Global ETD Search

11	A General Galois Theory for Operations and Relations in Arbitrary Categories Kerkhoff, Sebastian 20 September 2011 (has links) In this paper, we generalize the notions of polymorphisms and invariant relations to arbitrary categories. This leads us to a Galois connection that coincides with the classical case from universal algebra if the underlying category is the category of sets, but remains applicable no matter how the category is changed. In analogy to the situation in universal algebra, we characterize the Galois closed classes by local closures of clones of operations and local closures of what we will introduce as clones of (generalized) relations. Since the approach is built on purely category-theoretic properties, we will also discuss the dualization of our notions. info:eu-repo/classification/ddc/510 ddc:510
12	A General Duality Theory for Clones Kerkhoff, Sebastian 28 June 2011 (has links) In this thesis, we generalize clones (as well as their relational counterparts and the relationship between them) to categories. Based on this framework, we introduce a general duality theory for clones and apply it to obtain new results for clones on finite sets. info:eu-repo/classification/ddc/510 ddc:510
13	Categorical semantics and composition of tree transducers / Kategorielle Semantik und Komposition von Baumübersetzern Jürgensen, Claus 28 December 2004 (has links) (PDF) 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. Baumübersetzer Deforestation Fusion Haskel Monade Monadentransformer Programmtransformation funktionale Sprache Haskell deforestation functional program fusion monad monad transformer program transformation tree transducer ddc:004 rvk:ST 140 Formale Semantik Funktionale Programmiersprache Kategorientheorie Programmtransformation
14	Categorical semantics and composition of tree transducers Jürgensen, Claus 30 January 2004 (has links) 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. info:eu-repo/classification/ddc/004 ddc:004

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