Skip to Main content Skip to Navigation
Journal articles

Revisiting the categorical interpretation of dependent type theory

Pierre-Louis Curien 1, 2 Richard Garner 3 Martin Hofmann 4
2 PI.R2 - Design, study and implementation of languages for proofs and programs
PPS - Preuves, Programmes et Systèmes, Inria Paris-Rocquencourt, UPD7 - Université Paris Diderot - Paris 7, CNRS - Centre National de la Recherche Scientifique : UMR7126
Abstract : We show that Hofmann's and Curien's interpretations of Martin-Löf's type theory, which were both designed to cure a mismatch between syntax and semantics in Seely's original interpretation in locally cartesian closed categories, are related via a natural isomorphism. As an outcome, we obtain a new proof of the coherence theorem needed to show the soundness after all of Seely's interpretation.
Document type :
Journal articles
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01114033
Contributor : Pierre-Louis Curien <>
Submitted on : Friday, February 6, 2015 - 7:37:49 PM
Last modification on : Saturday, March 28, 2020 - 2:24:50 AM

Links full text

Identifiers

Collections

Citation

Pierre-Louis Curien, Richard Garner, Martin Hofmann. Revisiting the categorical interpretation of dependent type theory. Theoretical Computer Science, Elsevier, 2014, 546, pp.99-119. ⟨10.1016/j.tcs.2014.03.003⟩. ⟨hal-01114033⟩

Share

Metrics

Record views

355