Model Conjectures for Z Specifications

The primary purpose of a specification is to make explicit the intentions of designers. For these intentions to be expressed precisely, a formal (mathematical) language should be used. The use of a formal language per se does not guarantee that intentions will be expressed correctly, but provides a basis for arguments of correctness. Z is a rich and expressive formal language. Arguments of correctness translate, in Z, to arguments about models of specifications, i.e., the values assigned to components of the specification that simultaneously satisfy the constraints of the specification. A specification for which there is no model cannot be a correct expression of any reasonable intentions. A model conjecture for a specification is a conjecture the proof of which is a proof that the specification has a model. This paper shows how a model conjecture may be formally derived from a Z specification.