfinite, isDenormalized, isIEEE, isNegativeZero),
Monad((>>=), (>>), return),
MonadZero(zero),
MonadPlus((++)),
Functor(map),
succ, pred,
mapM, mapM_, guard, accumulate, sequence, filter, concat, applyM,
maybe, either,
(&&), (||), not, otherwise,
subtract, even, odd, gcd, lcm, (^), (^^),
fromIntegral, fromRealFrac, atan2,
fst, snd, curry, uncurry, id, const, (.), flip, ($), until,
asTypeOf, error, undefined ) where
import PreludeBuiltin -- Contains all `prim' values
import PreludeList
import PreludeText
import PreludeIO
import Ratio(Ratio, Rational, (%), numerator, denominator)
infixr 9 .
infixr 8 ^, ^^, **
infixl 7 *, /, `quot`, `rem`, `div`, `mod`
infixl 6 +, -
infixr 5 :, ++
infix 4 ==, /=, <, <=, >=, >
infixr 3 &&
infixr 2 ||
infixl 1 >>, >>=
infixr 0 $, `seq`
-- Standard types, classes, instances and related functions
-- Equality and Ordered classes
class Eq a where
(==), (/=) :: a -> a -> Bool
x /= y = not (x == y)
class (Eq a) => Ord a where
compare :: a -> a -> Ordering
(<), (<=),
(>=), (>) :: a -> a -> Bool
max, min :: a -> a -> a
-- An instance of Ord should define either compare or <=
-- Using compare can be more efficient for complex types.
compare x y
| x == y = EQ
| x <= y = LT
| otherwise = GT
x <= y = compare x y /= GT
x < y = compare x y == LT
x >= y = compare x y /= LT
x > y = compare x y == GT
-- note that (min x y, max x y) = (x,y) or (y,x)
max x y
| x >= y = x
| otherwise = y
min x y
| x < y = x
| otherwise = y
-- Enumeration and Bounded classes
class Enum a where
toEnum :: Int -> a
fromEnum :: a -> Int
enumFrom :: a -> [a] -- [n..]
enumFromThen :: a -> a -> [a] -- [n,n'..]
enumFromTo :: a -> a -> [a] -- [n..m]
enumFromThenTo :: a -> a -> a -> [a] -- [n,n'..m]
enumFromTo x y = map toEnum [fromEnum x .. fromEnum y]
enumFromThenTo x y z =
map toEnum [fromEnum x, fromEnum y .. fromEnum z]
succ, pred :: Enum a => a -> a
succ = toEnum . (+1) . fromEnum
pred = toEnum . (subtract 1) . fromEnum
class Bounded a where
minBound :: a
maxBound :: a
-- Numeric classes
class (Eq a, Show a, Eval a) => Num a where
(+), (-), (*) :: a -> a -> a
negate :: a -> a
abs, signum :: a -> a
fromInteger :: Integer -> a
x - y = x + negate y
class (Num a, Ord a) => Real a where
toRational :: a -> Rational
class (Real a, Enum a) => Integral a where
quot, rem :: a -> a -> a
div, mod :: a -> a -> a
quotRem, divMod :: a -> a -> (a,a)
toInteger :: a -> Integer
n `quot` d = q where (q,r) = quotRem n d
n `rem` d = r where (q,r) = quotRem n d
n `div` d = q where (q,r) = divMod n d
n `mod` d = r where (q,r) = divMod n d
divMod n d = if signum r == - signum d then (q-1, r+d) else qr
where qr@(q,r) = quotRem n d
class (Num a) => Fractional a where
(/) :: a -> a -> a
recip :: a -> a
fromRational :: Rational -> a
recip x = 1 / x
class (Fractional a) => Floating a where
pi :: a
exp, log, sqrt :: a -> a
(**), logBase :: a -> a -> a
sin, cos, tan :: a -> a
asin, acos, atan :: a -> a
sinh, cosh, tanh :: a -> a
asinh, acosh, atanh :: a -> a
x ** y = exp (log x * y)
logBase x y = log y / log x
sqrt x = x ** 0.5
tan x = sin x / cos x
tanh x = sinh x / cosh x
class (Real a, Fractional a) => RealFrac a where
properFraction :: (Integral b) => a -> (b,a)
truncate, round :: (Integral b) => a -> b
ceiling, floor :: (Integral b) => a -> b
truncate x = m where (m,_) = properFraction x
round x = let (n,r) = properFraction x
m = if r < 0 then n - 1 else n + 1
in case signum (abs r - 0.5) of
-1 -> n
0 -> if even n then n else m
1 -> m
ceiling x = if r > 0 then n + 1 else n
where (n,r) = properFraction x
floor x = if r < 0 then n - 1 else n
where (n,r) = properFraction x
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, isInfinite, isDenormalized, isNegativeZero, isIEEE
:: a -> Bool
exponent x = if m == 0 then 0 else n + floatDigits x
where (m,n) = decodeFloat x
significand x = encodeFloat m (- floatDigits x)
where (m,_) = decodeFloat x
scaleFloat k x = encodeFloat m (n+k)
where (m,n) = decodeFloat x
-- Numeric functions
subtract :: (Num a) => a -> a -> a
subtract = flip (-)
even, odd :: (Integral a) => a -> Bool
even n = n `rem` 2 == 0
odd = not . even
gcd :: (Integral a) => a -> a -> a
gcd 0 0 = error "Prelude.gcd: gcd 0 0 is undefined"
gcd x y = gcd' (abs x) (abs y)
where gcd' x 0 = x
gcd' x y = gcd' y (x `rem` y)
lcm :: (Integral a) => a -> a -> a
lcm _ 0 = 0
lcm 0 _ = 0
lcm x y = abs ((x `quot` (gcd x y)) * y)
(^) :: (Num a, Integral b) => a -> b -> a
x ^ 0 = 1
x ^ n | n > 0 = f x (n-1) x
where f _ 0 y = y
f x n y = g x n where
g x n | even n = g (x*x) (n `quot` 2)
| otherwise = f x (n-1) (x*y)
