Modelling Conditional Rewriting Logic in Structured Categories

We reformulate and generalize the functorial model of Meseguer's conditional full rewriting logic by using inserter, a weighted limit in 2-categories. Indeed 2-categories are categories enriched in Cat. Therefore this method also can be extended to sesqui-categories and other enriched categories, with which we can model various aspects of rewritings and strategies. 1 Introduction J. Meseguer introduced his conditional rewriting logic in [12,13], and gave a functorial semantics for it in [13] and a 2-algebraic theory semantics in [12]. But his treatments of conditionals are not fully 2-categorical because he essentially uses subequalizers. As Lambek pointed out in his original paper [11], a subequalizer is not a 2-categorical limit in the sense that this does not require the 2-dimensional universality. In 2-category (or enriched category) theory, the weighted limit was proposed as the more suitable notion than that of 2-limit [7,1]. Our first approach is to use a weighted limit in 2-ca..

Twenty years of rewriting logic

AbstractRewriting logic is a simple computational logic that can naturally express both concurrent computation and logical deduction with great generality. This paper provides a gentle, intuitive introduction to its main ideas, as well as a survey of the work that many researchers have carried out over the last twenty years in advancing: (i) its foundations; (ii) its semantic framework and logical framework uses; (iii) its language implementations and its formal tools; and (iv) its many applications to automated deduction, software and hardware specification and verification, security, real-time and cyber-physical systems, probabilistic systems, bioinformatics and chemical systems