License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.04381.2
URN: urn:nbn:de:0030-drops-1768
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2005/176/
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Setzer, Anton ; Hancock, Peter

Interactive Programs and Weakly Final Coalgebras in Dependent Type Theory (Extended Version)

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04381.SetzerAnton.Paper.176.pdf (0.3 MB)

Abstract

We reconsider the representation of interactive programs in dependent type theory that the authors proposed in earlier papers. Whereas in previous versions the type of interactive programs was introduced in an ad hoc way, it is here defined as a weakly final coalgebra for a general form of polynomial functor. The are two versions: in the first the interface with the real world is fixed, while in the second the potential interactions can depend on the history of previous interactions. The second version may be appropriate for working with specifications of interactive programs. We focus on command-response interfaces, and consider both client and server programs, that run on opposite sides such an interface. We give formation/introduction/elimination/equality rules for these coalgebras. These are explored in two dimensions: coiterative versus corecursive, and monadic versus non-monadic. We also comment upon the relationship of the corresponding rules with guarded induction. It turns out that the introduction rules are nothing but a slightly restricted form of guarded induction. However, the form in which we write guarded induction is not recursive equations (which would break normalisation -- we show that type checking becomes undecidable), but instead involves an elimination operator in a crucial way.

BibTeX - Entry

@InProceedings{setzer_et_al:DagSemProc.04381.2,
  author =	{Setzer, Anton and Hancock, Peter},
  title =	{{Interactive Programs and Weakly Final Coalgebras in Dependent Type Theory (Extended Version)}},
  booktitle =	{Dependently Typed Programming},
  pages =	{1--30},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4381},
  editor =	{Thorsten Altenkirch and Martin Hofmann and John Hughes},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2005/176},
  URN =		{urn:nbn:de:0030-drops-1768},
  doi =		{10.4230/DagSemProc.04381.2},
  annote =	{Keywords: Dependently types programming , interactive programs , coalgebras , weakly final coalgebras , coiteration , corecursion , monad}
}

Keywords: Dependently types programming , interactive programs , coalgebras , weakly final coalgebras , coiteration , corecursion , monad
Collection: 04381 - Dependently Typed Programming
Issue Date: 2005
Date of publication: 20.05.2005

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