HORPO with Computability Closure: A Reconstruction
نویسندگان
چکیده
This paper provides a new, decidable definition of the higherorder recursive path ordering in which type comparisons are made only when needed, therefore eliminating the need for the computability closure, and bound variables are handled explicitly, making it possible to handle recursors for arbitrary strictly positive inductive types.
منابع مشابه
The computability path ordering
This paper aims at carrying out termination proofs for simply typed higherorder calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by lifting a precedence on function symbols. A first version, core CPO, is essentially obtained from the higher-order recursive path ordering (HORPO) by elimina...
متن کامل(HO)RPO Revisited
The notion of computability closure has been introduced for proving the termination of the combination of higher-order rewriting and beta-reduction. It is also used for strengthening the higher-order recursive path ordering. In the present paper, we study in more details the relations between the computability closure and the (higher-order) recursive path ordering. We show that the first-order ...
متن کاملA Higher-Order Iterative Path Ordering
The higher-order recursive path ordering (HORPO) defined by Jouannaud and Rubio provides a method to prove termination of higher-order rewriting. We present an iterative version of HORPO by means of an auxiliary term rewriting system, following an approach originally due to Bergstra and Klop. We study well-foundedness of the iterative definition, discuss its relationship with the original HORPO...
متن کاملA Kleene characterization of computability
The recursively enumerable binary relations are the smallest class containing all singleton relations and closed under union, concatenation, Kleene star, composition, and transitive closure. © 2006 Elsevier B.V. All rights reserved.
متن کاملCertified Higher-Order Recursive Path Ordering
Recursive path ordering (RPO) is a well-known 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 higher-order case thus creating the higher-order recursive path ordering (HORPO) [8]. They proved that this ordering can be used for proving termination of higher-order TRSs wh...
متن کامل