Section: New Results

A Consistency model of Coq extended with decision procedures

Participants : Bruno Barras [Contact] , Qian Wang.

Bruno Barras and Qian Wang are working on the construction of a model for the Calculus of Constructions extended with the type of natural numbers. The definitional equality has been extended to include all equations derivable in Presburger arithmetic. Compared to previous work, this model can support strong eliminations. Since strong eliminations and extensions of the definitional equality with non-satisfiable equations (for instance $0=1$) leads to non-normalizing terms, it was necessary to give a precise account of Presburger arithmetic, seen as a specific instance of first-order logic. This work is described in a paper published in the proceedings of the LICS conference [21] .