A PVS Theory for Term Rewriting Systems

Authors:
André L. Galdino;Mauricio Ayala-Rincón
Affiliations:
Grupo de Teoria da Computação, Departamento de Matemática, Universidade de Brasília, Brasília D.F., Brazil and Departamento de Matemática, Universidade Federal de Goi ...;Grupo de Teoria da Computação, Departamento de Matemática, Universidade de Brasília, Brasília D.F., Brazil
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2009

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Abstract

A theory, called trs, for Term Rewriting Systems in the theorem Prover PVS is described. This theory is built on the PVS libraries for finite sequences and sets and a previously developed PVS theory named ars for Abstract Reduction Systems which was built on the PVS libraries for sets. Theories for dealing with the structure of terms, for replacements and substitutions jointly with ars allow for adequate specifications of notions of term rewriting such as critical pairs and formalization of elaborated criteria from the theory of Term Rewriting Systems such as the Knuth-Bendix Critical Pair Theorem. On the other hand, ars specifies definitions and notions such as reduction, confluence and normal forms as well as non basic concepts such as Noetherianity.