data Nat = Zero | Succ Nat
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by Claus Jürgensen, Even Zero True
http://www.cs.uu.nl/~johanj/afp/afp4/cjabstract.pdf
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Abstract:
– extended abstract — We try to combine the ‘syntactic composition of tree transducers ’ [FV98, KV01] on the one hand side and ‘short cut fusion ’ [GLP93] on the other hand side. Short cut fusion is based on the ‘cata/build-rule ’ [Joh01] or ‘acid rain theorem’ [TM95]. Therefore it is necessary to represent the recursive functions as catamorphisms. A catamorphism is a generalization of the well known list-function foldr for arbitrary algebraic datatypes. In terms of category theory a catamorphism is the unique mediating morphism from an initial algebra. We invented a new fusion technique using monads: instead of a catamorphism we use the unique mediating morphism from a free monad. Consider the small Haskell program:
Citations
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| 23 | Bottom-up and top-down tree series transformations – Engelfriet, Fülöp, et al. - 2002 |
| 16 | High level tree transducers and iterated pushdown tree transducers – Engelfriet, Vogler - 1988 |
| 8 | Syntax-Directed Semantics—Formal Models Based on Tree Transducers – Fülöp, Vogler - 1998 |
| 7 | cut fusion: Proved and improved – Short - 2001 |
| 6 | Tree transducer composition as deforestation method for functional programs – Kühnemann, Voigtländer - 2001 |
| 4 | Trees, transducers and transformations – Rounds - 1968 |
| 2 | Syntactic composition of top-down tree transducers is short cut fusion – Jürgensen - 2001 |
