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A Reflection on Types

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A List of Successes That Can Change the World

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9600))

Abstract

The ability to perform type tests at runtime blurs the line between statically-typed and dynamically-checked languages. Recent developments in Haskell’s type system allow even programs that use reflection to themselves be statically typed, using a type-indexed runtime representation of types called \(\textsf {\textit{TypeRep}}\). As a result we can build dynamic types as an ordinary, statically-typed library, on top of \(\textsf {\textit{TypeRep}}\) in an open-world context.

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Notes

  1. 1.

    There is another connection with Phil’s work here: an API like this was first proposed in “Imperative functional programming” [PJW93], a collaboration between one of the present authors and Phil, directly inspired by Phil’s ground-breaking paper “Comprehending monads” [Wad90].

  2. 2.

    For our present purposes you can safely ignore the “\(\textsf {\textit{s}}\)” type parameter; the paper “State in Haskell” explains what is going on [LPJ95].

  3. 3.

    https://hackage.haskell.org/package/vault.

  4. 4.

    These types also motivate the \(\textsf {\textit{Typeable}}\) constraint above. We discuss that constraint further in Sect. 5.2, but without looking that far ahead, Phil’s insight about “theorems for free” tells us that the type \(\textsf {\textit{fromDynamic}}\mathbin {::}\textsf {\textit{Dynamic}}\rightarrow \textsf {\textit{Maybe}}\;\textsf {\textit{a}}\) is a non-starter [Wad89]. Any function with that type must return \(\textsf {\textit{Nothing}}\), \(\textsf {\textit{Just}}\;\bot \), or diverge.

  5. 5.

    Although the set of type constructors is fixed, you can use them to build an infinite number of types; e.g. \((\textsf {\textit{Int}},\textsf {\textit{Bool}})\), \((\textsf {\textit{Int}},(\textsf {\textit{Bool}},\textsf {\textit{Int}}))\), etc.

  6. 6.

    Recall that \(\bot \) is not a value.

  7. 7.

    Here we are using GHC’s ability to define infix type constructors.

  8. 8.

    The kind signatures are optional. With \(\textsf {\textit{PolyKinds}}\) enabled, GHC infers them, but we often add them for clarity.

  9. 9.

    Though, some Haskellers have hacked around this restriction with abandon. See Kiselyov and Shan [KS04] and Edward Kmett’s \(\textsf {\textit{reflection}}\) package (at http://hackage.haskell.org/package/reflection).

  10. 10.

    See also http://stackoverflow.com/q/32576018/791604 for another use case for a map keyed on type representations.

  11. 11.

    The dependent-map library is an example of such a data structure. See https://hackage.haskell.org/package/dependent-map-0.1.1.3/docs/Data-Dependent-Map.html.

  12. 12.

    See the tree of wiki pages rooted at https://ghc.haskell.org/trac/ghc/wiki/DistributedHaskell for lots more information.

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Acknowledgements

Thanks to Neil Mitchell both for help in understanding Shake and for a rapid review. Kenneth Foner also provided feedback on a draft. Ben Price’s internship at Microsoft Research was helpful in bringing some of the key issues to the surface. This paper was typeset with \(\textsf {\textit{lhs2TeX}}\) (http://www.andres-loeh.de/lhs2tex/).

Finally, thanks to Phil, who has spent much of his professional life reflecting on types. Increasingly, Haskell can too. Happy birthday Phil!

Author information

Authors and Affiliations

  1. Microsoft Research, Cambridge, UK

    Simon Peyton Jones & Dimitrios Vytiniotis

  2. Department of Computer and Information Science, University of Pennsylvania, Philadelphia, USA

    Stephanie Weirich & Richard A. Eisenberg

Authors
  1. Simon Peyton Jones
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  2. Stephanie Weirich
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  3. Richard A. Eisenberg
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  4. Dimitrios Vytiniotis
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Corresponding author

Correspondence to Simon Peyton Jones .

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Editors and Affiliations

  1. Informatics Forum, University of Edinburgh Informatics Forum, Edinburgh, United Kingdom

    Sam Lindley

  2. University of Strathclyde , Glasgow, United Kingdom

    Conor McBride

  3. University of Glasgow , Glasgow, United Kingdom

    Phil Trinder

  4. Informatics Forum, University of Edinburgh Informatics Forum, Edinburgh, United Kingdom

    Don Sannella

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Peyton Jones, S., Weirich, S., Eisenberg, R.A., Vytiniotis, D. (2016). A Reflection on Types. In: Lindley, S., McBride, C., Trinder, P., Sannella, D. (eds) A List of Successes That Can Change the World. Lecture Notes in Computer Science(), vol 9600. Springer, Cham. https://doi.org/10.1007/978-3-319-30936-1_16

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