pointfree01.hs

-- Derivation of (f .) . g == f (g x y)

-- Examples
countWhere = (length .) . filter
duplicate  = (concat .) . replicate
concatMap  = (concat .) . map

-- Could also be written
countWhere p xs = length (filter p xs)
duplicate n xs = concat (replicate n xs)
concatMap f xs = concat (map f xs)

-- Reverse derivation
-- (f .) . g
-- == \x -> ((f .) . g) x
-- == \x -> (f .) (g x)
-- == \x -> f . (g x)
-- == \x y -> (f . (g x)) y
-- == \x y -> f ((g x) y)
-- == \x y -> f (g x y)