Computational higher-dimensional type theory

Abstract

Formal constructive type theory has proved to be an effective language for mechanized proof. By avoiding non-constructive principles, such as the law of the excluded middle, type theory admits sharper proofs and broader interpretations of results. From a computer science perspective, interest in type theory arises from its applications to programming languages. Standard constructive type theories used in mechanization admit computational interpretations based on meta-mathematical normalization theorems. These proofs are notoriously brittle; any change to the theory potentially invalidates its computational meaning. As a case in point, Voevodsky's univalence axiom raises questions about the computational meaning of proofs.

Document Details

Document Type
Pub Defense Publication
Publication Date
Jan 01, 2017
Source ID
10.1145/3093333.3009861

Entities

People

  • Carlo Angiuli
  • Robert Harper
  • Todd Wilson

Organizations

  • Air Force Office of Scientific Research
  • California State University, Fresno
  • Carnegie Mellon University

Tags

Fields of Study

  • Mathematics

Readers

  • Computational Linguistics
  • Educational Psychology
  • Linear Algebra