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Communication Dans Un Congrès Année : 2023

Engineering logical relations for MLTT in Coq

Résumé

We report on a mechanization in the Coq proof assistant of the decidability of conversion and type-checking for Martin-Löf Type Theory (MLTT), extending a previous Agda formalization. Our development proves the decidability not only of conversion, but also of type-checking, using bidirectional derivations that are canonical for typing. Moreover, we wish to narrow the gap between the object theory we formalize (currently MLTT with Π, Σ, N and one universe) and the metatheory used to prove the normalization result, e.g., MLTT, to a mere difference of universe levels. We thus avoid induction-recursion or impredicativity, which are central in previous work. Working in Coq, we also investigate how its features, including universe polymorphism and the metaprogramming facilities provided by tactics, impact the development of the formalization compared to the development style in Agda. The development is freely accessible on GitHub [2].
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Dates et versions

hal-04379245 , version 1 (08-01-2024)

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Paternité

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  • HAL Id : hal-04379245 , version 1

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Arthur Adjedj, Meven Lennon-Bertrand, Kenji Maillard, Loïc Pujet. Engineering logical relations for MLTT in Coq. TYPES 2023 - 29th International Conference on Types for Proofs and Programs, Jun 2023, Valencia, Spain. pp.1-3. ⟨hal-04379245⟩
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