A modular construction of type theories

Frédéric Blanqui; Gilles Dowek; Emilie Grienenberger; Gabriel Hondet; François Thiré

doi:10.46298/lmcs-19(1:12)2023

Frédéric Blanqui ; Gilles Dowek ; Emilie Grienenberger ; Gabriel Hondet ; François Thiré - A modular construction of type theories

lmcs:8637 - Logical Methods in Computer Science, February 14, 2023, Volume 19, Issue 1 - https://doi.org/10.46298/lmcs-19(1:12)2023

A modular construction of type theoriesArticle

Authors: Frédéric Blanqui ; Gilles Dowek ; Emilie Grienenberger ; Gabriel Hondet ; François Thiré

The lambda-Pi-calculus modulo theory is a logical framework in which many type systems can be expressed as theories. We present such a theory, the theory U, where proofs of several logical systems can be expressed. Moreover, we identify a sub-theory of U corresponding to each of these systems, and prove that, when a proof in U uses only symbols of a sub-theory, then it is a proof in that sub-theory.

https://doi.org/10.46298/lmcs-19(1:12)2023

Source: arXiv.org:2111.00543

Volume: Volume 19, Issue 1

Published on: February 14, 2023

Accepted on: December 2, 2022

Submitted on: November 2, 2021

Keywords: Computer Science - Logic in Computer Science, Mathematics - Logic

Licence: Attribution 4.0 International (CC BY 4.0)