module builtint.

type length   list A -> int -> o.
type countup  int -> list int -> int -> o.
type nth      int -> list A -> A -> o.

length nil 0.
length (X::L) N1 :- length L N, N1 is N + 1.

countup N nil M      :-  N > M, !.
countup N (N::nil) N :- !.
countup N (N::L) M   :- N1 is N + 1, countup N1 L M.

nth N L X :- N < 1, !, fail.
nth 1 (X::L) X :- !.
nth N (X::L) Y :- N1 is N - 1,  nth N1 L Y.