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

Published online by Cambridge University Press:  14 October 2022

Makoto Hamana Open the ORCID record for Makoto Hamana [Opens in a new window]
Makoto Hamana*
Affiliation:
Faculty of Informatics, Gunma University, Maebashi, Japan
*
Email: hamana@gunma-u.ac.jp
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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.

Keywords

Term rewritinghigher-order rewritingterminationalgebraic modelshigher-order abstract syntax
Type
Special Issue: The Power Festschrift
Information
Mathematical Structures in Computer Science , Volume 32 , Special Issue 4: The Power Festschrift , April 2022 , pp. 542 - 573
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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