Encoding impredicative hierarchy of type universes with variables - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2023

Encoding impredicative hierarchy of type universes with variables

Abstract

Logical frameworks can be used to translate proofs from a proof system to another one. For this purpose, we should be able to encode the theory of the proof system in the logical framework. The Lambda Pi calculus modulo theory is one of these logical frameworks. Powerful theories such as pure type systems with an infinite hierarchy of universes have been encoded, leading to partial encodings of proof systems such as Coq, Matita or Agda. In order to fully represent systems such as Coq and Lean, we introduce a representation of an infinite universe hierarchy with an impredicative universe and universe variables where universe equivalence is equality, and implement it as a terminating and confluent rewrite system.
Fichier principal
Vignette du fichier
encoding_impredicative_universes.pdf (631.43 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-04311936 , version 1 (28-11-2023)

Licence

Attribution

Identifiers

Cite

Yoan Géran. Encoding impredicative hierarchy of type universes with variables. 2023. ⟨hal-04311936⟩
56 View
15 Download

Altmetric

Share

Gmail Facebook X LinkedIn More