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Irrelevance in Type Theory with a Heterogeneous Equality Judgement

Summary: Irrelevance in Type Theory with a
Heterogeneous Equality Judgement
Andreas Abel
Department of Computer Science
Ludwig-Maximilians-University Munich
Abstract. Dependently typed programs contain an excessive amount of static
terms which are necessary to please the type checker but irrelevant for computa-
tion. To obtain reasonable performance of not only the compiled program but also
the type checker such static terms need to be erased as early as possible, prefer-
ably 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 eliminations. Novel is a heterogeneously
typed implementation of equality which allows the smooth construction of a uni-
versal Kripke model that proves normalization, consistency and decidability.
Keywords: dependent types, proof irrelevance, heterogeneously typed equality,
algorithmic equality, logical relation, universal Kripke model.
1 Introduction and Related Work
Dependently typed programming languages such as Agda [9], Coq [13], and Epigram
[15] allow the programmer to express in one language programs, their types, rich in-


Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universit√§t M√ľnchen


Collections: Computer Technologies and Information Sciences