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29 March 2024
 
  » arxiv » 0905.4813

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Representations of Stream Processors Using Nested Fixed Points
Neil Ghani ; Peter Hancock ; Dirk Pattinson ;
Date 29 May 2009
AbstractWe 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 arXiv, 0905.4813
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