Type inference in Z

Abstract

Generic definitions provide an important part of the power of the Z notation, allowing the standard toolkit of mathematical notation to be built up from a very small set of primitives, and permitting application-oriented theories to be constructed with an appropriate degree of abstraction and generality. Although there is a notation for supplying explicitly the actual generic parameters when a generic constant is used, it greatly improves the readability of a Z document if the actual parameters are left to be inferred from the context, especially since every symbol from the basic mathematical toolkit would otherwise need explicit generic type parameters. In this paper we present and justify a method by which a type-checking program can carry out this inference of implicit generic parameters and check that the context determines them unambiguously. In the appendix we show the text of a type-checker for Z written in standard ML.