Section: New Software and Platforms

Introduction

Deducteam develops several kinds of tools or libraries:

• Proof checkers:

  • Dedukti: proof checker for the $\lambda \Pi$-calculus modulo rewriting

  • Sukerujo: extension of Dedukti with syntactic constructions for records, strings, lists, etc.

  • Rainbow: CPF termination certificate verifier

• Tools for translating into Dedukti's proof format proofs coming from various other provers:

  • Coqine translates Coq proofs

  • Focalide translates Focalize proofs

  • Holide translates OpenTheory proofs (HOL-Light, HOL4, ProofPower)

  • Krajono translates Matita proofs

  • Sigmaid translates ς-calculus

• Automated theorem provers:

  • iProverModulo: theorem prover based on polarized resolution modulo

  • SuperZenon: extension of Zenon using superdeduction

  • ZenonArith: extension of Zenon using the simplex algorithm for arithmetic

  • ZenonModulo: extension of Zenon using deduction modulo and producing Dedukti proofs

  • Zipperposition: superposition prover featuring arithmetic and induction

  • HOT: automated termination prover for higher-order rewrite systems

• Libraries or generation tools:

  • CoLoR: Coq library on rewriting theory and termination

  • Logtk: library for first-order automated reasoning

  • mSat: modular SAT/SMT solver with proof output

  • Moca: generator of construction functions for types with relations on constructors

In the following, we only details software that received improvements in 2015.

In addition, Shuai Wang developed the ProofCloud prototype, a proof retrieval engine for verified higher order proofs. ProofCloud provides a fast proof searching service for mathematicians and computer scientists for the reuse of proofs and proof packages. Using ProofCloud, he conducted a statistical analysis of the OpenTheory repository.