Metaheuristic Algorithms for Proof Searching in HOL4

Abstract

User guided proof development in interactive theorem proving is a manual and time consuming activity. For automating proof searching and optimization in a higher-order logic proof assistant, we provide two metaheuristic algorithms that are based on Fitness Dependent Optimizer (FDO) and Bat Algorithm (BA). In both metaheuristic algorithms, random proof sequences are first created from a population of frequently occurring proof steps that are discovered using pattern mining techniques. Created proof sequences are then evolved till their fitness matches the fitness of the original (or target) proof sequences. Experiments are performed to investigate the performance of the proposed algorithms on different HOL4 theories. Moreover, the proposed FDO and BA-based proof searching approaches are compared with Simulated Annealing (SA) and Genetic Algorithm (GA)based methods. Results show that BA performs best, followed by FDO and SA for proof finding and optimization in HOL4.