Categorical semantics and composition of tree transducers
| Autor: | Jürgensen, Claus |
|---|---|
| Přispěvatelé: | Vogler, Heiko, Reichel, Horst, Fülöp, Zoltán |
| Jazyk: | angličtina |
| Rok vydání: | 2003 |
| Předmět: |
Haskell
deforestation functional program fusion monad monad transformer program transformation tree transducer Deforestation Formale Semantik Funktionale Programmiersprache Kategorientheorie Monade Programmtransformation Transduktor Mathematics::Category Theory Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ddc:004 Baumübersetzer Deforestation Fusion Haskel Monade Monadentransformer Programmtransformation funktionale Sprache Computer Science::Formal Languages and Automata Theory |
| Popis: | In this thesis we see two new approaches to compose tree transducers and more general to fuse functional programs. The first abroach is based on initial algebras. We prove a new variant of the acid rain theorem for mutually recursive functions where the build function is substituted by a concrete functor. Moreover, we give a symmetric form (i.e. consumer and producer have the same syntactic form) of our new acid rain theorem where fusion is composition in a category and thus in particular associative. Applying this to compose top-down tree transducers yields the same result (on a syntactic level) as the classical top-down tree transducer composition. The second approach is based on free monads and monad transformers. In the same way as monoids are used in the theory of character string automata, we use monads in the theory of tree transducers. We generalize the notion of a tree transducer defining the monadic transducer, and we prove an according fusion theorem. Moreover, we prove that homomorphic monadic transducers are semantically equivalent. The latter makes it possible to compose syntactic classes of tree transducers (or particular functional programs) by simply composing endofunctors. |
| Databáze: | OpenAIRE |
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