Automatic proof checking is about using a computer to check the validity of proofs of
mathematical statements. Since this verification is purely computational, it offers a high …

In the context of the multiplicity of formal systems, it has become a growing need to express
formal proofs into a common logical framework. This thesis focuses on the use of higher …

Dedukti is a Logical Framework based on the λΠ-Calculus Modulo Theory. We show that
many theories can be expressed in Dedukti: constructive and classical predicate logic …

Defining a theory, such as arithmetic, geometry, or set theory, in predicate logic just requires
to chose function and predicate symbols and axioms, that express the meaning of these …

The aim of this paper is to refine and extend proposals by Sozeau and Tabareau and by
Voevodsky for universe polymorphism in type theory. In those systems judgments can …

We introduce CompLF, a logical framework allowing for the definition of computational type
theories--that is, those whose definitional equality is purely generated by rewrite rules. Its …

Dedukti is a Logical Framework based on the $\lambda $$\Pi $-Calculus Modulo Theory.
We show that many theories can be expressed in Dedukti: constructive and classical …

In this thesis, I study the interaction between type theory and continuity, a mathematical
concept describing the intuition that a function can only query a finite part of its argument …

We use Dedukti as a logical framework for interoperability. We use automated tools to
translate different developments made in HOL and in Coq to Dedukti, and we combine them …

This thesis is about the metatheory of intuitionnistic type theory. The considered systems are
variants of Martin-Löf type theory of Calculus of Constructions, and we are interested in the …