Program committee

Abstract

Confluence is a critical property of computational systems which is related with determinism and non ambiguity and thus with other relevant computational attributes of functional specifications and rewriting system as termination and completion. Several criteria have been explored that guarantee confluence and their formalisations provide further interesting information. This talk will discuss topics related with the formalisation of confluence properties in the prototype verification system PVS. Syntactic criteria such as avoiding overlapping of rules as well as linearity of rules have been used as a discipline of functional programming which avoids ambiguity. In the context of term rewriting systems, well-known results such as Newman’s Lemma [7], Rosen’s Confluence of Orthogonal term rewriting systems [9] as well as the famous KnutBendix(-Huet) Critical Pair Theorem [6, 5] are of great theoretical and practical relevance. The first one, guarantees confluence of Noetherian and locally confluent abstract reduction systems; the second one, assures confluence of orthogonal term rewriting systems, that are systems which avoid ambiguities generated by overlapping of their rules and whose rules do not allow repetitions of variables in their left-hand side (i.e., left-linear); and, the third one provides local confluence of term rewriting systems whose critical pairs are joinable. Formalisations of these confluence criteria provide valuable and precise data about the theory of rewriting (cf. [4], [3], [8]). Several aspects that arise from these formalisations are of great relevance for the formal discussion about how these properties should be adequately ported to different computational contexts such as the nominal approach of rewriting (cf. [1] [2]).