Representations of Stream Processors Using Nested Fixed Points

Details Representations of Stream Processors Using Nested Fixed Points Representations of Stream Processors Using Nested Fixed Points

2009-05-29

arxiv.org/abs/0905.4813v2

LMCS 5 (3:9) 2009

Computer Science

Data Structures and Algorithms

Scientific paper

10.2168/LMCS-5(3:9)2009

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.

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