### Abstract

The delay datatype was introduced by Capretta as a means to deal with partial functions (as in computability theory) in Martin-Löf type theory. It is a monad and it constitutes a constructive alternative to the maybe monad. It is often desirable to consider two delayed computations equal, if they terminate with equal values, whenever one of them terminates. The equivalence relation underlying this identification is called weak bisimilarity. In type theory, one commonly replaces quotients with setoids. In this approach, the delay monad quotiented by weak bisimilarity is still a monad. In this paper, we consider Hofmann's alternative approach of extending type theory with inductive-like quotient types. In this setting, it is difficult to define the intended monad multiplication for the quotiented datatype. We give a solution where we postulate some principles, crucially proposition extensionality and the (semi-classical) axiom of countable choice. We have fully formalized our results in the Agda dependently typed programming language.

Original language | English |
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Title of host publication | Theoretical Aspects of Computing - ICTAC 2015 |

Subtitle of host publication | 12th International Colloquium, Cali, Colombia, October 29-31, 2015, Proceedings |

Place of Publication | Switzerland |

Publisher | Springer |

Pages | 110-125 |

Number of pages | 16 |

Volume | 9399 |

ISBN (Print) | 978-3-319-25149-3 |

DOIs | |

Publication status | Published - 20 Dec 2015 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |

Volume | 9399 |

### Keywords

- delay datatype
- weak bisimilarity
- non-terminal computations

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## Cite this

Chapman, J., Uustalu, T., & Veltri, N. (2015). Quotienting the delay monad by weak bisimilarity. In

*Theoretical Aspects of Computing - ICTAC 2015: 12th International Colloquium, Cali, Colombia, October 29-31, 2015, Proceedings*(Vol. 9399, pp. 110-125). (Lecture Notes in Computer Science; Vol. 9399). Springer. https://doi.org/10.1007/978-3-319-25150-9