map-filter-fold.ml

(* map *) 
 
fun map(_, nil) = nil
| map(f, (head::tail)) = f(head) :: map(f, tail)
 
(* filter *)
 
fun filter(_, nil) = nil
| filter(p, (head::tail)) = if p(head)
then (head :: filter(p, tail))
else filter(p, tail)
 
(* fold *)
 
fun fold(_, v, nil) = v
| fold(f, v, (head::tail)) = f(head, fold(f, v, tail))
 
(* map and filter defined in terms of fold *)
 
fun map(f, L) = fold((fn x, xs => (f(x):xs)), [], L)
fun filter(p, L) = fold((fn x, xs => if p(x) then x:xs else xs end), [], L)