We study tree-to-tree transformations that can be defined in first-order logic or monadic second-order logic. We prove a decomposition theorem, which shows that every transformation can be obtained from prime transformations, such as tree-to-tree homomorphisms or pre-order traversal, by using combinators such as function composition.

中文翻译：

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一阶树到树函数

我们研究可以在一阶逻辑或一元二阶逻辑中定义的树到树转换。我们证明了一个分解定理，它表明可以通过使用组合子（例如函数组合）从素数变换（例如树到树同态或前序遍历）中获得每个变换。