We present a framework for processing formulas in automatic theorem provers, with generation of detailed proofs. The main components are a generic contextual recursion algorithm and an extensible set of inference rules. Clausification, skolemization, theory-specific simplifications, and expansion of ‘let’ expressions are instances of this framework. With suitable data structures, proof generation adds only a linear-time overhead, and proofs can be checked in linear time. We implemented the approach in the SMT solver veriT. This allowed us to dramatically simplify the code base while increasing the number of problems for which detailed proofs can be produced, which is important for independent checking and reconstruction in proof assistants. To validate the framework, we implemented proof reconstruction in Isabelle/HOL.

中文翻译：

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用于公式处理的可扩展细粒度证明

我们提出了一个在自动定理证明器中处理公式的框架，并生成详细的证明。主要组件是通用上下文递归算法和一组可扩展的推理规则。分类、skolemization、特定于理论的简化和“让”表达式的扩展是这个框架的实例。使用合适的数据结构，证明生成只会增加线性时间开销，并且可以在线性时间内检查证明。我们在 SMT 求解器 veriT 中实施了该方法。这使我们能够显着简化代码库，同时增加可以生成详细证明的问题数量，这对于证明助手中的独立检查和重建非常重要。为了验证框架，我们在 Isabelle/HOL 中实现了证明重建。