Non-determinsitic algebraic rewriting as adjunction

• URL: http://arxiv.org/abs/2204.12133v1
• Date: Tue, 26 Apr 2022 07:55:09 GMT
• Title: Non-determinsitic algebraic rewriting as adjunction
• Authors: R\u{a}zvan Diaconescu
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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