PLPV '07 Proceedings of the 2007 workshop on Programming languages meets program verification
The identity type weak factorisation system
Theoretical Computer Science
Weak ω-Categories from Intensional Type Theory
TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
Two-dimensional models of type theory
Mathematical Structures in Computer Science
Dependently typed programming in Agda
AFP'08 Proceedings of the 6th international conference on Advanced functional programming
Univalent foundations of mathematics
WoLLIC'11 Proceedings of the 18th international conference on Logic, language, information and computation
Canonicity for 2-dimensional type theory
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A few constructions on constructors
TYPES'04 Proceedings of the 2004 international conference on Types for Proofs and Programs
| Hi-index | 0.00 |
Recent work on homotopy type theory exploits an exciting new correspondence between Martin-Lof's dependent type theory and the mathematical disciplines of category theory and homotopy theory. The mathematics suggests new principles to add to type theory, while the type theory can be used in novel ways to do computer-checked proofs in a proof assistant. In this paper, we formalize a basic result in algebraic topology, that the fundamental group of the circle is the integers. Our proof illustrates the new features of homotopy type theory, such as higher inductive types and Voevodsky's univalence axiom. It also introduces a new method for calculating the path space of a type, which has proved useful in many other examples.