Categorical Views on Computations on Trees (Extended Abstract)

  • Ichiro Hasuo
  • Bart Jacobs
  • Tarmo Uustalu
Conference paper

DOI: 10.1007/978-3-540-73420-8_54

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4596)
Cite this paper as:
Hasuo I., Jacobs B., Uustalu T. (2007) Categorical Views on Computations on Trees (Extended Abstract). In: Arge L., Cachin C., Jurdziński T., Tarlecki A. (eds) Automata, Languages and Programming. ICALP 2007. Lecture Notes in Computer Science, vol 4596. Springer, Berlin, Heidelberg

Abstract

Computations on trees form a classical topic in computing. These computations can be described in terms of machines (typically called tree transducers), or in terms of functions. This paper focuses on three flavors of bottom-up computations, of increasing generality. It brings categorical clarity by identifying a category of tree transducers together with two different behavior functors. The first sends a tree transducer to a coKleisli or biKleisli map (describing the contribution of each local node in an input tree to the global transformation) and the second to a tree function (the global tree transformation). The first behavior functor has an adjoint realization functor, like in Goguen’s early work on automata. Further categorical structure, in the form of Hughes’s Arrows, appears in properly parameterized versions of these structures.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Ichiro Hasuo
    • 1
  • Bart Jacobs
    • 1
  • Tarmo Uustalu
    • 2
  1. 1.Institute of Computing and Information Sciences, Radboud University Nijmegen, Postbus 9010, NL-6500 GL NijmegenThe Netherlands
  2. 2.Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, EE-12618 TallinnEstonia

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