 
Summary: Fundamenta Informaticae TLCA'05 153 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
abel@informatik.unimuenchen.de
Thierry Coquand #
Department of Computer Science, Chalmers University of Technology
coquand@cs.chalmers.se
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
