### Abstract

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

Pages (from-to) | 339-347 |

Number of pages | 41 |

Journal | Mathematics Magazine |

Volume | 65 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1992 |

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### Cite this

*Mathematics Magazine*,

*65*(5), 339-347. https://doi.org/10.2307/2691249

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*Mathematics Magazine*, vol. 65, no. 5, pp. 339-347. https://doi.org/10.2307/2691249

**Pairs of points : antigonal, isogonal, and inverse.** / IJzeren, van, J.

Research output: Contribution to journal › Article › Professional

TY - JOUR

T1 - Pairs of points : antigonal, isogonal, and inverse

AU - IJzeren, van, J.

PY - 1992

Y1 - 1992

N2 - Final coalgebras capture system behaviours such as streams, infinite trees and processes. Algebraic operations on a final coalgebra can be defined by distributive laws (of a syntax functor S over a behaviour functor F). Such distributive laws correspond to abstract specification formats. One such format is a generalisation of the GSOS rules known from structural operational semantics of processes. We show that given an abstract GSOS specification ¿ that defines operations s on a final F-coalgebra, we can systematically construct a GSOS specification ¿ that defines the pointwise extension s of s on a final FA-coalgebra. The construction relies on the addition of a family of auxiliary ‘buffer’ operations to the syntax. These buffer operations depend only on A, so the construction is uniform for all s and F.

AB - Final coalgebras capture system behaviours such as streams, infinite trees and processes. Algebraic operations on a final coalgebra can be defined by distributive laws (of a syntax functor S over a behaviour functor F). Such distributive laws correspond to abstract specification formats. One such format is a generalisation of the GSOS rules known from structural operational semantics of processes. We show that given an abstract GSOS specification ¿ that defines operations s on a final F-coalgebra, we can systematically construct a GSOS specification ¿ that defines the pointwise extension s of s on a final FA-coalgebra. The construction relies on the addition of a family of auxiliary ‘buffer’ operations to the syntax. These buffer operations depend only on A, so the construction is uniform for all s and F.

U2 - 10.2307/2691249

DO - 10.2307/2691249

M3 - Article

VL - 65

SP - 339

EP - 347

JO - Mathematics Magazine

JF - Mathematics Magazine

SN - 0025-570X

IS - 5

ER -