Abstract
Proof searching and proof automation are the two most desired properties in interactive theorem provers (ITPs) as they generally require manual user guidance, which can be quite cumbersome. In this paper, we provide an evolutionary proof searching approach for the HOL4 proof assistant, where a genetic algorithm (GA) with different crossover and mutation operators is used to search and optimize the proofs in different HOL theories. Random proof sequences are first generated from a population of frequently occurring HOL4 proof steps that are discovered with sequential pattern mining. Generated proof sequences are then evolved with GA operators (three crossover and two mutation) till their fitness match the fitness of the target proof sequences. Various crossover and mutation operators are used to compare their effect on the performance of GAs in proof searching. Obtained results suggest that integrating GAs with HOL4 allows us to efficiently support proof finding and optimization.
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