Lexicographic Path Induction

Carsten Schürmann, Jeffrey Sarnat

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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.
BogserieLecture Notes in Computer Science
Sider (fra-til)279
Antal sider293
StatusUdgivet - 2009
BegivenhedTyped Lambda Calculi and Applications - Brasilia, Brasilien
Varighed: 1 jul. 20093 jul. 2009


KonferenceTyped Lambda Calculi and Applications