Guarded Cubical Type Theory: Path Equality for Guarded Recursion
Paper in proceedings, 2016

This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of program logics, and for programming and reasoning with coinductive types. We wish to implement GDTT with decidable type checking, while still supporting non-trivial equality proofs that reason about the extensions of guarded recursive constructions. CTT is a variation of Martin-Löf type theory in which the identity type is replaced by abstract paths between terms. CTT provides a computational interpretation of functional extensionality, is conjectured to have decidable type checking, and has an implemented type checker. Our new type theory, called guarded cubical type theory, provides a computational interpretation of extensionality for guarded recursive types. This further expands the foundations of CTT as a basis for formalisation in mathematics and computer science. We present examples to demonstrate the expressivity of our type theory, all of which have been checked using a prototype type-checker implementation, and present semantics in a presheaf category.

Author

Lars Birkedal

Aarhus University

Aleš Bizjak

Aarhus University

Ranald Clouston

Aarhus University

Hans Bugge Grathwohl

Aarhus University

Bas Spitters

Aarhus University

Andrea Vezzosi

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

25th EACSL Annual Conference on Computer Science Logic (CSL 2016)

1868-8969 (ISSN)

Vol. 62 23:1-23:17

Roots

Basic sciences

Subject Categories

Computer Science

DOI

10.4230/LIPIcs.CSL.2016.23

ISBN

978-3-95977-022-4

More information

Latest update

2/28/2018