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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.
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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⟩



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