(*world*)

signature WORLD =
sig
 val remove: ''a -> ''a list -> ''a list
 val reverse: 'a list -> 'a list
end;

structure world:WORLD =
struct

fun accumulate f a [] = a
   |accumulate f a (b::x) = accumulate f (f a b) x;

fun append x y = x @ y;

fun member e [] = false
   |member e (a::x) = e=a orelse member e x;

fun remove e [] = []
   |remove e (a::x) = if e=a then remove e x else a::remove e x;

fun subset x y = let fun subsetp [] y = true
                        |subsetp (a::x) y = member a y andalso subsetp x y
                     in (length x) <= (length y) andalso subsetp x y end;

fun superset x y = subset y x;

fun filter p [] = []
   |filter p (a::x) = if p a then a::filter p x else filter p x;

fun exists p [] = false
   |exists p (a::x) = p a orelse exists p x;

fun all p [] = true
   |all p (a::x) = p a andalso all p x;

fun zip f [] [] = []
   |zip f [] (b::y) = []
   |zip f (a::x) [] = []
   |zip f (a::x) (b::y) = f a b::zip f x y;

fun nth n [] = []
   |nth 1 (a::x) = [a]
   |nth n (a::x) = nth (n-1) x;

fun reverse [] = []
   |reverse (a::x) = (reverse x) @ [a];

end;