by
Ulrich Berger

Citations: | 9 - 5 self |

@MISC{Berger_fromcoinductive,

author = {Ulrich Berger},

title = {From coinductive proofs to exact real arithmetic},

year = {}

}

Abstract. We give a coinductive characterisation of the set of continuous functions defined on a compact real interval, and extract certified programs that construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresponding to the coinductive definition of continuous functions consists of finitely branching non-wellfounded trees describing when the algorithm writes and reads digits. This is a pilot study in using proof-theoretic methods for obtaining certified algorithms in exact real arithmetic. 1

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27 | Proof theory at work: Program development in the Minlog system - Benl, Berger, et al. - 1998 |

27 | Modal mu-calculi - Bradfield, Stirling - 2007 |

24 | Lazy functional algorithms for exact real functionals, volume 1450 - Simpson |

16 | T.: Iteration and coiteration schemes for higherorder and nested datatypes. Theoretical Computer Science 333(1–2 - Abel, Matthes, et al. - 2005 |

16 | R.: Computing with real numbers: I. The LFT approach to real number computation; II. A domain framework for computational geometry
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- 2002
(Show Context)
Citation Context ...ork on exact real number computation describes algorithms for functions on certain exact representations of the reals (for example streams of signed digits [1, 2] or linear fractional transformations =-=[3]-=-) and proves their correctness using a certain proof method (for example coinduction [4–6]). Our work has a similar aim, and builds on the work cited above, but there are two important differences. Th... |

14 |
Semantics of a sequential language for exact real-number computation. Theoretical Computer Science
- Marcial-Romero, Escardó
- 2007
(Show Context)
Citation Context ...duction. 1 Introduction Most of the recent work on exact real number computation describes algorithms for functions on certain exact representations of the reals (for example streams of signed digits =-=[1, 2]-=- or linear fractional transformations [3]) and proves their correctness using a certain proof method (for example coinduction [4–6]). Our work has a similar aim, and builds on the work cited above, bu... |

12 | Affine functions and series with co-inductive real numbers - Bertot - 2007 |

9 |
F.: Constructive analysis, types and exact real numbers
- Geuvers, Niqui, et al.
- 2007
(Show Context)
Citation Context ...duction. 1 Introduction Most of the recent work on exact real number computation describes algorithms for functions on certain exact representations of the reals (for example streams of signed digits =-=[1, 2]-=- or linear fractional transformations [3]) and proves their correctness using a certain proof method (for example coinduction [4–6]). Our work has a similar aim, and builds on the work cited above, bu... |

6 | Realizability interpretation of proofs in constructive analysis - Schwichtenberg - 2008 |

5 | Efficient exact computation of iterated maps - Blanck |

5 | A calculator for exact real number computation - Plume |

4 | Realizability of monotone coinductive definitions and its application to program synthesis - Tatsuta - 1998 |

1 | Continuous functions on final coalgebras. volume 164 - Ghani, Hancock, et al. - 2006 |

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