# Programming Macro Tree Transducers

## Abstract

Tree transducers are tree automata defining functions from trees to trees. Put simply, a tree transducer is a set of mutually recursive functions transforming an input tree into an output tree. Macro tree transducers extend this recursion scheme by allowing each function to be defined in terms of an arbitrary number of accumulation parameters. We show how macro tree transducers can be concisely represented in Haskell, and demonstrate the benefits of utilising such an approach with a number of examples. In particular, tree transducers afford a modular programming style as they can be easily composed and manipulated. Our Haskell representation generalises the original definition of (macro) tree transducers, abolishing a restriction on finite state spaces. However, as we demonstrate, this generalisation does not affect compositionality.

Categories: Recursion Schemes, Type Systems

Tags: Tree Automaton, Transducer, Accumulation, Composition, Deforestation, Haskell, Recursion Scheme, Nested Recursion, Polymorphism