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Mapping Sets and Hypersets into Numbers

D’Agostino G., Omodeo E. G., Policriti A., Tomescu A. I.

Fundamenta Informaticae

2015

Vol. 140, nr 3/4

307--328

We introduce and prove the basic properties of encodings that generalize to non-wellfounded hereditarily finite sets the bijection defined by Ackermann in 1937 between hereditarily finite sets and natural numbers.

A uniform axiomatic view of lists, multisets, and sets, and the relevant unification algorithms

Dovier A., Policriti A., Rossi G.

Fundamenta Informaticae

1998

Vol. 36, nr 2,3

201-234

The first-order theories of lists, multisets, compact lists (i.e., lists, where the number of contiguous occurrences of each element is immaterial) , and sets are introduced via axioms. Such axiomatizations are shown to be very well-suited for the integration with free functor symbols governed by the classical Clark's axioms in the context of (Constraint) Logic Programming. Adaptations of the extensionally principle to the various theories taken into account is then exploited in the design of unification algorithms for the considered data structures. All the theories presented can be combined providing frameworks to deal with several of the proposed data structures simultaneously. The unification algorithms proposed can be combined (merged) as well, to produce engines for such combination theories.