International Colloquium on Theoretical Aspects of Computing

Theoretical Aspects of Computing - ICTAC 2015 pp 110-125

Quotienting the Delay Monad by Weak Bisimilarity

Conference paper

DOI: 10.1007/978-3-319-25150-9_8

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9399)
Cite this paper as:
Chapman J., Uustalu T., Veltri N. (2015) Quotienting the Delay Monad by Weak Bisimilarity. In: Leucker M., Rueda C., Valencia F. (eds) Theoretical Aspects of Computing - ICTAC 2015. Lecture Notes in Computer Science, vol 9399. Springer, Cham

Abstract

The delay datatype was introduced by Capretta [3] 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 [6] 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.

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of CyberneticsTallinn University of TechnologyTallinnEstonia

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