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

lmcs:713 - Logical Methods in Computer Science, September 15, 2009, Volume 5, Issue 3
Representations of Stream Processors Using Nested Fixed Points

Authors: Ghani, Neil and Hancock, Peter and Pattinson, Dirk

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.


Source : oai:arXiv.org:0905.4813
DOI : 10.2168/LMCS-5(3:9)2009
Volume: Volume 5, Issue 3
Published on: September 15, 2009
Submitted 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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