### 9Set Predicates

The goal

(%bag-of X G Bag)

unifies with Bag the list of all instantiations of X for which G succeeds. Thus, the following query asks for all the things known — ie, the collection of things such that someone knows them:

 > (%which (things-known) (%let (someone x) (%bag-of x (%knows someone x) things-known)))
 '((things-known TeX Racket Prolog Penelope TeX Prolog Odysseus TeX calculus archery))

This is the only solution for this goal:

 > (%more) #f

Note that some things — eg, TeX — are enumerated more than once. This is because more than one person knows TeX. To remove duplicates, use the predicate %set-of instead of %bag-of:

 > (%which (things-known) (%let (someone x) (%set-of x (%knows someone x) things-known)))

'((things-known TeX Racket Prolog Penelope Odysseus calculus archery))

In the above, the free variable someone in the %knows-goal is used as if it were existentially quantified. In contrast, Prolog’s versions of %bag-of and %set-of fix it for each solution of the set-predicate goal. We can do it too with some additional syntax that identifies the free variable. Eg,

 > (%which (someone things-known) (%let (x) (%bag-of x (%free-vars (someone) (%knows someone x)) things-known)))

'((someone . Odysseus) (things-known TeX Racket Prolog Penelope))

The bag of things known by one someone is returned. That someone is Odysseus. The query can be retried for more solutions, each listing the things known by a different someone:

 > (%more) '((someone . Penelope) (things-known TeX Prolog Odysseus)) > (%more) '((someone . Telemachus) (things-known TeX calculus)) > (%more) '((someone . Odysseus) (things-known archery)) > (%more) #f

Racklog also provides two variants of these set predicates, viz., %bag-of-1 and %set-of-1. These act like %bag-of and %set-of but fail if the resulting bag or set is empty.