# Verified and Optimized Implementation of Orthologic Proof Search

arXiv: https://arxiv.org/abs/2501.09418 · HTML: https://mlsanity.com/paper/2501.09418/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2025.

## Built on by (most cited first, 1 of 1)

- [Orthologic for SAT Solving](https://mlsanity.com/paper/2605.16421/) (2026)

## Abstract (arXiv)

We report on the development of an optimized and verified decision procedure for orthologic equalities and inequalities. This decision procedure is quadratic-time and is used as a sound, efficient and predictable approximation to classical propositional logic in automated reasoning tools. We formalize, in the Coq proof assistant, a proof system in sequent-calculus style for orthologic. We then prove its soundness and completeness with respect to the algebraic variety of ortholattices, and we formalize a cut-elimination theorem (in doing so, we discover and fix a missing case in a previously published proof). We then implement and verify a complete proof search procedure for orthologic. A naive implementation is exponential, and to obtain an optimal quadratic runtime, we optimize the implementation by memoizing its results and simulating reference equality testing. We leverage the resulting correctness theorem to implement a reflective Coq tactic. We present benchmarks showing the procedure, under various optimizations, matches its theoretical complexity. Finally, we develop tactics including normalization with respect to orthologic and a boolean solver, which we also benchmark. We make tactics available as a standalone Coq plugin.