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Lexicographic Path Induction

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Programming languages theory is full of problems that reduce to proving the consistency of a logic, such as the normalization of typed lambda-calculi, the decidability of equality in type theory, equivalence testing of traces in security, etc. Although the principle of transfinite induction is routinely employed by logicians in proving such theorems, it is rarely used by programming languages researchers, who often prefer alternatives such as proofs by logical relations and model theoretic constructions. In this paper we harness the well-foundedness of the lexicographic path ordering to derive an induction principle that combines the comfort of structural induction with the expressive strength of transfinite induction. Using lexicographic path induction, we give a consistency proof of Martin-Löf’s intuitionistic theory of inductive definitions. The consistency of Heyting arithmetic follows directly, and weak normalization for Gödel’s T follows indirectly; both have been formalized in a prototypical extension of Twelf.
Original languageEnglish
Book seriesLecture Notes in Computer Science
Pages (from-to)279
Number of pages293
ISSN0302-9743
DOIs
Publication statusPublished - 2009
EventTyped Lambda Calculi and Applications - Brasilia, Brazil
Duration: 1 Jul 20093 Jul 2009

Conference

ConferenceTyped Lambda Calculi and Applications
CountryBrazil
CityBrasilia
Period01/07/200903/07/2009

ID: 1036831