Lambda extensions of rewrite orderings

In this work we provide a new proof of the result by Gallier and Tannen that the combination of an arbitrary terminating first-order rewrite system with the simply typed lambda calculus is strongly normalizing. This proof proceeds via the explicit lifting of a rewrite ordering on first-order terms t...

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Bibliographic Details
Authors: Jouannaud, Jean Pierre, Rubio Gimeno, Alberto|||0000-0002-0501-9830
Format: report
Publication Date:1995
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/96993
Online Access:https://hdl.handle.net/2117/96993
Access Level:Open access
Keyword:First ordering rewriting
Lambda extensions
Description
Summary:In this work we provide a new proof of the result by Gallier and Tannen that the combination of an arbitrary terminating first-order rewrite system with the simply typed lambda calculus is strongly normalizing. This proof proceeds via the explicit lifting of a rewrite ordering on first-order terms to a rewrite ordering on (first-order) algebraic lambda-terms. For the definition of the ordering, we have used a technique developed by Kfoury and Wells, in order to delay the erasing beta-reductions (also called K-reductions) which may destroy the monotonicity property. This technique is extended to be able to handle the extensionality rule. As a particular case, the above construction yields an extension of the recursive path ordering of Dershowitz to a rewrite-ordering on (first-order) algebraic lambda-terms which contains simply typed lambda-derivations.