|• ref-all-cse-equ:||Existential Quantifier|
setof(Template, Generator, Set)
returns the set Set of all instances of Template
such that Generator is provable, where that set is non-empty. The term
Generator specifies a goal to be called as if by
Set is a set of terms represented as a list of those terms, without
duplicates, in the standard order for terms (see ref-lte-cte).
Obviously, the set to be enumerated should be finite, and should be enumerable by Prolog in finite time. It is possible for the provable instances to contain variables, but in this case Set will only provide an imperfect representation of what is in reality an infinite set.
If Generator is instantiated, but contains uninstantiated
variables that do not also appear in Template, then
setof/3 can succeed nondeterminately, generating alternative
values for Set corresponding to different instantiations of the
free variables of Generator. (It is to allow for such usage
that Set is constrained to be non-empty.) For example, if
your program contained the clauses
likes(tom, beer). likes(dick, beer). likes(harry, beer). likes(bill, cider). likes(jan, cider). likes(tom, cider).
then the call
| ?- setof(X, likes(X,Y), S).
might produce two alternative solutions via backtracking:
Y = beer, S = [dick,harry,tom] ; Y = cider, S = [bill,jan,tom] ; no
| ?- setof((Y,S), setof(X,likes(X,Y),S), SS).
would then produce
SS = [(beer,[dick,harry,tom]),(cider,[bill,jan,tom])] ; no