Untyped Algorithmic Equality for Martin-Löf's Logical Framework with Surjective Pairs

Authors:
Andreas Abel;Thierry Coquand
Affiliations:
Institut für Informatik, Ludwigs-Maximilians-Universität München, Germany. E-mail: abel@informatik.uni-muenchen.de;Department of Computer Science, Chalmers University of Technology, Sweden. E-mail: coquand@cs.chalmers.se
Venue:
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2005, Selected Papers
Year:
2007

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Abstract

Martin-Löf's Logical Framework is extended by strong Σ-types and presented via judgmental equality with rules for extensionality and surjective pairing. Soundness of the framework rules is proven via a generic PER model on untyped terms. An algorithmic version of the framework is given through an untyped βη-equality test and a bidirectional type checking algorithm. Completeness is proven by instantiating the PER model with η-equality on β-normal forms, which is shown equivalent to the algorithmic equality.