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On the Algebraic Foundation of Proof Assistants
 

Summary: On the Algebraic Foundation
of Proof Assistants
for Intuitionistic Type Theory
Andreas Abel1
, Thierry Coquand2
, and Peter Dybjer2
1
Institut f¨ur Informatik, Ludwig-Maximilians-Universit¨at
Oettingenstr. 67, D-80538 M¨unchen
2
Department of Computer Science, Chalmers University of Technology
R¨annv¨agen 6, S-41296 G¨oteborg
Abstract. An algebraic presentation of Martin-L¨of'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 cat-
egory 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.
1 Introduction

  

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

 

Collections: Computer Technologies and Information Sciences