An evolutionary/heuristic-based proof searching framework for interactive theorem prover

Abstract

The proof development process in interactive theorem provers (ITPs) requires the users to manually search for proofs by interacting with proof assistants. The activity of finding the correct proofs can become quite cumbersome and time consuming for users. To make the proof searching process easier in proof assistants, we provide an evolutionary/heuristic-based framework. The basic idea for the framework is to first generate random proof sequences from a population of frequently occurring proof steps that are discovered with sequential pattern mining. Generated proof sequences are then evolved till their fitness match the fitness of the target (or original) proof sequences. Three algorithms based on the proposed framework are developed using the Genetic Algorithm (GA), Simulated Annealing (SA) and Particle Swarm Optimization (PSO). Extensive experiments are performed to investigate the performance of the proposed algorithms using the HOL4 proof assistant. Results have shown that the proposed algorithms can efficiently evolve the random sequences to obtain the target sequences. In comparison, PSO performed better than SA and SA performed better than GA. In general, the experimental results suggest that combining evolutionary/heuristic algorithms with proof assistants allow efficient support for proof finding/optimization.