• ref-all-cse-equ: | Existential Quantifier |

`setof(`

returns the set `Template`, `Generator`, `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 `call/1`

.
`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 don’t also appear in `Template`,
`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).

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

The call

| ?-setof((Y,S), setof(X,likes(X,Y),S), SS).

would then produce

SS = [(beer,[dick,harry,tom]),(cider,[bill,jan,tom])];no

See mpg-ref-setof.

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