Representations of stream processors using nested fixed points

Peter Hancock, Dirk Pattinson, Neil Ghani

Research output: Contribution to journalArticle

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Abstract

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
Volume5
Issue number3
DOIs
Publication statusPublished - 15 Sep 2009

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Fixed point
Continuous Function
Fixpoint
Justification
Elimination
Proof by induction
Composite
Path
Composite materials

Keywords

  • streams
  • continuous functions
  • initial algebras
  • final coalgebras

Cite this

Hancock, Peter ; Pattinson, Dirk ; Ghani, Neil. / Representations of stream processors using nested fixed points. In: Logical Methods in Computer Science. 2009 ; Vol. 5, No. 3. pp. 1-17.
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Representations of stream processors using nested fixed points. / Hancock, Peter; Pattinson, Dirk; Ghani, Neil.

In: Logical Methods in Computer Science, Vol. 5, No. 3, 9, 15.09.2009, p. 1-17.

Research output: Contribution to journalArticle

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