Polymorphic computation systems: Theory and practice of confluence with call-by-value

Hamana, Makoto; Abe, Tatsuya; Kikuchi, Kentaro

doi:10.1016/j.scico.2019.102322

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Cited by 4 publications

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“…Remark 3.1. In the previous formulations (Hamana, 2017(Hamana, , 2019Hamana et al, 2020), the lhss of second-order rewrite rules are restricted to Miller's higher-order patterns at second order (Miller, 1991), or their slight extension of deterministic second-order patterns (Libal and Miller, 2016;Yokoyama et al, 2003Yokoyama et al, , 2004. Second-order patterns are meta-terms in which every occurrence of a meta-application is of the form M[x 1 , .…”

Section: Z N Tmentioning

confidence: 99%

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

Hamana

2022

Math. Struct. Comp. Sci.

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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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