A truly concurrent semantics for the K framework based on graph transformations

  • Authors:

  • Traian Florin Şerbӑnuţӑ;Grigore Roşu

  • Affiliations:

  • Alexandru Ioan Cuza University of Iaşi, Romania,University of Illinois at Urbana-Champaign;Alexandru Ioan Cuza University of Iaşi, Romania,University of Illinois at Urbana-Champaign

  • Venue:
  • ICGT'12 Proceedings of the 6th international conference on Graph Transformations
  • Year:
  • 2012

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Abstract

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.