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Categorical semantics and composition of tree transducers / Kategorielle Semantik und Komposition von Baumübersetzern

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.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa.de:swb:14-1107164334013-70165
Date28 December 2004
CreatorsJürgensen, Claus
ContributorsTechnische Universität Dresden, Informatik, Prof. Dr.-Ing. habil. Heiko Vogler, Prof. Dr. rer. nat. habil. Horst Reichel, Prof. Dr. habil. Zoltán Fülöp, Prof. Dr.-Ing. habil. Heiko Vogler
PublisherSaechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:doctoralThesis
Formatapplication/pdf

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