Curry: An Integrated Functional Logic Language

-- Is a list empty?
null :: [_] -> Bool
null [] = True
null (_:_) = False
-- Concatenation
(++) :: [a] -> [a] -> [a]
[] ++ ys = ys
(x:xs) ++ ys = x : xs++ys
-- List length
length :: [a] -> Int
length [] = 0
length (_:xs) = 1 + length xs
-- List index (subscript) operator, head has index 0
(!!) :: [a] -> Int -> a
(x:xs) !! n | n==0 = x
| n>0 = xs !! (n-1)
-- Map a function on a list
map :: (a->b) -> [a] -> [b]
map _ [] = []
map f (x:xs) = f x : map f xs
-- Accumulate all list elements by applying a binary operator from
-- left to right, i.e.,
-- foldl f z [x1,x2,...,xn] = (...((z ‘f‘ x1) ‘f‘ x2) ...) ‘f‘ xn :
foldl :: (a -> b -> a) -> a -> [b] -> a
foldl _ z [] = z
foldl f z (x:xs) = foldl f (f z x) xs
-- Accumulate a non-empty list from left to right:
foldl1 :: (a -> a -> a) -> [a] -> a
foldl1 f (x:xs) = foldl f x xs
-- Accumulate all list elements by applying a binary operator from
-- right to left, i.e.,
-- foldr f z [x1,x2,...,xn] = (x1 ‘f‘ (x2 ‘f‘ ... (xn ‘f‘ z)...)) :
foldr :: (a->b->b) -> b -> [a] -> b
foldr _ z [] = z
foldr f z (x:xs) = f x (foldr f z xs)
-- Accumulate a non-empty list from right to left:
foldr1 :: (a -> a -> a) -> [a] -> a
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