Partiality, revisited: the partiality monad as a quotient inductive-inductive type
Capretta's delay monad can be used to model partial computations, but it has the ``wrong'' notion of built-in equality, strong bisimilarity. An alternative is to quotient the delay monad by the ``right''notion of equality, weak bisimilarity. However, recent work by Chapman e...
| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Published: |
2016
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| Online Access: | https://eprints.nottingham.ac.uk/41533/ |
| _version_ | 1848796297042067456 |
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| author | Altenkirch, Thorsten Danielson, Nils Anders Kraus, Nicolai |
| author_facet | Altenkirch, Thorsten Danielson, Nils Anders Kraus, Nicolai |
| author_sort | Altenkirch, Thorsten |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Capretta's delay monad can be used to model partial computations, but it has the ``wrong'' notion of built-in equality, strong bisimilarity. An alternative is to quotient the delay monad by the ``right''notion of equality, weak bisimilarity. However, recent work by Chapman et al. suggests that it is impossible to define a monad structure on the resulting construction in common forms of type theory without assuming (instances of) the axiom of countable choice.
Using an idea from homotopy type theory---a higher inductive-inductive type---we construct a partiality monad without relying on countable choice. We prove that, in the presence of countable choice, our partiality monad is equivalent to the delay monad quotiented by weak bisimilarity. Furthermore we outline several applications. |
| first_indexed | 2025-11-14T19:45:44Z |
| format | Conference or Workshop Item |
| id | nottingham-41533 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:45:44Z |
| publishDate | 2016 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-415332020-05-04T18:24:43Z https://eprints.nottingham.ac.uk/41533/ Partiality, revisited: the partiality monad as a quotient inductive-inductive type Altenkirch, Thorsten Danielson, Nils Anders Kraus, Nicolai Capretta's delay monad can be used to model partial computations, but it has the ``wrong'' notion of built-in equality, strong bisimilarity. An alternative is to quotient the delay monad by the ``right''notion of equality, weak bisimilarity. However, recent work by Chapman et al. suggests that it is impossible to define a monad structure on the resulting construction in common forms of type theory without assuming (instances of) the axiom of countable choice. Using an idea from homotopy type theory---a higher inductive-inductive type---we construct a partiality monad without relying on countable choice. We prove that, in the presence of countable choice, our partiality monad is equivalent to the delay monad quotiented by weak bisimilarity. Furthermore we outline several applications. 2016-12-22 Conference or Workshop Item PeerReviewed Altenkirch, Thorsten, Danielson, Nils Anders and Kraus, Nicolai (2016) Partiality, revisited: the partiality monad as a quotient inductive-inductive type. In: FoSSaCs 2017, 24-29 April 2017, Uppsala, Sweden. (In Press) |
| spellingShingle | Altenkirch, Thorsten Danielson, Nils Anders Kraus, Nicolai Partiality, revisited: the partiality monad as a quotient inductive-inductive type |
| title | Partiality, revisited: the partiality monad as a quotient inductive-inductive type |
| title_full | Partiality, revisited: the partiality monad as a quotient inductive-inductive type |
| title_fullStr | Partiality, revisited: the partiality monad as a quotient inductive-inductive type |
| title_full_unstemmed | Partiality, revisited: the partiality monad as a quotient inductive-inductive type |
| title_short | Partiality, revisited: the partiality monad as a quotient inductive-inductive type |
| title_sort | partiality, revisited: the partiality monad as a quotient inductive-inductive type |
| url | https://eprints.nottingham.ac.uk/41533/ |