Formalising Generalised Substitutions

Abstract

Abstract. We use the theorem prover Isabelle to formalise and machinecheck results of the theory of generalised substitutions given by Dunne and used in the B method. We describe the model of computation implicit in this theory and show how this is based on a compound monad, and we contrast this model of computation and monad with those implicit in Dunne's theory of abstract commands. Subject to a qualification concerning frames, we prove, using the Isabelle/HOL theorem prover, that Dunne's results about generalised substitutions follow from the model of computation which we describe.

Software Component Design with the B Method — A Formalization in Isabelle/HOL

“…It is noteworthy that their work provides a semantics for the language in terms of state transition systems, and is quite complementary to ours. Dunne [12] produced a mathematical formalization of the generalized substitution language, which was implemented in Isabelle/HOL by Dawson [13]. More recently, Jacquel et al [14] have used Coq to formalize a proof system for B, therefore providing another rigorous framework to reason about the expression language of B.…”