Summary: A Theory for Abstract Reduction Systems in PVS
Andr´e Luiz Galdino
Departamento de Matem´atica, Universidade Federal de Goi´as
Campus de Catal~ao, Brazil
Instituto de Ci^encias Exatas, Universidade de Bras´ilia
Bras´ilia D.F., Brazil
A theory for Abstract Reduction Systems (ARS) in the proof assistant PVS (Prototype Verification System)
is described. Adequate specifications of basic definitions and notions such as reduction, confluence, normal
form are given and well-known results proved, which includes non trivial ones such as Noetherian Induction,
Newman's Lemma and its generalizations, and Commutation Lemma among others. Although term rewrit-
ing proving technologies have been specified in several specification languages and proof assistants, to our
knowledge this has not been done in PVS. This makes relevant our ARS specification as the initial step in
the formulation of a complete theory for Term Rewriting Systems (TRS) in PVS.
Keywords: Abstract Reduction Systems, Term Rewriting Systems, Automated Theorem Proving, PVS.