Isabelle-Driven Modeling and Automated Verification of Search Tree Algorithms

Search tree algorithms are widely used in areas such as database indexing, compiler design, and file systems, where the functional correctness of these algorithms is a critical factor in ensuring software reliability. However, traditional development process face two major challenges: first, algorithm design often lacks rigorous mathematical modeling, causing correctness verification to remain at an empirical level; second, existing verification approaches heavily rely on manual or interactive theorem proving, making the verification complexity grow exponentially with increasing algorithm scale. To address the above issues, an Isabelle-driven method for modeling and automated verification of search tree algorithms is proposed, This method builds on a formally verified functional modeling library to construct a modular modeling strategy that supports various search tree structures, and introduces a formal specification–driven framework for automatically synthesizing algorithmic code. Developers are required to supply only minimal functional expressions to complete the implementation. In addition, a reusable lemma library has been developed to support an automated block-wise verification strategy, significantly reducing verification costs. Furthermore, a method for generating functional executable programs is proposed. Experimental evaluation using a representative case study demonstrates that the proposed method substantially reduces verification costs. Compared to interactive verification approaches, the average reductions in code size and manual effort are 88.60% and 61.51%, respectively; compared with generative AI plus interactive verification methods, the average reductions in code size and manual effort are 88.09% and 41.76%, respectively. Overall, the proposed framework provides a systematic and highly automated solution for the formal verification of complex data structure algorithms in specific domains, while also offering a feasible pathway and methodological support for generating correct functional executable programs.