### Abstract

Original language | English |
---|---|

Article number | 9 |

Pages (from-to) | 1-17 |

Number of pages | 17 |

Journal | Logical Methods in Computer Science |

Volume | 5 |

Issue number | 3 |

DOIs | |

Publication status | Published - 15 Sep 2009 |

### Fingerprint

### Keywords

- streams
- continuous functions
- initial algebras
- final coalgebras

### Cite this

*Logical Methods in Computer Science*,

*5*(3), 1-17. [9]. https://doi.org/10.2168/LMCS-5(3:9)2009

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*Logical Methods in Computer Science*, vol. 5, no. 3, 9, pp. 1-17. https://doi.org/10.2168/LMCS-5(3:9)2009

**Representations of stream processors using nested fixed points.** / Hancock, Peter; Pattinson, Dirk; Ghani, Neil.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Representations of stream processors using nested fixed points

AU - Hancock, Peter

AU - Pattinson, Dirk

AU - Ghani, Neil

PY - 2009/9/15

Y1 - 2009/9/15

N2 - 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.

AB - 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.

KW - streams

KW - continuous functions

KW - initial algebras

KW - final coalgebras

U2 - 10.2168/LMCS-5(3:9)2009

DO - 10.2168/LMCS-5(3:9)2009

M3 - Article

VL - 5

SP - 1

EP - 17

JO - Logical Methods in Computer Science

JF - Logical Methods in Computer Science

SN - 1860-5974

IS - 3

M1 - 9

ER -