A formalized proof of strong normalization for guarded recursive types
Paper in proceeding, 2014
We consider a simplified version of Nakano’s guarded fixed-point types in a representation by infinite type expressions, defined coinductively. Smallstep reduction is parametrized by a natural number “depth” that expresses under how many guards we may step during evaluation. We prove that reduction is strongly normalizing for any depth. The proof involves a typed inductive notion of strong normalization and a Kripke model of types in two dimensions: depth and typing context. Our results have been formalized in Agda and serve as a case study of reasoning about a language with coinductive type expressions.
Author
Andreas Abel
University of Gothenburg
Andrea Vezzosi
Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
03029743 (ISSN) 16113349 (eISSN)
Vol. 8858 140-158978-3-319-12735-4 (ISBN)
Subject Categories
Computer and Information Science
DOI
10.1007/978-3-319-12736-1_8
ISBN
978-3-319-12735-4