Can LLM Aid in Solving Constraints with Inductive Definitions?
This addresses a specific bottleneck in automated theorem proving for constraints involving inductive definitions, such as algebraic data types, which is incremental but practically useful for formal verification and program analysis.
The paper tackles the challenge of solving constraints with inductive definitions by using structured prompts to elicit LLMs to generate auxiliary lemmas and integrating them with constraint solvers in a neuro-symbolic approach. The result shows a 25% improvement in solving proof tasks compared to state-of-the-art SMT and CHC solvers.
Solving constraints involving inductive (aka recursive) definitions is challenging. State-of-the-art SMT/CHC solvers and first-order logic provers provide only limited support for solving such constraints, especially when they involve, e.g., abstract data types. In this work, we leverage structured prompts to elicit Large Language Models (LLMs) to generate auxiliary lemmas that are necessary for reasoning about these inductive definitions. We further propose a neuro-symbolic approach, which synergistically integrates LLMs with constraint solvers: the LLM iteratively generates conjectures, while the solver checks their validity and usefulness for proving the goal. We evaluate our approach on a diverse benchmark suite comprising constraints originating from algebrai data types and recurrence relations. The experimental results show that our approach can improve the state-of-the-art SMT and CHC solvers, solving considerably more (around 25%) proof tasks involving inductive definitions, demonstrating its efficacy.