## Abstract

A new notion is given for the implementation of one specification by another. Unlike most previous notions, this generalises to handle parameterised specifications as well as loose specifications (having an assortment of non-isomorphic models). Examples are given to illustrate the notion. The definition of implementation is based on a new notion of the simulation of a theory by an algebra. For the bulk of the paper we employ a variant of the Clear specification language [BG 77] in which the notion of a data constraint is replaced by the weaker notion of a hierarchy constraint. All results hold for Clear with data constraints as well, but only under more restrictive conditions.

We prove that implementations compose vertically (two successive implementation steps compose to give one large step) and that they compose horizontally under application of (well-behaved) parameterised specifications (separate implementations of the parameterised specification and the actual parameter compose to give an implementation of the application).

We prove that implementations compose vertically (two successive implementation steps compose to give one large step) and that they compose horizontally under application of (well-behaved) parameterised specifications (separate implementations of the parameterised specification and the actual parameter compose to give an implementation of the application).

Original language | English |
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Title of host publication | Automata, Languages and Programming |

Subtitle of host publication | Ninth Colloquium Aarhus, Denmark, July 12–16, 1982 |

Editors | Mogens Nielsen, Erik Meineche Schmidt |

Publisher | Springer-Verlag GmbH |

Pages | 473-488 |

Number of pages | 16 |

ISBN (Electronic) | 978-3-540-39308-5 |

ISBN (Print) | 978-3-540-11576-2 |

DOIs | |

Publication status | Published - 1982 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer Berlin / Heidelberg |

Volume | 140 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |