Mixing HOL and Coq in Dedukti (Extended Abstract)

  title={Mixing HOL and Coq in Dedukti (Extended Abstract)},
  author={Ali Assaf and Rapha{\"e}l Cauderlier},
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. 

Figures from this paper

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

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)

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

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

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,

Aligning concepts across proof assistant libraries

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

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.



Translating HOL to Dedukti

This paper shows how to translate the proofs of a family of HOL proof assistants to Dedukti, a logical framework based on the λΠ-calculus modulo rewriting, and implements this translation in an automated tool and used to successfully translate the OpenTheory standard library.

Importing HOL Light into Coq

This translation has been implemented and allows the importation of the HOL Light basic library into Coq, where they can be re-used and re-checked and kept intelligible.

An Executable Formalization of the HOL/Nuprl Connection in the Metalogical Framework Twelf

The present paper presents the first rigorous formalization of Howe's HOL/Nuprl connection treatment in a logical framework, and hence provides a safe alternative to the translation of proofs.

Checking Zenon Modulo Proofs in Dedukti

A shallow embedding is presented into Dedukti of proofs produced by Zenon Modulo, an extension of the tableau-based first-order theorem prover Zenon to deduction modulo and typing that is applied to the verification of programs in both academic and industrial projects.

CoqInE: Translating the Calculus of Inductive Constructions into the λΠ-calculus Modulo

We show how to translate the Calculus of Inductive Constructions (CIC) as implemented by Coq into the ??-calculus modulo, a proposed common backend proof format for heterogeneous proof assistants.

Zenon : An Extensible Automated Theorem Prover Producing Checkable Proofs

Zenon is intended to be the dedicated prover of the Focal environment, an objectoriented algebraic specification and proof system, which is able to produce OCaml code for execution and Coq code for certification.

A Calculus of Constructions with Explicit Subtyping

An alternative version of the calculus of constructions where subtyping is explicit is presented, which avoids problems related to coercions and dependent types by using the Tarski style of universes and by introducing additional equations to reflect equality.

Zenon Modulo: When Achilles Outruns the Tortoise Using Deduction Modulo

An extension of the tableau-based first order automated theorem prover Zenon to deduction modulo, and an additional backend for Zenon that outputs proof certificates for Dedukti, which is a proof checker based on the λΠ-calculus modulo.

Importing HOL into Isabelle/HOL

The importer works by replaying proofs within Isabelle/HOL that have been recorded in HOL 4 or HOL-light and is therefore completely safe and facilitates a true integration of imported theorem and theorems that are already available in Isabelle /HOL.

A Shallow Embedding of Resolution and Superposition Proofs into the λΠ-Calculus Modulo

  • G. Burel
  • Computer Science, Mathematics
  • 2013
This work provides a shallow embedding of resolution and superposition proofs in the λΠ-calculus modulo, thus offering a way to check these proofs in a trusted setting, and to combine them with other proofs.