crush: Extensible Proof Automation for Lean

Mike He; Dexin Zhang; Aarti Gupta

Home/Archive/arXiv

arXiv · 2610.40538

crush: Extensible Proof Automation for Lean

Mike He·Dexin Zhang·Aarti Gupta

View original source ↗Read source document ↗Export metadata ↓

Abstract

Lean's rich expressiveness supports higher-order functions, inductive datatypes, and user-defined abstractions, making it challenging to translate proof obligations into first-order Satisfiability Modulo Theory (SMT) queries and reconstruct kernel checked proofs. We present crush, an extensible SMT-backed proof automation framework for Lean. To bridge the gap between Lean's higher-order constructs and the solver's first-order logic, crush uses defunctionalization to encode function values and their applications. We formalize this translation for a supported higher-order fragment and prove its soundness. Moreover, crush provides metaprogramming interfaces for extending both Lean-to-SMT translation and the reconstruction of Lean proofs from solver certificates without modifying the translation pipeline. We implement crush as both a tactic and a backend for other third-party automation systems. We show that across four such use cases that target verification and general proof automation, crush discharges more obligations than the competing backends and reconstructs more kernel-checked proofs than the baselines.

Explore related subjects

cs.LO cs.PL

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Mike He, Dexin Zhang, Aarti Gupta. 2026-10-29. crush: Extensible Proof Automation for Lean. https://arxiv.org/abs/2610.40538

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Negative Translations for Affine and Lukasiewicz Logic

We investigate four well-known negative translations of classical logic into intuitionistic logic within a substructural setting. We find that in \emph{affine logic} the translation schemes due to Kolmogorov and Gödel both satisfy Troelstra's criteria for a negative translation. On the other hand, the schemes of Glivenko and Gentzen both fail for affine logic, but for different reasons: one can extend affine logic to make Glivenko work and Gentzen fail and {\it vice versa}. By contrast, in the setting of \emph{Łukasiewicz logic}, we can prove a general result asserting that a wide class of formula translations including those of Kolmogorov, Gödel, Gentzen and Glivenko not only satisfy Troelstra's criteria with respect to a natural intuitionistic fragment of Łukasiewicz logic but are all equivalent.

cs.LO↗

arXiv2026

A Complete Mental Temporal Logic for Intelligent Agents

In this paper, we present a mental temporal logic BPICTL together with a sound and complete axiomatization, which generalizes CTL by introducing mental modalities. A sound and complete inference system of BPICTL is given. We also prove the finite model property and decidability of BPICTL. Furthermore, we present a model checking algorithm for BPICTL.

cs.LO↗

arXiv2026

Hereditary History-Preserving Bisimilarity: Characterizations via Backward Ready Multisets

We devise two complementary characterizations of hereditary history-preserving bisimilarity (HHPB): a denotational one, over stable configuration structures, and an operational one, in a reversible process calculus. Our characterizations rely on forward-reverse bisimilarity (FRB) augmented with backward ready multiset equality, which is able to distinguish between autoconcurrency and autocausation. With respect to previous work, we thus shift the emphasis from uniquely identifying events, as done in other characterizations, to counting occurrences of identically labeled events associated with incoming transitions. This yields a more lightweight behavioral equivalence than HHPB: our bisimulations are still binary relations instead of ternary ones and do not need to incrementally build any labeling- and causality-preserving bijection for occurred events. We show that our characterizations are valid in the absence of non-local autoconflicts. We then study the logical foundations of these characterizations by relating event identifier logic, which captures HHPB, and backward ready multiset logic, developed for our extension of FRB.

cs.LO↗