Partiality, revisited: the partiality monad as a quotient inductive-inductive type

Altenkirch, Thorsten and 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)

[img]
Preview
PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (495kB) | Preview

Abstract

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.

Item Type: Conference or Workshop Item (Paper)
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Computer Science
Depositing User: Altenkirch, Thorsten
Date Deposited: 24 Mar 2017 09:12
Last Modified: 13 Oct 2017 01:17
URI: http://eprints.nottingham.ac.uk/id/eprint/41533

Actions (Archive Staff Only)

Edit View Edit View