Syntactic composition of top-down tree transducers is short cut fusion

@article{Jrgensen2004SyntacticCO,
  title={Syntactic composition of top-down tree transducers is short cut fusion},
  author={Claus J{\"u}rgensen and Heiko Vogler},
  journal={Mathematical Structures in Computer Science},
  year={2004},
  volume={14},
  pages={215 - 282}
}
We compare two deforestation techniques: short cut fusion formalised in category theory and the syntactic composition of tree transducers. The former strongly depends on types and uses the parametricity property or free theorem, whereas the latter makes no use of types at all and allows more general compositions. We introduce the notion of a categorical transducer, which is a generalisation of a catamorphism, and show a corresponding fusion result, which is a generalisation of the ‘acid rain… 
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