Aligning HOL-Light and Rocq Libraries Formally

20 pages•Published: October 23, 2026

Abstract

We report on our efforts to translate HOL-Light theorems on HOL-Light types/functions into Rocq theorems on Rocq types/functions. To this end, we developed in Rocq tactics to automate the proofs required for replacing a HOL-Light inductive type or recursive function definition by an equivalent but more idiomatic one in Rocq. We also explain how we replaced the definition of real numbers, as well as a number of mathematical notions like R^n spaces and the definition of limit, hence providing to Rocq users many definitions and theorems in logic and analysis that had not been formalized in Rocq before.

Keyphrases: calculus of inductive constructions, higher order logic, library alignment

In: Erika Ábrahám, Nikolaj Bjørner and Michael Rawson (editors). Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning, vol 112, pages 22-41.

Links:	https://easychair.org/publications/paper/RZx3
	https://doi.org/10.29007/cc85

BibTeX entry

@inproceedings{LPAR-26:Aligning_HOL_Light_Rocq,
  author    = {Frédéric Blanqui and Antoine Gontard},
  title     = {Aligning HOL-Light and Rocq Libraries Formally},
  booktitle = {Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning},
  editor    = {Erika Ábrahám and Nikolaj Bjørner and Michael Rawson},
  series    = {EPiC Series in Computing},
  volume    = {112},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/RZx3},
  doi       = {10.29007/cc85},
  pages     = {22-41},
  year      = {2026}}

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