Nicolas Behr ; Jean Krivine - Compositionality of Rewriting Rules with Conditions

compositionality:13512 - Compositionality, April 22, 2021, Volume 3 (2021) - https://doi.org/10.32408/compositionality-3-2
Compositionality of Rewriting Rules with ConditionsArticle

Authors: Nicolas Behr ORCID1; Jean Krivine 1

We extend the notion of compositional associative rewriting as recently studied in the rule algebra framework literature to the setting of rewriting rules with conditions. Our methodology is category-theoretical in nature, where the definition of rule composition operations encodes the non-deterministic sequential concurrent application of rules in Double-Pushout (DPO) and Sesqui-Pushout (SqPO) rewriting with application conditions based upon $\mathcal{M}$-adhesive categories. We uncover an intricate interplay between the category-theoretical concepts of conditions on rules and morphisms, the compositionality and compatibility of certain shift and transport constructions for conditions, and thirdly the property of associativity of the composition of rules.


Volume: Volume 3 (2021)
Published on: April 22, 2021
Imported on: May 2, 2024
Keywords: Computer Science - Logic in Computer Science,Mathematics - Category Theory,16B50, 60J27, 68Q42 (Primary) 60J28, 16B50, 05E99 (Secondary),F.4.2,G.3,G.2.2
Funding:
    Source : OpenAIRE Graph
  • Rule-algebraic Simple Rewriting; Funder: European Commission; Code: 753750

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