:- use_module(library(clpfd)).
:- use_module(library(lists)).
:- use_module(library(time)).

elem_at(Index, List, Elem) :-
    elem_at_inner(Index, 0, List, Elem).
elem_at_inner(Index, Index, [Elem | _], Elem).
elem_at_inner(Index, IndexCandidate, [_ | Rest], Elem) :-
    Index #> IndexCandidate,
    NewIndexCandidate #= IndexCandidate + 1,
    elem_at_inner(Index, NewIndexCandidate, Rest, Elem).

lookup1(List, N, M, Elem) :-
    nth0(Index, List, Elem),
    N =< Index, Index < M.

lookup2(List, N, M, Elem) :-
    between(N, M, Index),
    nth0(Index, List, Elem).

lookup3(List, N, M, Elem) :-
    N #=< Index, Index #< M,
    elem_at(Index, List, Elem).

testall :-
    length(List, 10 000),
    time(findall(E, lookup1(List, 0, 5000, E), _)), % 'naive'),
    time(findall(E, lookup2(List, 0, 5000, E), _)), % 'between'),
    time(findall(E, lookup3(List, 0, 5000, E), _)). % 'constraint').