On the algebraic foundation of proof assistants for intuitionistic type theory

Authors:
Andreas Abel;Thierry Coquand;Peter Dybjer
Affiliations:
Institut für Informatik, Ludwig-Maximilians-Universität, München;Department of Computer Science, Chalmers University of Technology, Göteborg;Department of Computer Science, Chalmers University of Technology, Göteborg
Venue:
FLOPS'08 Proceedings of the 9th international conference on Functional and logic programming
Year:
2008

Citing 6
Cited 2

Programming in Martin-Lo¨f's type theory: an introduction

Programming in Martin-Lo¨f's type theory: an introduction
An algorithm for type-checking dependent types

Science of Computer Programming - Special issue on mathematics of program construction
Internal Type Theory

TYPES '95 Selected papers from the International Workshop on Types for Proofs and Programs
Interactive Theorem Proving and Program Development

Interactive Theorem Proving and Program Development
Normalization by Evaluation for Martin-Löf Type Theory with One Universe

Electronic Notes in Theoretical Computer Science (ENTCS)
Normalization by Evaluation for Martin-Lof Type Theory with Typed Equality Judgements

LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science

The Interpretation of Intuitionistic Type Theory in Locally Cartesian Closed Categories -- an Intuitionistic Perspective

Electronic Notes in Theoretical Computer Science (ENTCS)
A Modular Type-Checking Algorithm for Type Theory with Singleton Types and Proof Irrelevance

TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

An algebraic presentation of Martin-Löf's intuitionistic type theory is given which is based on the notion of a category with families with extra structure. We then present a type-checking algorithm for the normal forms of this theory, and sketch how it gives rise to an initial category with families with extra structure. In this way we obtain a purely algebraic formulation of the correctness of the type-checking algorithm which provides the core of proof assistants for intuitionistic type theory.