First-order tree-to-tree functions

Abstract

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.

arXiv commentThis version contains an erratum. Theorem 6.1 in the published version was not valid in its full generality