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Certified higherorder recursive path ordering
 In RTA, LNCS
, 2006
"... Abstract. Recursive path ordering (RPO) is a wellknown reduction ordering introduced by Dershowitz [6], that is useful for proving termination of term rewriting systems (TRSs). Jouannaud and Rubio generalized this ordering to the higherorder case thus creating the higherorder recursive path order ..."
Abstract

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Abstract. Recursive path ordering (RPO) is a wellknown reduction ordering introduced by Dershowitz [6], that is useful for proving termination of term rewriting systems (TRSs). Jouannaud and Rubio generalized this ordering to the higherorder case thus creating the higherorder recursive path ordering (HORPO) [8]. They proved that this ordering can be used for proving termination of higherorder TRSs which essentially comes down to proving wellfoundedness of the union of HORPO and βreduction relation of simply typed lambda calculus (λ →), [1]. This result entails wellfoundedness of RPO and termination of λ →. This paper describes author’s undertaking of providing a complete, axiomfree, fully constructive formalization of those results in the theorem prover Coq. Formalization is complete and hence it contains all the dependant results for λ → , multisets and multiset extension of the relation. Also decidability of HORPO has been proven and due to constructive nature of this proof a certified algorithm to verify whether two terms can be oriented with HORPO can be extracted from this proof. 1