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Verification of Newman's and Yokouchi's Lemmas in PVS Andre Luiz Galdino1,2

Summary: Verification of Newman's and Yokouchi's Lemmas in PVS
Andr´e Luiz Galdino1,2
, Mauricio Ayala-Rinc´on1
Grupo de Teoria da Computac¸~ao
Instituto de Ci^encias Exatas ­ Universidade de Bras´ilia
Bras´ilia, Brazil
Departamento de Matem´atica ­ Campus de Catal~ao ­ Universidade Federal de Goi´as
Catal~ao, Brazil
Abstract. This paper shows how a previously specified theory for Abstract Re-
duction Systems (ARSs) in which noetherianity was defined by the notion of well-
foundness over binary relations is used in order to prove results such as the well-
known Newman's Lemma and the Yokouchi's Lemma. The former one known as
the diamond lemma and the later which states a property of commutation be-
tween ARSs. The ars theory was specified in the Prototype Verification System
(PVS) for which to the best of our knowledge there are no available theory for
dealing with rewriting techniques in general. In addition to proof techniques
available in PVS the verification of these lemmas implies an elaborated use of


Source: Ayala-Rincón, Mauricio - Departamento de Matemática, Universidade de Brasília


Collections: Mathematics