setof

Setof is a Prolog built-in predicate used to collect all solutions of a goal into a single, sorted, deduplicated list. It has the form setof(Template, Goal, Set). Set is the list of all instances of Template that make Goal true, with duplicates removed and the results ordered according to the standard term order.

Key points about its behavior:

- Template specifies the form of the elements to collect. Each solution of Goal yields one Template, and those Templates are gathered into Set.

- Variables that appear in Goal but do not appear in Template are treated as existentially quantified. This means the set of solutions can be partitioned by the bindings of those variables; in practice, this grouping can lead to multiple distinct result sets depending on how the existential variables can be instantiated. If you want to collect all groups, bagof/3 is often used; if you want to collect all solutions without any grouping, findall/3 can be used.

- Setof returns a single Set for the current binding of existential variables; it fails if there are no solutions for Goal.

- The produced Set is sorted and contains no duplicates, forming a true “set” in the mathematical sense.

Examples:

- setof(X, member(X, [a, b, a]), S). S = [a, b].

- color(apple, Color). Facts: color(apple, red). color(apple, green). Then setof(Color, color(apple, Color), Colors) yields Colors = [green, red].

Relation to other predicates:

- bagof/3 behaves similarly but groups results according to the values of existential variables, producing separate sets for different groupings.

- findall/3 collects all solutions without sorting or removing duplicates.