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Representations of stream processors using nested fixed points

Hancock, Peter and Pattinson, Dirk and Ghani, Neil (2009) Representations of stream processors using nested fixed points. Logical Methods in Computer Science, 5 (3). pp. 1-17.

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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.

Item type: Article
ID code: 18887
Keywords: streams, continuous functions, initial algebras, final coalgebras, Electronic computers. Computer science, Computer Science(all), Theoretical Computer Science
Subjects: Science > Mathematics > Electronic computers. Computer science
Department: Faculty of Science > Computer and Information Sciences
Depositing user: Strathprints Administrator
Date deposited: 20 May 2010 08:43
Last modified: 22 Sep 2017 00:13
URI: https://strathprints.strath.ac.uk/id/eprint/18887
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