Origami: (un)folding the abstraction of recursion schemes for program synthesis (2402.13828v2)

Abstract: Program synthesis with Genetic Programming searches for a correct program that satisfies the input specification, which is usually provided as input-output examples. One particular challenge is how to effectively handle loops and recursion avoiding programs that never terminate. A helpful abstraction that can alleviate this problem is the employment of Recursion Schemes that generalize the combination of data production and consumption. Recursion Schemes are very powerful as they allow the construction of programs that can summarize data, create sequences, and perform advanced calculations. The main advantage of writing a program using Recursion Schemes is that the programs are composed of well defined templates with only a few parts that need to be synthesized. In this paper we make an initial study of the benefits of using program synthesis with fold and unfold templates, and outline some preliminary experimental results. To highlight the advantages and disadvantages of this approach, we manually solved the entire GPSB benchmark using recursion schemes, highlighting the parts that should be evolved compared to alternative implementations. We noticed that, once the choice of which recursion scheme is made, the synthesis process can be simplified as each of the missing parts of the template are reduced to simpler functions, which are further constrained by their own input and output types.

• The paper introduces Origami, a novel method that employs recursion schemes like catamorphisms and anamorphisms to simplify program synthesis.
• The approach narrows the search space by evolving specific parts of program templates through inductive synthesis, ensuring efficient termination.
• Experimental results demonstrate that Origami outperforms methods such as PushGP and CBGP, highlighting its promise for future automatic programming.

Unveiling the Potential of Recursion Schemes in Program Synthesis with Origami

Introduction to Recursion Schemes in Program Synthesis

The automation of computer program generation, known as Program Synthesis, is a critical area in computer science that promises to revolutionize the way we approach programming tasks. A significant challenge in program synthesis is effectively handling iterative processes such as loops and recursion, particularly ensuring programs terminate properly. Recursion Schemes offer a compelling abstraction that can address this challenge by generalizing data production and consumption patterns, thus simplifying the synthesis process. This paper introduces Origami, an initial exploration into leveraging Recursion Schemes, specifically fold and unfold patterns, to facilitate program synthesis.

Recursion Schemes: A Primer

Recursion, pivotal in functional programming, often brings about concerns, especially regarding program termination and memory usage. To mitigate such issues, the paper leans on the abstraction provided by Recursion Schemes. These schemes encapsulate common recursive patterns in programming, allowing for a structured approach to constructing recursive algorithms. The essence of Recursion Schemes lies in dividing the programming task into simpler, manageable steps, thereby offering an elegant solution to traditionally complex problems in program synthesis. Key recursion schemes discussed include catamorphisms and anamorphisms, which correspond to generalized forms of folding and unfolding.

The Origami Approach

Origami aims to reduce the complexity of program synthesis by breaking down the synthesis process into smaller, more manageable parts. By identifying the appropriate recursion scheme and base inductive type, Origami significantly narrows the search space for potential programs. This process involves determining the recursion scheme, selecting the base data type, crafting program templates, and evolving these templates through inductive synthesis. This structured approach ensures that only specific parts of the program template need evolution, guided by clear input and output types. Origami not only simplifies the task at hand but also enhances the efficiency of creating correct and efficient programs.

Experimentation and Results

The experimentation with Origami involved adapting the Higher-Order Typed Genetic Programming (HOTGP) algorithm to focus exclusively on evolving parts defined by catamorphism templates. The comparison of Origami's performance against established methods in the field, such as PushGP and CBGP, highlights its efficacy. Origami demonstrated superior performance in many of the benchmark tests, indicating the advantage of employing recursion schemes in program synthesis. These promising results underscore the potential of Origami to revolutionize the program synthesis landscape by providing a structured and efficient methodology.

Future Directions

The exploration presented in this paper is but an initial foray into the potential of Recursion Schemes in program synthesis. Future work aims to explore this promising area, including expanding the use of different recursion schemes and exploring multi-gene approaches for evolving programs with multiple parts. Furthermore, the implication of monoids in simplifying programs presents another exciting avenue for research.

Conclusion

The introduction of Origami marks a significant step forward in the field of program synthesis. By harnessing the power of Recursion Schemes, Origami presents a structured, efficient, and effective approach to synthesizing programs that handle iterative processes elegantly. The promising results from initial experiments pave the way for further exploration and innovation in program synthesis, promising to make automatic programming more accessible and reliable.