setof/3 — all unique solutions for a goal, sorted
bagof/3 — all solutions for a goal, not sorted
findall/3 — all solutions for a goal, not sorted
b_findall/4 — bound list of solutions for a goal, not sorted
setof(Template, Goal, Collection) bagof(Template, Goal, Collection) findall(Template, Goal, Collection) b_findall(Template, Goal, Collection, Bound)
These predicates collect in the list
Collection, the set of all instances of
Template such that the goal,
Goal, is provable.
Template is a term that usually shares variables with
setof/3 produces a
Collection which is sorted according to the standard order with all duplicate elements removed. Both
Collections that are not sorted.
If there are no solutions to
bagof/3 will fail, whereas,
Variables that occur in
Goal and not within
Template are known as free, variables.
bagof/3 will generate alternative bindings for free variables upon backtracking.
Within a call to
bagof/3, free variables can be existentially quantified in
Goal by using the notation
Variable^Query. This means that there exists a
Variable such that
Query is true.
The collection to be enumerated should be finite, and should be enumerable by Prolog in finite time. It is possible for the provable instances of
Template to contain variables, but in this case
Collection will only provide an imperfect representation of what is actually an infinite collection.
setof/3 calls upon
sort/2 to eliminate duplicate solutions from
Collection, which seriously impacts its efficiency. In addition, even though
bagof/3 leaves duplicate solutions, it still calls
findall/3 neither removes duplicates nor generates alternative bindings for free variables; it assumes that all variables occurring within
Goal are existentially quantified. As a result,
findall/3 is much more efficient than either
Bound is a positive integer,
b_findall/4 operates similarly to
findall/3, except that it returns at most
Bound number of solutions on the list
Collection. It fails if
Bound is anything other than a positive integer.
?- listing. % user:likes/2 likes(kev,running). likes(kev,lifting). likes(keith,running). likes(keith,lifting). likes(ken,swimming). likes(sally,swimming). likes(andy,bicycling). likes(chris,lifting). likes(chris,running). yes.
?- setof(Person, likes(Person, Sport), SetOfPeople). Person = _1 Sport = bicycling SetOfPeople = [andy]; Person = _1 Sport = lifting SetOfPeople = [chris,keith,kev]; Person = _1 Sport = running SetOfPeople = [chris,keith,kev]; Person = _1 Sport = swimming SetOfPeople = [sally,ken]; no.
?- setof((Sport,People), setof(Person, likes(Person, Sport), People), Set). Sport = _1 People = _2 Person = _4 Set = [(bicycling,[andy]),(lifting,[chris,keith,kev]), (running,[chris,keith,kev]),(swimming,[sally,ken])] yes.
?- setof(Person, Sport^(Person likes Sport), SetOfPeople). Person = _1 Sport = _2 SetOfPeople = [andy,chris,sally,keith,ken,kev] yes.