Translating HOL-Light proofs to Coq

18 pages•Published: May 26, 2024

Abstract

We present a method and a tool, hol2dk, to fully automatically translate proofs from the proof assistant HOL-Light to the proof assistant Coq, by using Dedukti as an intermediate language. Moreover, a number of types, functions and predicates defined in HOL-Light are proved (by hand) to be equal to their counterpart in the Coq standard library. By replacing those types and functions by their Coq counterpart everywhere, we obtain a library of theorems (based on classical logic like HOL-Light) that can directly be used and applied in other Coq developments.

Keyphrases: certification, concept alignment, dependent type theory, higher order logic, logical frameworks, proof transformation, proof translation, rewriting

In: Nikolaj Bjørner, Marijn Heule and Andrei Voronkov (editors). Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 100, pages 1-18.

Links:	https://easychair.org/publications/paper/mtFT
	https://doi.org/10.29007/6k4x

BibTeX entry

@inproceedings{LPAR2024:Translating_HOL_Light_proofs,
  author    = {Frédéric Blanqui},
  title     = {Translating HOL-Light proofs to Coq},
  booktitle = {Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Nikolaj Bjørner and Marijn Heule and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {100},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/mtFT},
  doi       = {10.29007/6k4x},
  pages     = {1-18},
  year      = {2024}}

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