On the Semantic Relation of Z and HOL

We 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.