Automata-Theoretic Semantics of Idealized Algol with Passive Expressions

Passive expressions in Algol-like languages represent computations that read the state but do not modify it. The need for such read-only computations arises in programming logics as well as in concurrent programming. It is also a central facet in Reynolds@?s Syntactic Control of Interference. Despite its importance and essentially basic character, capturing the notion of passivity in semantic models has proved to be difficult. In this paper, we provide a new model of passive expressions using an automata-theoretic framework recently proposed by the author. The central idea is that the store of a program is viewed as an abstract form of an automaton, with a representation of its states as well as state transitions. The framework allows us to combine the strengths of conventional state-based models and the more recent event-based models to synthesize new ''automata-based'' models. Once this basic framework is set up, relational parametricity does the job of identifying passive computations.