by
John Power

Citations: | 4 - 0 self |

@MISC{Power06semanticsfor,

author = {John Power},

title = {Semantics for Local Computational Effects},

year = {2006}

}

Starting with Moggi’s work on monads as refined to Lawvere theories, we give a general construct that extends denotational semantics for a global computational effect canonically to yield denotational semantics for a corresponding local computational effect. Our leading example yields a construction of the usual denotational semantics for local state from that for global state. Given any Lawvere theory L, possibly countable and possibly enriched, we first give a universal construction that extends L, hence the global operations and equations of a given effect, to incorporate worlds of arbitrary finite size. Then, making delicate use of the final comodel of the ordinary Lawvere theory L, we give a construct that uniformly allows us to model block, the universality of the final comodel yielding a universal property of the construct. We illustrate both the universal extension of L and the canonical construction of block by seeing how they work in the case of state.

920 | Categories for the Working Mathematician - Lane - 1971 |

439 | Computational lambda-calculus and monads - Moggi - 1989 |

377 | Basic concepts of enriched category theory, volume 64 - Kelly - 1982 |

39 | Categorical models for local names - Stark - 1996 |

30 | Adequacy for algebraic effects - Plotkin, Power - 2001 |

29 | Call-by-Push-Value. A Functional/Imperative Synthesis - Levy - 2004 |

26 | Computational effects and operations: an overview - Plotkin, Power - 2004 |

15 | Call-by-push-value: A subsuming paradigm - Levy - 1999 |

12 | Notions of computation and monads. Information and computation 93(1 - Moggi - 1991 |

10 | Discrete lawvere theories and computational effects - Hyland, Power - 2006 |

5 | Generic models for computational effects - Power - 2006 |

2 | Logic for Computational Effects: work in progress - Plotkin, Power - 2003 |

1 | Olha Shkaravska, From Models to Comodels: State and Arrays - Power - 2004 |

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