Stochastic synthesis of recursive functions has historically proved difficult, not least due to issues of non-termination and the often ad hoc methods for addressing this. This article presents a general method of implicit recursion which operates via an automatically-derivable decomposition of datatype structure by cases, thereby ensuring well-foundedness. The method is applied to recursive functions of long-standing interest and the results outperform recent work which combines two leading approaches and employs ‘human in the loop’ to define the recursion structure. We show that stochastic synthesis with the proposed method on benchmark functions is effective even with random search, motivating a need for more difficult recursive benchmarks in future.

中文翻译：

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使用香蕉、透镜、信封和带刺铁丝网轻松实现递归函数的随机合成

递归函数的随机合成历来被证明是困难的，尤其是由于非终止问题和解决这个问题的通常是特别的方法。本文介绍了一种隐式递归的通用方法，该方法通过案例对数据类型结构的自动可推导分解进行操作，从而确保有充分根据。该方法应用于长期关注的递归函数，结果优于最近结合两种领先方法并采用“人在循环”来定义递归结构的工作。我们表明，即使使用随机搜索，使用所提出的基准函数方法的随机合成也是有效的，这促使未来需要更困难的递归基准。