Categorical views on computations on trees

Authors:
Ichiro Hasuo;Bart Jacobs;Tarmo Uustalu
Affiliations:
Institute of Computing and Information Sciences, Radboud University Nijmegen, Nijmegen, The Netherlands;Institute of Computing and Information Sciences, Radboud University Nijmegen, Nijmegen, The Netherlands;Institute of Cybernetics at Tallinn University of Technology, Tallinn, Estonia
Venue:
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Year:
2007

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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.