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.

翻译：遗传规划中的程序合成旨在搜索满足输入规范（通常以输入-输出示例形式提供）的正确程序。一个特殊的挑战是如何有效处理循环和递归，以避免程序永不终止。缓解此问题的有用抽象是采用递归方案，该方案将数据生产与消费的组合加以泛化。递归方案非常强大，允许构建能够汇总数据、创建序列以及执行高级计算的程序。使用递归方案编写程序的主要优势在于，程序由良好定义的模板组成，仅需合成少数几个部分。本文初步研究了使用折叠与展开模板进行程序合成的优势，并概述了初步实验成果。为突出此方法的优劣，我们手动使用递归方案解决了整个GPSB基准测试问题，指出了与替代实现相比应进化的部分。我们注意到，一旦选定递归方案，合成过程便可简化，因为模板中每个缺失部分都可简化为更简单的函数，且这些函数进一步受其自身输入和输出类型的约束。