A Truly Concurrent Semantics for the K Framework Based on Graph Transformations

This paper gives a truly concurrent semantics with sharing of resources for the $\mathbb{K}$ semantic framework, an executable (term-)rewriting-based formalism for defining programming languages and calculi. Akin to graph rewriting rules, the $\mathbb{K}$ (rewrite) rules explicitly state what can be concurrently shared with other rules. The desired true concurrency is obtained by translating the $\mathbb{K}$ rules into a novel instance of term-graph rewriting with explicit sharing, and then using classical concurrency results from the double-pushout (DPO) approach to graph rewriting. The resulting parallel term-rewriting relation is proved sound, complete, and serializable with respect to the jungle rewriting flavor of term-graph rewriting, and, therefore, also to term rewriting.

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