4 UNEMAT: UN Encuentro de Matemáticas 2016 Conferencia

4 UNEMAT: UN Encuentro de Matemáticas 2016 Conferencia

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UNEMAT: UN Encuentro de Matemáticas 2016
7 al 10 de junio de 2016, Universidad Nacional de Colombia, Bogotá, Colombia
Conferencia
Mechanical formalization of computational
properties
Mauricio Ayala Rincón
[email protected]
Departamento de Matemática
Universidade de Brasilia, Brasil
Abstract
Ensuring that programs and computer specifications meet computational requirements as termination and confluence is closely related with guaranteeing quality of software and hardware: processes progress and conclude, user?s requests and queries are
effectively addressed, computed answers are unique, computational actions are unambiguous, etc. In the context of functional specifications (where only recursion, branching
and assignment commands are admissible) and in particular in the rewriting framework, non ambiguity is guaranteed by well established mathematical criteria such as
the Knuth-Bendix Critical Pairs Lemma, in the case of terminating term rewriting systems, and the criterion of orthogonality, according to Rosen Parallel Moves Lemma,
for the case of non necessarily terminating systems. In this talk, aspects related with
the formalization in the proof assistant PVS, of these and other criteria to guarantee
confluence and termination of rewriting systems will be addressed.
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