Higher-order constrained Horn clauses (HoCHC) are a semantically-invariant system of higher-order logic modulo theories. With semi-decidable unsolvability over a semi-decidable background theory, HoCHC is suitable for safety verification. Less is known about its relation to larger classes of higher-order verification problems. Motivated by program equivalence, we introduce a coinductive version of HoCHC that enjoys a greatest model property. We define an encoding of higher-order recursion schemes (HoRS) into HoCHC logic programs. Correctness of this encoding reduces decidability of the open HoRS equivalence problem -- and, thus, the LambdaY-calculus B\"ohm tree equivalence problem -- to semi-decidability of coinductive HoCHC over a complete and decidable theory of trees.

中文翻译：

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减少高阶递归方案等价于共导高阶约束喇叭子句

高阶约束 Horn 子句 (HoCHC) 是高阶逻辑模理论的语义不变系统。由于半可判定背景理论的半可判定不可解性，HoCHC 适用于安全性验证。关于它与更大类别的高阶验证问题的关系知之甚少。受程序等效性的启发，我们引入了具有最大模型属性的 HoCHC 的共归纳版本。我们将高阶递归方案 (HoRS) 的编码定义为 HoCHC 逻辑程序。这种编码的正确性降低了开放式 HoRS 等价问题的可判定性——因此，将 LambdaY 演算 B\“ohm 树等价问题——降低到 coductive HoCHC 在完整和可判定的树理论上的半可判定性。