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Reflections on the Work of C.A.R. Hoare pp 301–331Cite as

Fun with Type Functions

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Abstract

Tony Hoare has always been a leader in writing down and proving properties of programs. To prove properties of programs automatically, the most widely used technology today is the ubiquitous type checker. Alas, static type systems inevitably exclude some good programs and allow some bad ones. Thus motivated, we describe some fun we have been having with Haskell, by making the type system more expressive without losing the benefits of automatic proof and compact expression. Specifically, we offer a programmer’s tour of so-calledtype families, a recent extension to Haskell that allows functions on types to be expressed as straightforwardly as functions on values. This facility makes it easier for programmers to effectively extend the compiler by writing functional programs that execute during type checking. Source code for all the examples is available at http://research.microsoft.com/simonpj/papers/assoc-types/fun-with-type-funs.zip.

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Notes

  1. 1.

    “=” is used for too many other things.

  2. 2.

    A possible extension, not currently implemented by GHC, would be to allow an associatedtypesynonym declaration optionally to specify that it should be injective, and to check that this property is maintained as eachinstanceis added.

  3. 3.

    http://hackage.haskell.org/cgi-bin/hackage-scripts/package/pointless-haskell

  4. 4.

    “Cmp” is short for “compose”.

  5. 5.

    GHC requires the alarming flag-XAllowUndecidableInstancesto accept the(Cf1f2)instance forTPrinter, because thenestedrecursive call toTPrinterdoes not “obviously terminate.” Of course, every call toTPrinterdoes terminate, because the second argument (where the nested recursive call is made) is not scrutinised by any of the equations, but this is a non-local property that GHC does not check. The flag promises the compiler thatTPrinterwill terminate; the worst that can happen if the programmer makes an erroneous promise is that the type checker diverges.

  6. 6.

    http://okmij.org/ftp/Haskell/types.html#polyvar-fn

  7. 7.

    http://okmij.org/ftp/Haskell/typecast.html#solving-read-show

  8. 8.

    http://okmij.org/ftp/Haskell/typecast.html#is-function-type

  9. 9.

    http://okmij.org/ftp/Haskell/keyword-arguments.lhs

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Acknowledgements

We would like to thank people who responded to our invitation to suggest interesting examples of programming with type families, or commented on a draft of the chapter: Lennart Augustsson, Neil Brown, Toby Hutton, Ryan Ingram, Chris Kuklewicz, Dave Menendez, Benjamin Moseley, Hugh Pacheco, Conrad Parker, Bernie Pope, Tom Schrijvers, Josef Svenningsson, Paulo Tanimoto, Magnus Therning, Ashley Yakeley and Brent Yorgey.

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Authors and Affiliations

  1. FNMOC, Monterey, CA, USA

    Oleg Kiselyov

  2. Microsoft Research Ltd, 7 JJ Thomson Avenue, Cambridge, CB3 0FB, England

    Simon Peyton Jones

  3. Rutgers University, Newark, USA

    Chung-chieh Shan

Authors
  1. Oleg Kiselyov
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  2. Simon Peyton Jones
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  3. Chung-chieh Shan
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Correspondence to Simon Peyton Jones .

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Editors and Affiliations

  1. Oxford University Computing Laboratory, Parks Road, Oxford, OX13QD, United Kingdom

    A.W. Roscoe

  2. Dept. Computing Science, University of Newcastle upon Tyne, Newcastle upon Tyne, NE17RU, United Kingdom

    Cliff B. Jones

  3. Microsoft Research Ltd., J. J. Thomson Avenue 7, Cambridge, CB30FB, United Kingdom

    Kenneth R. Wood

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Kiselyov, O., Jones, S.P., Shan, Cc. (2010). Fun with Type Functions. In: Roscoe, A., Jones, C., Wood, K. (eds) Reflections on the Work of C.A.R. Hoare. Springer, London. https://doi.org/10.1007/978-1-84882-912-1_14

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