Gilles Dowek

Models and termination of proof reduction in the $\\lambda$$\\Pi$-calculus\n modulo theory

2015 · arXiv (Cornell University)

We define a notion of model for the $\\lambda$$\\Pi$-calculus modulo theory and\nprove a soundness theorem. We then define a notion of super-consistency and\nprove that proof reduction terminates in the $\\lambda$$\\Pi$-calculus modulo any\nsuper-consistent theory. We prove …

Embedding Pure Type Systems in the lambda-Pi-calculus modulo

2023 · arXiv (Cornell University)

The lambda-Pi-calculus allows to express proofs of minimal predicate logic. It can be extended, in a very simple way, by adding computation rules. This leads to the lambda-Pi-calculus modulo. We show in this paper that …