Rule Formats for Determinism and Idempotence

Operational semantics describes the behaviour of programs in a language in terms of their execution on an abstract machine, which is often represented as a, possibly infinite, state machine. Structural Operational Semantics is a rule-based and syntax-driven approach to giving operational semantics to programming and specification languages. Determinism is a semantic property of (a fragment of) a language that specifies that a program cannot evolve operationally in several different ways. Idempotence is a property of binary language constructs requiring that the composition of two identical specifications or programs will result in a piece of specification or program that is equivalent to the original components. In this talk, I will discuss two (related) meta-theorems for guaranteeing determinism and idempotence of binary operators. These meta-theorems are formulated in terms of syntactic templates for operational semantics, called rule formats. I will argue for the applicability of the proposed formats by applying them to various operational semantics from the literature. The talk is based on joint work with Arnar Birgisson (Chalmers), Anna Ingolfsdottir (Reykjavik University), MohammadReza Mousavi (TU Eindhoven) and Michel A. Reniers (TU Eindhoven). A journal paper based on this work will appear in Science of Computer Programming (http://dx.doi.org/10.1016/j.scico.2010.04.002).