2022/04/26 by Răzvan Diaconescu, Diaconescu, Răzvan
Computer Science · #Logic, programming, and type systems #Logic, Reasoning, and Knowledge #Distributed systems and fault tolerance
paper · pdf · doi:10.48550/arxiv.2204.12133
We develop a general model theoretic semantics to rewriting beyond the usual confluence and termination assumptions. This is based on preordered algebra which is a model theory that extends many sorted algebra. In this framework we characterise rewriting in arbitrary algebras rather than term algebras (called algebraic rewriting) as a persistent adjunction and use this result, on the one hand for proving the soundness and the completeness of an abstract computational model of rewriting that underlies the non-deterministic programming with Maude and CafeOBJ, and on the other hand for developing a compositionality result for algebraic rewriting in the context of the pushout-based modularisation technique.