Models and termination of proof reduction in the $λ$$Π$-calculus modulo theory

Gilles Dowek

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arXiv · 1501.06522

Models and termination of proof reduction in the $λ$$Π$-calculus modulo theory

Gilles Dowek

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Abstract

We define a notion of model for the $λ$$Π$-calculus modulo theory and prove a soundness theorem. We then define a notion of super-consistency and prove that proof reduction terminates in the $λ$$Π$-calculus modulo any super-consistent theory. We prove this way the termination of proof reduction in several theories including Simple type theory and the Calculus of constructions .

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Gilles Dowek. 2017-04-27. Models and termination of proof reduction in the $λ$$Π$-calculus modulo theory. https://arxiv.org/abs/1501.06522

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