Dependently typed programming languages and proof assistants such as Agda and Coq
rely on computation to automatically simplify expressions during type checking. To …

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 …

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 …

Dependently typed languages such as Coq and Agda can statically guarantee the
correctness of our proofs and programs. To provide this guarantee, they restrict users to …

Abstract GAPT (General Architecture for Proof Theory) is a proof theory framework
containing data structures, algorithms, parsers and other components common in proof …

The main aim of this thesis is to make formal proofs more universal by expressing them in a
common logical framework. More specifically, we use the lambda-Pi-calculus modulo …

We propose an extension of the tableau-based first order automated theorem prover Zenon
to deduction modulo. The theory of deduction modulo is an extension of predicate calculus …

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 …

Theorem provers produce evidence of proof in many different formats, such as proof scripts,
natural deductions, resolution refutations, Herbrand expansions, and equational rewritings …

Dedukti is a logical framework based on the lambda-Pi-calculus modulo rewriting, which
extends the lambda-Pi-calculus with rewrite rules. In this paper, we show how to translate …