A Natural Semantic Framework for ECATNets

Abstract

Rewriting logic seems to have good properties recommending its use as a general semantic framework in which many concurrent systems and languages can be naturally specified and prototyped. The aim of this paper is to set the ECATNet formalism, a form of high level algebraic nets, in the more general triangular correspondence between rewriting logic, concurrent systems and categories as proposed by J. Meseguer. We give an alternative description of an ECATNet as a rewrite theory. The deduced concurrent systems (models) provide a meaningful semantic interpretation to the ECATNet behaviour, where proofs and ECATNets computations are formally identical. The potential benefit of this correspondence is that dynamic properties of ECATNets can be checked and deduced in a natural way. Category theory is applied to ECATNets in two ways. First, we show how a category of ECATNets can be viewed as a subcategory of rewrite theories category: this casts ECATNets in a familiar framework and provides a useful idea of morphism (refinement) on ECATNets. Second, we define a category whose objects are ECATNets behaviours which themselves are categories. This abstract setting makes possible formal proofs of some ECATNets properties; categorical constructions (as product and coproduct) that result provide a useful way to reason about modular ECATNets.