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. 9.

[img]
Preview
 PDF (Logical_methods_in_computer_science.pdf)
Logical_methods_in_computer_science.pdf
Accepted Author Manuscript
Download (228kB)| Preview

    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.

    Author(s):Hancock, Peter, Pattinson, Dirk and Ghani, Neil ORCID logoORCID: https://orcid.org/0000-0002-3988-2560
    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:11 Feb 2020 03:02
    URI:https://strathprints.strath.ac.uk/id/eprint/18887
    Export data:
    CORE (COnnecting REpositories)