{- A list of selected functions from the Haskell modules:
Prelude, Data.{List, Maybe, Char} -}
------------------------------------------------------
-- standard type classes
class Show a where
show :: a -> String
class Eq a where
(==), (/=) :: a -> a -> Bool
class (Eq a) => Ord a where
(<), (<=), (>=), (>) :: a -> a -> Bool
max, min :: a -> a -> a
class (Eq a, Show a) => Num a where
(+), (-), (*) :: a -> a -> a
negate :: a -> a
abs, 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, rem :: a -> a -> a
div, mod :: a -> a -> a
toInteger :: a -> Integer
class (Num a) => Fractional a where
(/) :: a -> a -> a
fromRational :: Rational -> a
class (Fractional a) => Floating a where
exp, log, sqrt :: a -> a
sin, cos, tan :: a -> a
class (Real a, Fractional a) => RealFrac a where
truncate, round :: (Integral b) => a -> b
ceiling, floor :: (Integral b) => a -> b
-----------------------------------------------------
-- numerical functions
even, odd :: (Integral a) => a -> Bool
even n = n `rem` 2 == 0
odd = not . even
-------------------------------------------------------
-- monadic functions
sequence :: Monad m => [m a] -> m [a]
sequence = foldr mcons (return [])
where mcons p q = do x <- p; xs <- q; return (x:xs)
sequence_ :: Monad m => [m a] -> m ()
sequence_ xs = do sequence xs; return ()
------------------------------------------------------
-- functions on functions
id :: a -> a
id x = x
const :: a -> b -> a
const x _ = x
(.) :: (b -> c) -> (a -> b) -> a -> c
f . g = \x -> f (g x)
flip :: (a -> b -> c) -> b -> a -> c
flip f x y = f y x
($) :: (a -> b) -> a -> b
f $ x = f x
-----------------------------------------------------
-- functions on Bools
data Bool = False | True
(&&), (||) :: Bool -> Bool -> Bool
True && x = x
False && _ = False
True || _ = True
False || x = x
not :: Bool -> Bool
not True = False
not False = True
------------------------------------------------------
-- functions on Maybe
data Maybe a = Nothing | Just a
isJust :: Maybe a -> Bool
isJust (Just a) = True
isJust Nothing = False
isNothing :: Maybe a -> Bool
isNothing = not . isJust
fromJust :: Maybe a -> a
fromJust (Just a) = a
maybeToList :: Maybe a -> [a]
maybeToList Nothing = []
maybeToList (Just a) = [a]
listToMaybe :: [a] -> Maybe a
listToMaybe [] = Nothing
listToMaybe (a:_) = Just a
-------------------------------------------------------
-- a hidden goodie
instance Monad [] where
return x = [x]
xs >>= f = concat (map f xs)
--------------------------------------------------------
-- functions on pairs
fst :: (a, b) -> a
fst (x, y) = x
snd :: (a, b) -> b
snd (x, y) = y
curry :: ((a, b) -> c) -> a -> b -> c
curry f x y = f (x, y)
uncurry :: (a -> b -> c) -> (a, b) -> c
uncurry f p = f (fst p) (snd p)
--------------------------------------------------------
-- functions on lists
map :: (a -> b) -> [a] -> [b]
map f xs = [ f x | x <- xs ]
(++) :: [a] -> [a] -> [a]
xs ++ ys = foldr (:) ys xs
filter :: (a -> Bool) -> [a] -> [a]
filter p xs = [ x | x <- xs, p x ]
concat :: [[a]] -> [a]
concat xss = foldr (++) [] xss
concatMap :: (a -> [b]) -> [a] -> [b]
concatMap f = concat . map f
head, last :: [a] -> a
head (x:_) = x
last [x] = x
last (_:xs) = last xs
tail, init :: [a] -> [a]
tail (_:xs) = xs
init [x] = []
init (x:xs) = x : init xs
null :: [a] -> Bool
null [] = True
null (_:_) = False
length :: [a] -> Int
length [] = 0
length (_:l) = 1 + length l
(!!) :: [a] -> Int -> a
(x:_) !! 0 = x
(_:xs) !! n = xs !! (n-1)
foldr :: (a -> b -> b) -> b -> [a] -> b
foldr f z [] = z
foldr f z (x:xs) = f x (foldr f z xs)
