A Uniform Axiomatic View of Lists, Multisets, and Sets, and the Relevant Unification Algorithms (1998)
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@MISC{Dovier98auniform,
author = {Agostino Dovier and Alberto Policriti and Gianfranco Rossi},
title = {A Uniform Axiomatic View of Lists, Multisets, and Sets, and the Relevant Unification Algorithms},
year = {1998}
}
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Abstract
. The rst-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 extensionality principle to the various theories taken into account is then exploited in the design of unication algorithms for the considered data structures. All the theories presented can be combined providing frameworks to deal with We acknowledge partial support from C.N.R. Grant 97.02426.CT12, C.N.R. project SETA, and from the MURST project \Tecniche formali per la specica, l'analisi, la verica, la sintesi e la trasformazione di sistemi software". 202 Dovier, Policriti, and Rossi / A uniform axiomatic view of lists, multisets, and sets several of the proposed data structures simultan...
