Stochastic synthesis of recursive functions made easy with bananas, lenses, envelopes and barbed wire

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.