Why is the list [1] not included in the answer P = [[]]? Prolog

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I'm learning Prolog but I came across this questions when learning about database manipulation. when I ask the Prolog interpreter:

 findall(X,subset(X,[1]),P).

the only subset give is

P = [[]].

Why is this?

prolog
1 Answers

In SWI-Prolog, the predicate subset/2 is defined as:

% subset(+SubSet, +Set)

subset([], _) :- !.
subset([E|R], Set) :-
    memberchk(E, Set),
    subset(R, Set).

To obtain the desired result, you can use the following alternative definition:

% sub_set(?SubSet, +Set)

sub_set([], []).
sub_set(SubSet, [_|Set]) :- sub_set(SubSet, Set).
sub_set([X|SubSet], [X|Set]) :- sub_set(SubSet, Set).

Examples:

?- sub_set(S,[a,b,c]).
S = [] ;
S = [c] ;
S = [b] ;
S = [b, c] ;
S = [a] ;
S = [a, c] ;
S = [a, b] ;
S = [a, b, c] ;
false.

?- sub_set([a,c],[a,b,c]).
true ;
false.

?- findall(SubSet, sub_set(SubSet,[1]), PowerSet).
PowerSet = [[], [1]].
user_115359400
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