Among the biggest challenges in property-based testing (PBT) is the constrained random generation problem: given a predicate on program values, randomly sample from the set of all values satisfying that predicate, and only those values. Efficient solutions to this problem are critical, since the executable specifications used by PBT often have preconditions that input values must satisfy in order to be valid test cases, and satisfying values are often sparsely distributed. We propose a novel approach to this problem using ideas from deductive program synthesis. We present a set of synthesis rules, based on a denotational semantics of generators, that give rise to an automatic procedure for synthesizing correct generators. Our system handles recursive predicates by rewriting them as catamorphisms and then matching with appropriate anamorphisms; this is theoretically simpler than other approaches to synthesis for recursive functions, yet still extremely expressive. Our implementation, Palamedes, is an extensible library for the Lean theorem prover. The synthesis algorithm itself is built on standard proof-search tactics, reducing implementation burden and allowing the algorithm to benefit from further advances in Lean proof automation.

翻译：在基于属性的测试（PBT）中，最大的挑战之一是约束随机生成问题：给定程序值上的谓词，从满足该谓词的所有值集合中随机采样，且仅采样这些值。该问题的高效解决方案至关重要，因为PBT使用的可执行规范通常包含输入值必须满足的前提条件才能成为有效测试用例，而满足条件的值往往稀疏分布。我们提出了一种利用演绎程序合成思想解决该问题的新方法。基于生成器的指称语义，我们提出了一套合成规则，这些规则可自动生成正确的生成器。我们的系统通过将递归谓词重写为范畴态射，并与适当的反范畴态射匹配来处理递归问题；这在理论上比其他递归函数合成方法更简洁，同时仍具有极强的表达能力。我们的实现Palamedes是Lean定理证明器的可扩展库。合成算法本身基于标准证明搜索策略构建，降低了实现负担，并使算法能够受益于Lean证明自动化的进一步进展。