Preprints, Working Papers, ... Year : 2017

Models and termination of proof reduction in the λΠ-calculus modulo theory

Abstract

We define a notion of model for the λΠ-calculus modulo theory and prove a soundness theorem. We then define a notion of super-consistency and prove that proof reduction terminates in the λΠ-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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Dates and versions

hal-01101834 , version 1 (26-01-2015)
hal-01101834 , version 2 (26-04-2017)

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Gilles Dowek. Models and termination of proof reduction in the λΠ-calculus modulo theory. 2017. ⟨hal-01101834v2⟩
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