We developed a formal framework for conflict-driven clause learning (CDCL) using the Isabelle/HOL proof assistant. Through a chain of refinements, an abstract CDCL calculus is connected first to a more concrete calculus, then to a SAT solver expressed in a functional programming language, and finally to a SAT solver in an imperative language, with total correctness guarantees. The framework offers a convenient way to prove metatheorems and experiment with variants, including the Davis–Putnam–Logemann–Loveland (DPLL) calculus. The imperative program relies on the two-watched-literal data structure and other optimizations found in modern solvers. We used Isabelle’s Refinement Framework to automate the most tedious refinement steps. The most noteworthy aspects of our work are the inclusion of rules for forget, restart, and incremental solving and the application of stepwise refinement.

中文翻译：

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具有学习、忘记、重启和增量功能的经过验证的 SAT 求解器框架

我们使用 Isabelle/HOL 证明助手开发了一个用于冲突驱动条款学习 (CDCL) 的正式框架。通过一系列细化，抽象的 CDCL 演算首先连接到更具体的微积分，然后连接到用函数式编程语言表达的 SAT 求解器，最后连接到命令式语言的 SAT 求解器，并保证完全正确。该框架提供了一种方便的方法来证明元定理和试验变体，包括 Davis-Putnam-Logemann-Loveland (DPLL) 演算。命令式程序依赖于现代求解器中的两个观察字面数据结构和其他优化。我们使用 Isabelle 的 Refinement Framework 来自动化最繁琐的细化步骤。我们工作中最值得注意的方面是包含了忘记、重新启动、