_ ^ _ = error "Prelude.^: negative exponent"
(^^) :: (Fractional a, Integral b) => a -> b -> a
x ^^ n = if n >= 0 then x^n else recip (x^(-n))
fromIntegral :: (Integral a, Num b) => a -> b
fromIntegral = fromInteger . toInteger
fromRealFrac :: (RealFrac a, Fractional b) => a -> b
fromRealFrac = fromRational . toRational
atan2 :: (RealFloat a) => a -> a -> a
atan2 y x = case (signum y, signum x) of
( 0, 1) -> 0
( 1, 0) -> pi/2
( 0,-1) -> pi
(-1, 0) -> -pi/2
( _, 1) -> atan (y/x)
( _,-1) -> atan (y/x) + pi
( 0, 0) -> error "Prelude.atan2: atan2 of origin"
-- Monadic classes
class Functor f where
map :: (a -> b) -> f a -> f b
class Monad m where
(>>=) :: m a -> (a -> m b) -> m b
(>>) :: m a -> m b -> m b
return :: a -> m a
m >> k = m >>= \_ -> k
class (Monad m) => MonadZero m where
zero :: m a
class (MonadZero m) => MonadPlus m where
(++) :: m a -> m a -> m a
accumulate :: Monad m => [m a] -> m [a]
accumulate = foldr mcons (return [])
where mcons p q = p >>= \x -> q >>= \y -> return (x:y)
sequence :: Monad m => [m a] -> m ()
sequence = foldr (>>) (return ())
mapM :: Monad m => (a -> m b) -> [a] -> m [b]
mapM f as = accumulate (map f as)
mapM_ :: Monad m => (a -> m b) -> [a] -> m ()
mapM_ f as = sequence (map f as)
guard :: MonadZero m => Bool -> m ()
guard p = if p then return () else zero
-- This subsumes the list-based filter function.
filter :: MonadZero m => (a -> Bool) -> m a -> m a
filter p = applyM (\x -> if p x then return x else zero)
-- This subsumes the list-based concat function.
concat :: MonadPlus m => [m a] -> m a
concat = foldr (++) zero
applyM :: Monad m => (a -> m b) -> m a -> m b
applyM f x = x >>= f
-- Eval Class
class Eval a where
seq :: a -> b -> b
strict :: (a -> b) -> a -> b
strict f x = x `seq` f x
-- Trivial type
data () = () deriving (Eq, Ord, Enum, Bounded)
-- Function type
data a -> b -- No constructor for functions is exported.
-- identity function
id :: a -> a
id x = x
-- constant function
const :: a -> b -> a
const x _ = x
-- function composition
(.) :: (b -> c) -> (a -> b) -> a -> c
f . g = \ x -> f (g x)
-- flip f takes its (first) two arguments in the reverse order of f.
flip :: (a -> b -> c) -> b -> a -> c
flip f x y = f y x
-- right-associating infix application operator (useful in continuation-
-- passing style)
($) :: (a -> b) -> a -> b
f $ x = f x
-- Empty type
data Void -- No constructor for Void is exported. Import/Export
-- lists must use Void instead of Void(..) or Void()
-- Boolean type
data Bool = False | True deriving (Eq, Ord, Enum, Read, Show, Bounded)
-- Boolean functions
(&&), (||) :: Bool -> Bool -> Bool
True && x = x
False && _ = False
True || _ = True
False || x = x
not :: Bool -> Bool
not True = False
not False = True
otherwise :: Bool
otherwise = True
-- Character type
data Char = ... 'a' | 'b' ... -- 2^16 unicode values
instance Eq Char where
c == c' = fromEnum c == fromEnum c'
instance Ord Char where
c <= c' = fromEnum c <= fromEnum c'
instance Enum Char where
toEnum = primIntToChar
fromEnum = primCharToInt
enumFrom c = map toEnum [fromEnum c .. fromEnum (maxBound::Char)]
enumFromThen c c' = [fromEnum c, fromEnum c' .. fromEnum lastChar]
where lastChar :: Char
lastChar | c' < c = minBound
| otherwise = maxBound
instance Bounded Char where
minBound = '\0'
maxBound = '\xffff'
type String = [Char]
-- Maybe type
data Maybe a = Nothing | Just a deriving (Eq, Ord, Read, Show)
maybe :: b -> (a -> b) -> Maybe a -> b
maybe n f Nothing = n
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maybe n f (Just Ep; = n
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maybe n f (Just Ep; = n
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maybe n f (Just Ep; = n
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maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
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maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
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maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
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maybe n f (Just Ep; = n
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maybe n f (Just Ep; = n
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maybe n f (Just Ep; = n
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maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
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maybe n f (Just Ep; = n
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maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = n
maybe n f (Just Ep; = &n