### Abstract

Given a signature of basic operations for a computational effect such as side-effects, interactive input/output, or exceptions, we give a unified construction that determines equations that should hold between derived operations of the same arity. We then show how to construct a canonical model for the signature, together with the first-order fragment of the computational λ-calculus, subject to the equations, done at the level of generality of an arbitrary computational effect. We prove a universality theorem that characterises the canonical model, and we recall, from a previous paper, how to extend such models to the full computational λ-calculus. Our leading example is that of side-effects, with occasional reference to interactive input/output, exceptions, and nondeterminism.

Original language | English |
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Title of host publication | Foundations of Software Science and Computation Structures 7th International Conference, FOSSACS 2004, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2004, Barcelona, Spain, March 29 – April 2, 2004. Proce |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 438-452 |

Number of pages | 15 |

Volume | 2987 |

DOIs | |

Publication status | Published - 2004 |

### Publication series

Name | Lecture Notes in Comput. Sci. |
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Publisher | Springer |

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## Cite this

Power, J. (2004). Canonical models for computational effects. In

*Foundations of Software Science and Computation Structures 7th International Conference, FOSSACS 2004, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2004, Barcelona, Spain, March 29 – April 2, 2004. Proce*(Vol. 2987, pp. 438-452). (Lecture Notes in Comput. Sci.). Springer. https://doi.org/10.1007/978-3-540-24727-2_31