Z Mathematical Toolkit in Isabelle/HOL

Simon Foster 📧, Pedro Ribeiro, Frank Zeyda 📧 and Jim Woodcock

October 16, 2025

Abstract

The objective of this theory development is an implementation of the Z mathematical toolkit in Isabelle/HOL that is both efficient for proof and faithful to the standard. We construct the Z metalanguage and type universe on top of HOL, and link this to corresponding concrete types (finite functions, lists etc.) in Isabelle, to enable efficient proof automation. We then utilise coercive subtyping and overloading to support processing of Z-like expressions in Isabelle/HOL. We then use this to develop the mathematical toolkit for sets, relations, functions, and sequences.

License

BSD License

Topics

Related publications

  • Foster, S., Baxter, J., Cavalcanti, A., Woodcock, J., & Zeyda, F. (2020). Unifying semantic foundations for automated verification tools in Isabelle/UTP. Science of Computer Programming, 197, 102510. https://doi.org/10.1016/j.scico.2020.102510
  • Foster, S., Hur, C.-K., & Woodcock, J. (2025). Unifying Model Execution and Deductive Verification with Interaction Trees in Isabelle/HOL. ACM Transactions on Software Engineering and Methodology, 34(4), 1–40. https://doi.org/10.1145/3702981

Session Z_Toolkit

Depends on