Quotienting the delay monad by weak bisimilarity

James Chapman, Tarmo Uustalu, Niccolò Veltri

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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 languageEnglish
Title of host publicationTheoretical Aspects of Computing - ICTAC 2015
Subtitle of host publication12th International Colloquium, Cali, Colombia, October 29-31, 2015, Proceedings
Place of PublicationSwitzerland
PublisherSpringer
Pages110-125
Number of pages16
Volume9399
ISBN (Print)978-3-319-25149-3
DOIs
Publication statusPublished - 20 Dec 2015

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume9399

Keywords

  • delay datatype
  • weak bisimilarity
  • non-terminal computations

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    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