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On Parametric Polymorphism and Irrelevance in Martin-Lof Type Theory Andreas Abel

Summary: On Parametric Polymorphism and Irrelevance in Martin-L®of Type Theory
Andreas Abel
Project PI.R2, INRIA Rocquencourt and PPS, Paris
We devise a typed equality judgement for a predicative
version of Miquel's Implicit Calculus and complete it with
a calculus for explicit substitutions. The resulting theory
IITT, Implicit Intensional Type Theory, is shown consis-
tent by a partial equivalence model. We further present a
bidirectional type checking and extraction algorithm and
briefly sketch the integration of another notion of irrele-
vance, Awodey and Bauer's bracket types. This work is
aimed at providing a solid an practical foundation for ex-
traction of efficient programs from type theory.
Keywords: Explicit Substitutions, Program Extraction,
Implicit Quantification, PER Model, Typed Equality.
1 Introduction
Dependently typed programming languages such as
Agda [18] and Coq [11] allow the programmer to express


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


Collections: Computer Technologies and Information Sciences