Representations of Stream Processors Using Nested Fixed Points

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 representa...

Full description

Saved in:
Bibliographic Details
Published in:Logical methods in computer science 2009-09, Vol.5, Issue 3
Main Authors: Ghani, Neil, Hancock, Peter, Pattinson, Dirk
Format: Article
Language:English
Subjects:
computer science - data structures and algorithms
computer science - logic in computer science
e.1
e.2
f.2.1
f.2.2
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1860-5974
1860-5974
DOI:10.2168/LMCS-5(3:9)2009