Complete algebraic semantics for second-order rewriting systems based on abstract syntax with variable binding

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Mathematical Structures in Computer Science Pub Date : 2022-04-01 DOI:10.1017/S0960129522000287

M. Hamana

引用次数: 0

Abstract

Abstract By using algebraic structures in a presheaf category over finite sets, following Fiore, Plotkin and Turi, we develop sound and complete models of second-order rewriting systems called second-order computation systems (CSs). Restricting the algebraic structures to those equipped with well-founded relations, we obtain a complete characterisation of terminating CSs. We also extend the characterisation to rewriting on meta-terms using the notion of $\Sigma$ -monoid.

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基于变量绑定抽象语法的二阶重写系统的完全代数语义

摘要继Fiore、Plotkin和Turi之后，我们利用有限集上预剪切范畴中的代数结构，建立了二阶重写系统的健全完整模型，称为二阶计算系统（CS）。将代数结构限制为那些具有良好基础关系的代数结构，我们获得了终止CS的完整刻画。我们还使用$\Sigma$-monoid的概念将特征化扩展到元项上的重写。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Structures in Computer Science 工程技术-计算机：理论方法

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. The journal welcomes applications to computing based on the use of specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results.