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

Altenkirch, Thorsten, Danielsson, Nils Anders and Kraus, Nicolai (2017) Partiality, revisited: the partiality monad as a quotient inductive-inductive type. Lecture Notes in Computer Science, 10203 . pp. 534-549. ISSN 0302-9743

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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: Article
Additional Information: The final publication is available at Springer via Chapter in: 20th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2017, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017, Uppsala, Sweden, April 22-29, 2017. ISBN 9783662544570 (Print) 9783662544587 (eBook)
Keywords: homotopy type theory, quotient inductive-inductive type, partiality, partial computation
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Computer Science
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Depositing User: Kraus, Nicolai
Date Deposited: 20 Jul 2017 13:04
Last Modified: 04 May 2020 18:38

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