Program Synthesis on Single-Layer Loop Behavior in Pure Functional Programming

Program synthesis (PS) is a field devoted to auto-matically generating computer programs from high-level specifications, and genetic programming (GP) is one commonly-used way to achieve PS. PushGP, operating on a stack-based language, is considered as a state-of-the-art program synthesizer among GPs, while another research trend foucus on the grammar-based languages due to the readability and the ease of maintenance. In this paper, we propose the repetitive structure genetic programming (RSGP), a new grammar-based program synthesizer under the pure functional programming paradigm. RSGP defines a recursive function to simulate the single-layer loop behavior and leverages the minimum redundancy maximum relevance $(\text{mRMR})$ feature selection with the Pearson correlation coefficient (PCC) to select the capable and diverse programs for the next generation. The experiment results show that RSGP outperforms PushGP, CBGP, and HOTGP in terms of the number of successful programs on CountOdds and LastIndexofZero from PSBl, Luhn from PSB2, and 3 out of 4 designed problems. Additionally, the ablation study indicates that using $\text{mRMR}$ with PCC does encourage proper problem decomposition with the trade-off of diminishing the search ability within a similar neighborhood. RSGP utilizes an adaptation mechanism to balance the trade-off to automatically fit the needs of different problems.