Formalising General Correctness

Abstract

We consider the abstract command language of Dunne, and his account of general correctness. We provide an operational interpretation of his abstract commands, and use the automated theorem proving system Isabelle to prove that this operational interpretation leads to Dunne's semantics. We consider the difficulties in precisely formalising some formulae found in the literature.

Formalising Generalised Substitutions

“…Firstly, we review the operational model of [6], which we used for abstract commands, based on general correctness. Then we describe the model, on which this paper is based, which fits the total correctness framework of generalised substitutions.…”

“…To express that a command can either terminate in a new state or fail to terminate, in [6] we considered command outcomes, where an outcome is either termination in a new state or non-termination. Then we model a command as a function, of type state → outcome set, from states to sets of outcomes.…”

“…Furthermore, this distributive law is also a monad morphism from the monad of [6] to the monad described in this paper.…”

“…In this paper we formalise this theory of generalised substitutions, using a similar approach to our work on abstract commands in [6], and using some of its results. That is, we develop a model of computation and define the theory in terms of it.…”

“…He defined a language of "abstract commands", giving several basic abstract commands and operators for joining them, for which he gave rules in terms of weakest liberal preconditions and termination conditions. In [6] we considered this abstract command language and described the operational interpretation of the abstract commands, showing how it is based on a compound monad. We used the automated theorem proving system Isabelle to prove that the operational interpretation implies the rules given by Dunne. In [3] Chartier formalised the operations of the B method of Abrial [1] in Isabelle/HOL.…”