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Fundamenta Informaticae TLCA'05 1--53 1 Untyped Algorithmic Equality for MartinL of's Logical Framework

Summary: Fundamenta Informaticae TLCA'05 1--53 1
IOS Press
Untyped Algorithmic Equality for Martin­L˜ of's Logical Framework
with Surjective Pairs
Andreas Abel # C
Institut f ˜
ur Informatik, Ludwigs­Maximilians­Universit˜ at M˜ unchen
Thierry Coquand #
Department of Computer Science, Chalmers University of Technology
Abstract. Martin­L˜of's Logical Framework is extended by strong #­types and presented via judg­
mental 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 ##­equality test and a bidirectional type checking algorithm. Complete­
ness is proven by instantiating the PER model with #­equality on #­normal forms, which is shown
equivalent to the algorithmic equality.
1. Introduction
Central to dependent type theories is the rule of conversion: The type of an expression can be converted to
an equal type, where in intensional type theories the notion of equality between types is decidable. In the


Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universität München


Collections: Computer Technologies and Information Sciences