Hancock, P. and Pattinson, D. and Ghani, N. (2009) Representations of stream processors using nested fixed points. Logical Methods in Computer Science, 5 (3).
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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.
|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:||10 Feb 2017 22:53|