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ON IRRELEVANCE AND ALGORITHMIC EQUALITY IN PREDICATIVE TYPE THEORY
 

Summary: ON IRRELEVANCE AND ALGORITHMIC EQUALITY IN
PREDICATIVE TYPE THEORY
(DRAFT OF May 25, 2011)
ANDREAS ABEL AND GABRIEL SCHERER
Department of Computer Science, Ludwig­Maximilians­University Munich
e­mail address: andreas.abel@ifi.lmu.de
Department of Computer Science, Ludwig­Maximilians­University Munich
e­mail address: gabriel.scherer@ifi.lmu.de
Abstract. Dependently typed programs contain an excessive amount of static terms
which are necessary to please the type checker but irrelevant for computation. To ob­
tain reasonable performance of not only the compiled program but also the type checker
such static terms need to be erased as early as possible, preferably immediately after type
checking. To this end, Pfenning's type theory with irrelevant quantification, that models
a distinction between static and dynamic code, is extended to universes and large elimi­
nations. Normalization, consistency, and decidability are obtained via a universal Kripke
model based on algorithmic equality.
1. Introduction and Related Work
Dependently typed programming languages such as Agda [BDN09], Coq [INR10], and
Epigram [MM04] allow the programmer to express in one language programs, their types,
rich invariants, and even proofs of these invariants. Besides code executed at run­time,

  

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

 

Collections: Computer Technologies and Information Sciences