Check if all numbers in a list are different in prolog

Question

I want to create a rule in prolog that checks if there's a repeated number in a list.

For example:

• for [1,2,3,4] it will return true.
• for [1,2,3,3] it will return false because the 3 is repeated

I came up with this rule but it doesn't work

Different([]).
Different([H|T]):-
     Member(H,T),
     Different(T).

Any ideas?

Answer 1

a compact definition could be

all_diff(L) :- \+ (select(X,L,R), memberchk(X,R)).

i.e. all elements are different if we can't peek one and find it in the rest...

edit

Let's (marginally) improve efficiency: it's useless to check if X is member of the prefix sublist, so:

all_diff(L) :- \+ (append(_,[X|R],L), memberchk(X,R)).

Answer 2

The simplest way to check that all list members are unique is to sort list and check that length of the sorted list is equal of length of the original list.

different(X) :-
    sort(X, Sorted),
    length(X, OriginalLength),
    length(Sorted, SortedLength),
    OriginalLength == SortedLength.

Your solution doesn't work because of wrong syntax (facts and predicates should not begin with a capital letter) and a logic error. List is unique if head H is not a member of a tail T of a list and tail T is unique:

different([]).
different([H|T]):-
    \+member(H,T),
    different(T).