Recursive way in Prolog

Question

How does intersect(L1,L2,L3) in second rule work? Can someone trace me through it? Still a beginner in Prolog.

intersect([],L,[]).
intersect([A|L1],L2,[A|L3]) :-
   member(A,L2),
   intersect(L1,L2,L3).

Answer 1

The second rule means:

If the head of the first list is present in the second list,
then it is also present in the third.

Consider the lists L1 = [a, b, c] and L2 = [d, b]. We calculate their insection as follows:

intersect([a|[b,c]], L2, [a|L3]) :- member(a, L2), intersect([b,c], L2, L3)

a is not in L2, so this is false. Proceeding:

intersect([b|[c]], L2, [b|L3]) :- member(b, L2), intersect([c], L2, L3)

b is in L2, so b is in the intersection. Proceeding:

intersect([c|[]], L2, [c|L3]) :- member(c, L2), intersect([], L2, L3)

c is not in L2, so this is false. Proceeding:

intersect([], L2, [])

This is the base case. So the intersection is [b].