 
Summary: On the Algebraic Foundation
of Proof Assistants
for Intuitionistic Type Theory
Andreas Abel1
, Thierry Coquand2
, and Peter Dybjer2
1
Institut f¨ur Informatik, LudwigMaximiliansUniversit¨at
Oettingenstr. 67, D80538 M¨unchen
2
Department of Computer Science, Chalmers University of Technology
R¨annv¨agen 6, S41296 G¨oteborg
Abstract. An algebraic presentation of MartinL¨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 typechecking 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 typechecking algorithm
which provides the core of proof assistants for intuitionistic type theory.
1 Introduction
