Question

In Prolog how do you write a procedure that can be used to test whether or not a list represents a set with no duplicates?

Answer 1

There are several ways to do this. @thanosQR is right in pointing to SWI-Prolog’s is_set/1, but if you want a portable solution, you can define that predicate in terms of setof:

is_set(Lst) :-
    setof(X, member(X, Lst), Set),
    length(Lst, N),
    length(Set, N).

A list contains no duplicates if its number of elements is equal to the number of elements in the setof its elements.

You can also use the (I believe non-standard, but commonly available) sort/2, which eliminates duplicates:

is_set(Lst) :-
    sort(Lst, Set),
    length(Lst, N),
    length(Set, N).

This takes O(n lg n) time to run.