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Origami: (un)folding the Abstraction of Recursion Schemes for Program Synthesis

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Genetic Programming Theory and Practice XX

Part of the book series: Genetic and Evolutionary Computation ((GEVO))

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.

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Notes

  1. 1.

    In this paper, we employ the Haskell language notation, which is similar to the ML notation.

  2. 2.

    Similar to generics in Java and templates in C++.

  3. 3.

    In category theory, this is called an endofunctor.

  4. 4.

    https://hackage.haskell.org/package/recursion-schemes-5.2.2.4/docs/docs/flowchart.svg.

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Acknowledgements

This research was partially funded by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), grant numbers #2021/12706-1, #2019/26702-8, #2021/06867-2, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) and CNPq grant number 301596/2022-0.

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Authors and Affiliations

  1. Federal University of ABC, Santo Andre, SP, Brazil

    Matheus Campos Fernandes, Fabricio Olivetti de Franca & Emilio Francesquini

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  1. Matheus Campos Fernandes
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  2. Fabricio Olivetti de Franca
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  3. Emilio Francesquini
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Correspondence to Matheus Campos Fernandes .

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Editors and Affiliations

  1. School of Information, Communications and Media, University of Applied Sciences Upper Austria, Hagenberg, Austria

    Stephan Winkler

  2. Engineering Sciences Graduate Program, Tecnológico Nacional de México, IT de Tijuana, Tijuana, Baja California, Mexico

    Leonardo Trujillo

  3. Department of Computer Science and Engineering, Michigan State University, East Lansing, MI, USA

    Charles Ofria

  4. School of Computing, Queen's University, Kingston, ON, Canada

    Ting Hu

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Fernandes, M.C., de Franca, F.O., Francesquini, E. (2024). Origami: (un)folding the Abstraction of Recursion Schemes for Program Synthesis. In: Winkler, S., Trujillo, L., Ofria, C., Hu, T. (eds) Genetic Programming Theory and Practice XX. Genetic and Evolutionary Computation. Springer, Singapore. https://doi.org/10.1007/978-981-99-8413-8_14

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  • DOI: https://doi.org/10.1007/978-981-99-8413-8_14

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