Akama et al. introduced a hierarchical classification of first-order formulas for a hierarchical
prenex normal form theorem in semi-classical arithmetic. In this paper, we give a justification …

This paper makes contributions to" pure" sheaf model theory, the part of model theory in
which the models are sheaves over a complete Heyting algebra. We start by outlining the …

We introduce the flower calculus, a deep inference proof system for intuitionistic first-order
logic inspired by Peirce's existential graphs. It works as a rewriting system over inductive …

Les assistants de preuve sont des logiciels permettant de vérifierrigoureusement les
raisonnements mathématiques. Ils peuvent être généraux (commeCoq, Lean, Isabelle...) ou …

Proof assistants are software systems that allow for the precise checking of mathematical
reasoning. They can be general purpose (like Coq, Lean, Isabelle...) or more specialized …

Lambda calculi with algebraic data types lie at the core of functional programming
languages and proof assistants, but conceal at least two fundamental theoretical problems …

In this chapter, we propose some future directions of work, potentially beneficial to
Mathematics and its foundations, based on the recent import of methodology from the theory …

We show some applications of the formulas-as-polynomials correspondence: 1) a method
for (dis) proving formula isomorphism and equivalence based on showing (in) equality; 2) a …