foldl :: (a -> b -> a) -> a -> [b] -> a
foldl f z [] = z
foldl f z (x:xs) = foldl f (f z x) xs
iterate :: (a -> a) -> a -> [a]
iterate f x = x : iterate f (f x)
repeat :: a -> [a]
repeat x = xs where xs = x:xs
replicate :: Int -> a -> [a]
replicate n x = take n (repeat x)
cycle :: [a] -> [a]
cycle [] = error "Prelude.cycle: empty list"
cycle xs = xs' where xs' = xs++xs'
take, drop :: Int -> [a] -> [a]
take n _ | n <= 0 = []
take _ [] = []
take n (x:xs) = x : take (n-1) xs
drop n xs | n <= 0 = xs
drop _ [] = []
drop n (_:xs) = drop (n-1) xs
splitAt :: Int -> [a] -> ([a],[a])
splitAt n xs = (take n xs, drop n xs)
takeWhile, dropWhile :: (a -> Bool) -> [a] -> [a]
takeWhile p [] = []
takeWhile p (x:xs)
| p x = x : takeWhile p xs
| otherwise = []
dropWhile p [] = []
dropWhile p xs@(x:xs')
| p x = dropWhile p xs'
| otherwise = xs
lines, words :: String -> [String]
-- lines "apa\nbepa\ncepa\n" == ["apa","bepa","cepa"]
-- words "apa bepa\n cepa" == ["apa","bepa","cepa"]
unlines, unwords :: [String] -> String
-- unlines ["apa","bepa","cepa"] == "apa\nbepa\ncepa"
-- unwords ["apa","bepa","cepa"] == "apa bepa cepa"
reverse :: [a] -> [a]
reverse = foldl (flip (:)) []
and, or :: [Bool] -> Bool
and = foldr (&&) True
or = foldr (||) False
any, all :: (a -> Bool) -> [a] -> Bool
any p = or . map p
all p = and . map p
elem, notElem :: (Eq a) => a -> [a] -> Bool
elem x = any (== x)
notElem x = all (/= x)
lookup :: (Eq a) => a -> [(a,b)] -> Maybe b
lookup key [] = Nothing
lookup key ((x,y):xys)
| key == x = Just y
| otherwise = lookup key xys
sum, product :: (Num a) => [a] -> a
sum = foldl (+) 0
product = foldl (*) 1
maximum, minimum :: (Ord a) => [a] -> a
maximum [] = error "Prelude.maximum: empty list"
maximum xs = foldl1 max xs
minimum [] = error "Prelude.minimum: empty list"
minimum xs = foldl1 min xs
zip :: [a] -> [b] -> [(a,b)]
zip = zipWith (,)
zipWith :: (a->b->c) -> [a]->[b]->[c]
zipWith z (a:as) (b:bs)
= z a b : zipWith z as bs
zipWith _ _ _ = []
unzip :: [(a,b)] -> ([a],[b])
unzip = foldr (\(a,b) ~(as,bs) -> (a:as,b:bs)) ([],[])
nub :: (Eq a) => [a] -> [a]
nub [] = []
nub (x:xs) = x : nub [ y | y <- xs, x /= y ]
delete :: Eq a => a -> [a] -> [a]
delete y [] = []
delete y (x:xs) = if x == y then xs else x : delete y xs
(\\) :: Eq a => [a] -> [a]-> [a]
(\\) = foldl (flip delete)
union :: Eq a => [a] -> [a] -> [a]
union xs ys = xs ++ ( ys \\ xs )
intersect :: Eq a => [a] -> [a]-> [a]
intersect xs ys = [ x | x <- xs, x `elem` ys ]
intersperse :: a -> [a] -> [a]
-- intersperse 0 [1,2,3,4] == [1,0,2,0,3,0,4]
transpose :: [[a]] -> [[a]]
-- transpose [[1,2,3],[4,5,6]] == [[1,4],[2,5],[3,6]]
partition :: (a -> Bool) -> [a] -> ([a],[a])
partition p xs = (filter p xs, filter (not . p) xs)
group :: Eq a => [a] -> [[a]]
-- group "aapaabbbeee" == ["aa","p","aa","bbb","eee"]
isPrefixOf, isSuffixOf :: Eq a => [a] -> [a] -> Bool
isPrefixOf [] _ = True
isPrefixOf _ [] = False
isPrefixOf (x:xs) (y:ys) = x == y && isPrefixOf xs ys
isSuffixOf x y = reverse x `isPrefixOf` reverse y
sort :: (Ord a) => [a] -> [a]
sort = foldr insert []
insert :: (Ord a) => a -> [a] -> [a]
insert x [] = [x]
insert x (y:xs) = if x <= y then x:y:xs else y:insert x xs
------------------------------------------------------------
-- functions on Char
type String = [Char]
toUpper, toLower :: Char -> Char
-- toUpper 'a' == 'A'
-- toLower 'Z' == 'z'
digitToInt :: Char -> Int
-- digitToInt '8' == 8
intToDigit :: Int -> Char
-- intToDigit 3 == '3'
ord :: Char -> Int
chr :: Int -> Char
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