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Implementation of Two Layers Type Theory in Dedukti and Application to Cubical Type Theory

Authors :
Valentin Maestracci
Bruno Barras
Deduction modulo, interopérabilité et démonstration automatique (DEDUCTEAM)
Inria Saclay - Ile de France
Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Spécification et Vérification (LSV)
Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay)
Source :
LFMPT 2020-Logical Frameworks and Meta-Languages: Theory and Practice 2020, LFMPT 2020-Logical Frameworks and Meta-Languages: Theory and Practice 2020, Jun 2020, Paris, France
Publication Year :
2021

Abstract

In this paper, we make a substantial step towards an encoding of Cubical Type Theory (CTT) in the Dedukti logical framework. Type-checking CTT expressions features a decision procedure in a de Morgan algebra that so far could not be expressed by the rewrite rules of Dedukti. As an alternative, 2 Layer Type Theories are variants of Martin-L\"of Type Theory where all or part of the definitional equality can be represented in terms of a so-called external equality. We propose to split the encoding by giving an encoding of 2 Layer Type Theories (2LTT) in Dedukti, and a partial encoding of CTT in 2LTT.<br />Comment: In Proceedings LFMTP 2020, arXiv:2101.02835

Details

Language :
English
Database :
OpenAIRE
Journal :
LFMPT 2020-Logical Frameworks and Meta-Languages: Theory and Practice 2020, LFMPT 2020-Logical Frameworks and Meta-Languages: Theory and Practice 2020, Jun 2020, Paris, France
Accession number :
edsair.doi.dedup.....615c50709bb6550c1d8283cd69acee49