--
-- file:    prelude.es
--
-- created: 14/11/96 by Andrew Rock.
--
-- purpose: File of bindings automatically loaded by entre.
--


------ Lists.

-- Length of a list.
-- length :: [a] -> Integer
   length xs = if xs == [] 
                  then 0 
                  else 1 + length (tail xs)


-- is x an element of list xs
-- elem :: a -> [a] -> Bool
   elem x xs = if xs == []
                  then False
                  else if x == head xs
                          then True
                          else elem x (tail xs)


------ Higher order functions (handy combinators).

-- function composition.
-- compose :: (b -> c) -> (a -> b) -> (a -> c)
   compose f g x = f (g x)

-- flip the order of arguments in a function of arity 2
-- flip :: (a -> b -> c) -> b -> a -> c
   flip f x y = f y x


------ Higher order functions for lists.

-- map
-- map :: (a -> b) -> [a] -> [b]
   map f xs = if xs == []
                 then []
                 else (f (head xs)) : (map f (tail xs))

-- filter
-- filter :: (a -> Bool) -> [a] -> [a]
   filter f xs = if xs == []
                    then []
                    else if f (head xs)
                            then (head xs) : (filter f (tail xs))
                            else filter f (tail xs)

-- foldl
-- foldl :: (a -> b -> a) -> a -> [b] -> a
   foldl f z xs = if xs == []
                     then z
                     else foldl f (f z (head xs)) (tail xs)

-- foldr
-- foldr :: (a -> b -> b) -> b -> [a] -> b
   foldr f z xs = if xs == []
                     then z
                     else f (head xs) (foldr f z (tail xs))