Representations of stream processors using nested fixed points

Peter Hancock, Dirk Pattinson, Neil Ghani

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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.
Original languageEnglish
Article number9
Pages (from-to)1-17
Number of pages17
JournalLogical Methods in Computer Science
Issue number3
Publication statusPublished - 15 Sept 2009


  • streams
  • continuous functions
  • initial algebras
  • final coalgebras


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