crush：面向 Lean 的可扩展证明自动化
crush: Extensible Proof Automation for Lean
Mike He, Dexin Zhang, Aarti Gupta
AI 速览：提出一个基于 SMT 的可扩展 Lean 证明自动化框架 crush，用去函数化桥接高阶构造与一阶求解器，并支持可扩展的翻译与证明重建。
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.