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

This paper gives a truly concurrent semantics with sharing of resources for the K semantic framework, an executable (term-)rewritingbased formalism for defining programming languages and calculi. Akin to graph rewriting rules, the K (rewrite) rules explicitly state what can be concurrently shared with other rules. The desired true concurrency is obtained by translating the K rules into a novel instance of term-graph rewriting with explicit sharing, and then using classical concurrency 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.