On the Semantic Relation of Z and HOL

Abstract

AbstractWe investigate the relation between the semantic models of Z, as proposed by the Z draft standard, and of the polymorphic version of higher-order logic that is the basis for proof systems such as HOL and Isabelle/HOL. Disregarding the names in schema types, the type models of the two systems can be identified up to isomorphism. That isomorphism determines to a large extent how terms of Z can be represented in higher-order logic. This justifies the soundness of proof support for Z based on higher-order logic, such as the encoding \(\ensuremath{\mathcal{HOL\mbox{-}Z}}\) of Z in Isabelle/HOL.The comparison of the two semantic models also motivates a discussion of open issues in the development of a complete semantics of Z, in particular concerning the type system, generic constructs, and approaches to base the semantics of Z on a small kernel language.KeywordsSchema SignatureType VariableSemantic RelationSemantic ModelProof SystemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.