How would you define map and filter using foldr in Haskell?

Question

I\'m doing a bit of self study on functional languages (currently using Haskell). I came across a Haskell based assignment which requires defining map and filter in terms of

Answer 1

Your solution almost works .) The problem is that you've got two differend bindings for x in both your functions (Inside the patternmatching and inside your lambda expression), therefore you loose track of the first Element.

map'            :: (a -> b) -> [a] -> [b]
map' f []       = []
map' f (x:xs)   = foldr (\x xs -> (f x):xs) [] (x:xs)

filter'             :: (a -> Bool) -> [a] -> [a]
filter' p []        = []
filter' p (x:xs)    = foldr (\x xs -> if p x then x:xs else xs ) [] (x:xs)

This should to the trick :). Also: you can write your functions pointfree style easily.