Abstract
We propose a categorical framework for structural operational semantics, in which we prove that under suitable hypotheses bisimilarity is a congruence. We then refine the framework to prove soundness of bisimulation up to context, an efficient method for reducing the size of bisimulation relations. Finally, we demonstrate the flexibility of our approach by reproving known results in three variants of the π-calculus.
Highlights
1.1 Motivation Structural operational semantics [Plotkin 1981] is a method for specifying the dynamics of programming languages by induction on their syntax
Instead, our aim is to find the right level of generality, by proposing a new theory of structural operational semantics which attempts to get closer to operational intuitions, while still proving useful abstract results – congruence of bisimilarity and soundness of bisimulation up to context
To get a feel for why monads on transition categories are relevant to operational semantics, let us consider the example of combinatory logic, viewed as a labelled transition system on just one label, i.e., a graph
Summary
1.1 Motivation Structural operational semantics [Plotkin 1981] is a method for specifying the dynamics of programming languages by induction on their syntax. Just like congruence of bisimilarity, soundness of bisimulation up to context has proved to be a subtle matter The difficulty of such questions, the former, led to a rich variety of syntactic formats [Mousavi et al 2007], which ensure good behaviour of the generated labelled transition system, up to some constraints on the considered specification. Instead, our aim is to find the right level of generality, by proposing a new theory of structural operational semantics which attempts to get closer to operational intuitions, while still proving useful abstract results – congruence of bisimilarity and soundness of bisimulation up to context. We recast in our setting two standard ways of working around this issue: (1) prove the weaker claim that bisimilarity is a non-input congruence [Sangiorgi and Walker 2001]; (2) restrict attention to a more constrained notion, wide-open bisimulation [Fiore and Staton 2006; Sangiorgi and Walker 2001; Staton 2008], to which Corollary 4.30 applies
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