Database gathering proofs from the proof systems Coq, HOL-Light and Matita, and their translations.

The proofs translated to Dedukti, and from Dedukti to other provers, are not currently gathered into a single database but are dispatched in several places:

  • Logipedia is a browsable website providing a library of arithmetic theorems in various systems: Matita, Coq, Lean, PVS, OpenTheory, Dedukti. It has been obtained by translating the Matita arithmetic library to Dedukti and then to the other systems using STTfaXport.

  • Nubo is a set of metadata and scripts to download and check Dedukti libraries. It contains links to a number of proof libraries translated to Dedukti: the arithmetic library of Matita, some part of the Coq library GeoCoq on geometry, the OpenTheory library, some proofs generated by some old version of the veriT SMT prover, some proofs generated by some old version of the ZenonModulo theorem prover, some proofs from the Isabelle/HOL standard library.

  • matita_lib_in_agda is a translation of the Matita arithmetic library into Agda, using predicativize.

Moreover, now, more and newer libraries can be automatically generated from HOL-Light and Isabelle/HOL using:

  • hol2dk to translate HOL-Light files to Dedukti or Lambdapi, and then to Coq. For instance, one can translate the whole HOL-Light base library to Dedukti or Lambdapi, and then to Coq.

  • isabelle_dedukti to translate Isabelle/HOL proofs to Dedukti or Lambdapi, including proofs coming from the Isabelle Archive of Formal Proofs (AFP).

We plan to add links to these new libraries in Nubo, or to gather some of them into a single place. But, to make them readily usable, we also need to align the concepts used in the source system with the concepts used in the target system, and this cannot be done automatically. As a first step, we started to add in the Coq Opam Archive the translation of parts of the HOL-Light base library:

  • coq-hol-light is a translation in Coq of the base arithmetic library of HOL-Light.