Debates concerning philosophical grounds for the validity of classical and intuitionistic
logics often have the very nature of logical proofs as one of the main points of controversy …

As the development of formal proofs is a time-consuming task, it is important to devise ways
of sharing the already written proofs to prevent wasting time redoing them. One of the …

The λ Π-calculus modulo theory is an extension of simply typed λ-calculus with dependent
types and user-defined rewrite rules. We show that it is possible to replace the rewrite rules …

We present a method and a tool, hol2dk, to fully automatically translate proofs from the proof
assistant HOL-Light to the proof assistant Coq, by using Dedukti as an intermediate …

Kuroda's translation embeds classical first-order logic into intuitionistic logic, through the
insertion of double negations. Recently, Brown and Rizkallah extended this translation to …

The two open access volumes LNCS 14574 and 14575 constitute the proceedings of the
27th International Conference on Foundations of Software Science and Computation …

Parametricity allows the transfer of proofs between different implementations of the same
data structure. The lambdaPi-calculus modulo theory is an extension of the lambda-calculus …

Ecumenism can be understood as a pursuit of unity, where diverse thoughts, ideas, or points
of view coexist harmoniously. In logic, ecumenical systems refer, in a broad sense, to proof …

Automated Theorem Proving is a core area of artificial intelligence research, focusing on the
development of software that autonomously proves complex statements from given premises …

Proof assistants such as Coq implement a type theory featuring three important features:
impredicativity, cumulativity and product covariance. This combination has proven difficult to …