4.29 Finding all Solutions to a Goal

[ISO]findall(+Template, :Goal, -Bag)

Create a list of the instantiations Template gets successively on backtracking over Goal and unify the result with Bag. Succeeds with an empty list if Goal has no solutions. findall/3 is equivalent to bagof/3 with all free variables bound with the existential operator (^), except that bagof/3 fails when Goal has no solutions.

findall(+Template, :Goal, -Bag, +Tail)

As findall/3, but returns the result as the difference list Bag-Tail. The 3-argument version is defined as

findall(Templ, Goal, Bag) :-
        findall(Templ, Goal, Bag, [])

[ISO]bagof(+Template, :Goal, -Bag)

Unify Bag with the alternatives of Template. If Goal has free variables besides the one sharing with Template, bagof/3 will backtrack over the alternatives of these free variables, unifying Bag with the corresponding alternatives of Template. The construct +Var^Goal tells bagof/3 not to bind Var in Goal. bagof/3 fails if Goal has no solutions.

The example below illustrates bagof/3 and the ^ operator. The variable bindings are printed together on one line to save paper.

2 ?- listing(foo).
foo(a, b, c).
foo(a, b, d).
foo(b, c, e).
foo(b, c, f).
foo(c, c, g).
true.

3 ?- bagof(C, foo(A, B, C), Cs).
A = a, B = b, C = G308, Cs = [c, d] ;
A = b, B = c, C = G308, Cs = [e, f] ;
A = c, B = c, C = G308, Cs = [g].

4 ?- bagof(C, A^foo(A, B, C), Cs).
A = G324, B = b, C = G326, Cs = [c, d] ;
A = G324, B = c, C = G326, Cs = [e, f, g].

5 ?-

[ISO]setof(+Template, +Goal, -Set)

Equivalent to bagof/3, but sorts the result using sort/2 to get a sorted list of alternatives without duplicates.