# Mixing HOL and Coq in Dedukti (Extended Abstract)

@inproceedings{Assaf2015MixingHA, title={Mixing HOL and Coq in Dedukti (Extended Abstract)}, author={Ali Assaf and Rapha{\"e}l Cauderlier}, booktitle={PxTP@CADE}, year={2015} }

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 to prove new results. We illustrate our approach with a concrete example where we instantiate a sorting algorithm written in Coq with the natural numbers of HOL.

## 6 Citations

### Higher Order Proof Engineering: Proof Collaboration, Transformation, Checking and Retrieval

- Computer Science
- 2016

An introduction and an overview of related recent advances are given, followed by the proof checking benchmarks of a proof sharing repository, namely OpenTheory (after proof transformation by the upgraded Holide), and ProofCloud, the first proof retrieval engine for higher order proofs.

### A framework for defining computational higher-order logics. (Un cadre de définition de logiques calculatoires d'ordre supérieur)

- Computer Science
- 2015

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 rewriting, a lambda…

### Interactive Theorem Proving: 8th International Conference, ITP 2017, Brasília, Brazil, September 26–29, 2017, Proceedings

- Computer ScienceITP
- 2017

The metaprogramming language currently in use in Lean, a new open source theorem prover that is designed to bridge the gap between interactive use and automation, is described and evidence is provided to show that the implementation is performant, and that it provides a convenient and flexible way of writing not only small-scale interactive tactics, but also more substantial kinds of automation.

### Expressing theories in the λΠ-calculus modulo theory and in the Dedukti system

- Philosophy
- 2016

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 symbols. Using,…

### Applications of Foundational Proof Certificates in theorem proving. (Applications des Certificats de Preuve Fondamentaux à la démonstration automatique de théorèmes)

- Computer Science, Mathematics
- 2017

This thesis extends initial results in certification of first-order proofs in several directions and applies developments to fully certify results produced by two families of standard automated theorem provers: resolution- and satisfiability-based.

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