Development Method of Three Kinds of Typical Tree Structure Algorithms and Isabelle-based Machine Assisted Verification

Abstract

The tree structure algorithms have been widely used in many computer fields. Developing efficient and reliable tree structure algorithms is a challenging problem in the field of software formalization and trusted software. In this paper, initially, the binary tree algorithms are divided into three kinds through induction of the loop invariant structures and output features. Then, PAR method can conveniently develop loop invariants and corresponding non-recursive algorithm programs. Finally, Isabelle is used to formally verify these developed algorithms. This development method not only overcomes the tediousness and error-proneness of traditional manual verification, but also greatly improves the efficiency and reliability of the developed algorithm program. To the best of our knowledge, this is the maiden attempt in the literature to verify a series of non-recursive and efficient binary tree algorithms. The above process forms a theorem proving library that include data types, data structures and lemma related binary tree algorithms, which can significantly reduce the cost of future verification.