Checking Zenon Modulo Proofs in Dedukti

نویسندگان

  • Raphaël Cauderlier
  • Pierre Halmagrand
چکیده

Dedukti has been proposed as a universal proof checker. It is a logical framework based on the λΠcalculus modulo that is used as a backend to verify proofs coming from theorem provers, especially those implementing some form of rewriting. We present a shallow embedding into Dedukti of proofs produced by Zenon Modulo, an extension of the tableau-based first-order theorem prover Zenon to deduction modulo and typing. Zenon Modulo is applied to the verification of programs in both academic and industrial projects. The purpose of our embedding is to increase the confidence in automatically generated proofs by separating untrusted proof search from trusted proof verification.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

ML Pattern-Matching, Recursion, and Rewriting: From FoCaLiZe to Dedukti

The programming environment FoCaLiZe allows the user to specify, implement, and prove programs. It produces as output OCaml executable programs along with proof hints that help the first-order theorem prover Zenon to find proofs. In the actual version, those proofs found by Zenon are verified by Coq. In this paper we propose to extend the FoCaLiZe compiler by a backend to the Dedukti language –...

متن کامل

Proof Certification in Zenon Modulo: When Achilles Uses Deduction Modulo to Outrun the Tortoise with Shorter Steps∗

We present the certifying part of the Zenon Modulo automated theorem prover, which is an extension of the Zenon tableau-based first order automated theorem prover to deduction modulo. The theory of deduction modulo is an extension of predicate calculus, which allows us to rewrite terms as well as propositions, and which is well suited for proof search in axiomatic theories, as it turns axioms i...

متن کامل

Automated Deduction in the B Set Theory using Typed Proof Search and Deduction Modulo

We introduce an encoding of the set theory of the B method using polymorphic types and deduction modulo, which is used for the automated verification of proof obligations in the framework of the BWare project. Deduction modulo is an extension of predicate calculus with rewriting both on terms and propositions. It is well suited for proof search in theories because it turns many axioms into rewr...

متن کامل

Dedukti: a Logical Framework based on the λΠ-Calculus Modulo Theory

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, Simple type theory, programming languages, Pure type systems, the Calculus of inductive constructions with universes, etc. and that permits to used it to check large libraries of proofs developed in other proof systems: Zenon,...

متن کامل

Development of a termination checker for Dedukti

Dedukti [12] is a formal proof checker based on a logical framework called the λΠ-calculus modulo, which is an extension of the simply-typed lambdacalculus with dependent types (e.g. lists of size n) and an equivalence relation on types generated by user-defined rewrite rules (like in Agda or Haskell). Proofs generated by some automated theorem provers (e.g. Zenon, iProver) or proof assistants ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2015