Fast, Verified Computation for HOL ITPs
Journal article, 2025

We add an efficient function for computation to the kernels of higher-order logic interactive theorem provers. First, we develop and prove sound our approach for Candle. Candle is a port of HOL Light which has been proved sound with respect to the inference rules of its higher-order logic; we extend its implementation and soundness proof. Second, we replicate our now-verified implementation for HOL4 with only minor changes, and build additional automation for ease of use. The automation exists outside of the HOL4 kernel, and requires no additional trust. We exercise our new computation function and associated automation on the evaluation of the CakeML compiler backend within HOL4’s logic, demonstrating an order of magnitude speedup. This is an extended version of our previous conference paper [2], which described implementation and soundness proofs for Candle. Our HOL4 implementation and automation are new, as are the CakeML benchmarks.

Interactive theorem proving

Prover soundness

Higher-order logic

Author

Oskar Abrahamsson

Chalmers, Computer Science and Engineering (Chalmers), Formal methods

Magnus Myreen

University of Gothenburg

ARM Limited

Chalmers, Computer Science and Engineering (Chalmers), Formal methods

M. Norrish

Australian National University

Hrutvik Kanabar

ARM Limited

Johannes Åman Pohjola

Chalmers, Computer Science and Engineering (Chalmers), Computing Science

University of Gothenburg

Journal of Automated Reasoning

0168-7433 (ISSN) 1573-0670 (eISSN)

Vol. 69 1 7

Subject Categories (SSIF 2025)

Computer Sciences

Computer Engineering

Computer Systems

DOI

10.1007/s10817-025-09719-8

More information

Latest update

3/7/2025 9