Representations of Stream Processors Using Nested Fixed Points
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.
Cite
@article{arxiv.0905.4813,
title = {Representations of Stream Processors Using Nested Fixed Points},
author = {Neil Ghani and Peter Hancock and Dirk Pattinson},
journal= {arXiv preprint arXiv:0905.4813},
year = {2015}
}