Neil Ghani ; Peter Hancock ; Dirk Pattinson - Representations of Stream Processors Using Nested Fixed Points

lmcs:713 - Logical Methods in Computer Science, September 15, 2009, Volume 5, Issue 3 - https://doi.org/10.2168/LMCS-5(3:9)2009
Representations of Stream Processors Using Nested Fixed PointsArticle

Authors: Neil Ghani ; Peter Hancock ; Dirk Pattinson

    We define representations of continuous functions on infinite streams of discrete values, both in the case of discrete-valued functions, and in the case of stream-valued functions. We define also an operation on the representations of two continuous functions between streams that yields a representation of their composite. In the case of discrete-valued functions, the representatives are well-founded (finite-path) trees of a certain kind. The underlying idea can be traced back to Brouwer's justification of bar-induction, or to Kreisel and Troelstra's elimination of choice-sequences. In the case of stream-valued functions, the representatives are non-wellfounded trees pieced together in a coinductive fashion from well-founded trees. The definition requires an alternating fixpoint construction of some ubiquity.


    Volume: Volume 5, Issue 3
    Published on: September 15, 2009
    Imported on: July 14, 2008
    Keywords: Computer Science - Data Structures and Algorithms,Computer Science - Logic in Computer Science,E.1,E.2,F.2.1,F.2.2

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