Certified Higher-Order Recursive Path Ordering

Koprowski, Adam

doi:10.1007/11805618_17

Cited by 3 publications

(1 citation statement)

References 6 publications

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“…polynomial interpretations (Hinderer 2004); recursive path ordering (Coupet-Grimal and Delobel 2006); multiset ordering and higher-order recursive path ordering (Koprowski 2006;Koprowski 2008;Koprowski 2009); matrix and arctic interpretations (Koprowski and Zantema 2008;Koprowski and Waldmann 2008;Koprowski 2008).…”

Section: Outlinementioning

confidence: 99%

CoLoR: a Coq library on well-founded rewrite relations and its application to the automated verification of termination certificates

Blanqui¹,

Koprowski²

2011

Math. Struct. Comp. Sci.

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International audienceTermination is an important property of programs; notably required for programs formulated in proof assistants. It is a very active subject of research in the Turing-complete formalism of term rewriting systems, where many methods and tools have been developed over the years to address this problem. Ensuring reliability of those tools is therefore an important issue. In this paper we present a library formalizing important results of the theory of well-founded (rewrite) relations in the proof assistant Coq. We also present its application to the automated verification of termination certificates, as produced by termination tools

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Section: Outlinementioning

confidence: 99%

CoLoR: a Coq library on well-founded rewrite relations and its application to the automated verification of termination certificates

Blanqui¹,

Koprowski²

2011

Math. Struct. Comp. Sci.

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Modeling Permutations in Coq for Coccinelle

Contejean

Rewriting, Computation and Proof

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Coq formalization of the higher-order recursive path ordering

Koprowski

2009

AAECC

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Recursive path ordering (RPO) is a well-known reduction ordering introduced by Dershowitz [14], that is useful for proving termination of term rewriting systems (TRSs). Jouannaud and Rubio generalized this ordering to the higher-order case thus creating the higher-order recursive path ordering (HORPO) [19]. They proved that this ordering can be used for proving termination of higher-order TRSs which essentially comes down to proving well-foundedness of the union of HORPO and the β-reduction relation of the simply typed lambda calculus (λ → ). This result entails well-foundedness of RPO and termination of λ → . This paper describes author's undertaking of providing a complete, axiom-free, fully constructive formalization of those results in the theorem prover Coq. Formalization is complete and hence it contains all the dependant results. It can be divided into three parts:• finite multisets and two variants of multiset extensions of a relation,• λ → with termination of β as the main result,• HORPO with proof of well-foundedness of its union with β-reduction. Also decidability of HORPO has been proven and due to the constructive nature of this proof a certified algorithm to verify whether two terms can be oriented with HORPO can be extracted from this proof.CONTENTS

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Certified Higher-Order Recursive Path Ordering

Cited by 3 publications

References 6 publications

CoLoR: a Coq library on well-founded rewrite relations and its application to the automated verification of termination certificates

CoLoR: a Coq library on well-founded rewrite relations and its application to the automated verification of termination certificates

Modeling Permutations in Coq for Coccinelle

Coq formalization of the higher-order recursive path ordering

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