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**Harvard**

Birkedal, L., Bizjak, A., Clouston, R., Grathwohl, H., Spitters, B. och Vezzosi, A. (2016) *Guarded Cubical Type Theory: Path Equality for Guarded Recursion*.

** BibTeX **

@conference{

Birkedal2016,

author={Birkedal, Lars and Bizjak, Aleš and Clouston, Ranald and Grathwohl, Hans Bugge and Spitters, Bas and Vezzosi, Andrea},

title={Guarded Cubical Type Theory: Path Equality for Guarded Recursion},

booktitle={25th EACSL Annual Conference on Computer Science Logic (CSL 2016)},

isbn={978-3-95977-022-4},

pages={23:1-23:17},

abstract={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. },

year={2016},

}

** RefWorks **

RT Conference Proceedings

SR Electronic

ID 247980

A1 Birkedal, Lars

A1 Bizjak, Aleš

A1 Clouston, Ranald

A1 Grathwohl, Hans Bugge

A1 Spitters, Bas

A1 Vezzosi, Andrea

T1 Guarded Cubical Type Theory: Path Equality for Guarded Recursion

YR 2016

T2 25th EACSL Annual Conference on Computer Science Logic (CSL 2016)

SN 978-3-95977-022-4

SP 231

OP 2317

AB 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.

LA eng

DO 10.4230/LIPIcs.CSL.2016.23

LK http://dx.doi.org/10.4230/LIPIcs.CSL.2016.23

OL 30