The first-order theory of finite and infinite trees has been studied since the eighties, especially by the logic programming community. Following Djelloul, Dao and Fr\"uhwirth, we consider an extension of this theory with an additional predicate for finiteness of trees, which is useful for expressing properties about (not just datatypes but also) codatatypes. Based on their work, we present a simplification procedure that determines whether any given (not necessarily closed) formula is satisfiable, returning a simplified formula which enables one to read off all possible models. Our extension makes the algorithm usable for algebraic (co)datatypes, which was impossible in their original work due to restrictive assumptions. We also provide a prototype implementation of our simplification procedure and evaluate it on instances from the SMT-LIB.

中文翻译：

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树和代数 (Co) 数据类型的扩展理论

自八十年代以来，一直在研究有限树和无限树的一阶理论，尤其是逻辑编程社区。继 Djelloul、Dao 和 Fr\"uhwirth 之后，我们考虑对该理论的扩展，并为树的有限性添加一个额外的谓词，这对于表达关于（不仅是数据类型而且还有）codatatype 的属性很有用。基于他们的工作，我们提出了一个确定任何给定（不一定是封闭的）公式是否可满足的简化过程，返回一个简化的公式，使人们能够读取所有可能的模型。我们的扩展使算法可用于代数（共）数据类型，这在他们的原始工作中是不可能的由于限制性假设，我们还提供了简化程序的原型实现，并在来自 SMT-LIB 的实例上对其进行评估。