Skip to main content
SpringerLink
Log in

Functorial ML

  • Typing and Structuring Systems
  • Conference paper
  • First Online:
Programming Languages: Implementations, Logics, and Programs (PLILP 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1140))

Abstract

We present an extension of the Hindley-Milner type system that supports a generous class of type constructors called functors, and provide a parametrically polymorphic algorithm for their mapping, i.e. for applying a function to each datum appearing in a value of constructed type. The algorithm comes from shape theory, which provides a uniform method for locating data within a shape. The resulting system is Church-Rosser and strongly normalising, and supports type inference.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. Aczel. A general Church-Rosser theorem. Technical report, Univ. of Manchester, 1978.

    Google Scholar 

  2. H.P. Barendregt. The Lambda Calculus: Its Syntax and Semantics. North Holland, 1984. revised edition.

    Google Scholar 

  3. H.P. Barendregt. Lambda calculi with types. In Handbook of Logic in Computer Science. Oxford Univ. Press, 1992.

    Google Scholar 

  4. J. Benabou. Introduction to bicategories, volume 47. Springer, 1967.

    Google Scholar 

  5. E.S. Bainbridge, P.J. Freyd, A. Scedrov, and P.J. Scott. Functorial polymorphism. Theoretical Computer Science, 70:35–64, 1990.

    Google Scholar 

  6. G. Bellè, C. B. Jay, and E. Moggi. Functorial ML. available from ftp://ftp.disi.unige.it/person/MoggiE/functorial_ml.dvi, 1996.

    Google Scholar 

  7. M. Barr and C. Wells. Category Theory for Computing Science. International Series in Computer Science. Prentice Hall, 1990.

    Google Scholar 

  8. J.R.B. Cockett and T. Fukushima. About charity. Technical Report 92/480/18, University of Calgary, 1992.

    Google Scholar 

  9. J.-Y. Girard, Y. Lafont, and P. Taylor. Proofs and Types, volume 7. CUP, 1989.

    Google Scholar 

  10. R. Harper and G. Morrisett. Compiling polymorphism using intensional type analysis. In Conference Record of POPL '95: 22nd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pages 130–141, San Francisco, California, January 1995.

    Google Scholar 

  11. C.B. Jay. Type-free term reduction for covariant types. Tech. report to appear.

    Google Scholar 

  12. C.B. Jay. Polynomial polymorphism. In R. Kotagiri, editor, Proceedings of the Eighteenth Australasian Computer Science Conference: Glenelg, South Australia 1–3 February, 1995, volume 17, pages 237–243. A.C.S. Communications, 1995.

    Google Scholar 

  13. C.B. Jay. A semantics for shape. Science of Computer Programming, 25:251–283, 1995.

    Google Scholar 

  14. C.B. Jay. Shape analysis for parallel computing. In Parallel Computing Workshop '95 at Fujitsu Parallel Computing Centre, Imperial College, 1995.

    Google Scholar 

  15. C.B. Jay. A fresh look at parametric polymorphism: covariant types. In Proceedings of the 19th Australasian Computer Science Conference, Melbourne, Australia, January 31–February 2 1996., pages 525–533, 1996.

    Google Scholar 

  16. J. Jeuring. Polytypic pattern matching. In Conference on Functional Programming Languages and Computer Architecture, pages 238–248, 1995.

    Google Scholar 

  17. M.P. Jones. A system of constructor classes: overloading and implicit higherorder polymorphism. J. of Functional Programming, 5(1), 1995.

    Google Scholar 

  18. J.W. Klop. Combinatory Reduction Systems. PhD thesis, Mathematical Center Amsterdam, 1980. Tracts 129.

    Google Scholar 

  19. X. Leroy. Unboxed objects and polymorphic typing. In 19th Symp. on Principle of Programming Languages. ACM Press, 1992.

    Google Scholar 

  20. J. Lambek and P.J. Scott. Introduction to Higher-Order Categorical Logic, volume 7 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, 1986.

    Google Scholar 

  21. N.P. Mendler. Inductive types and type constraints in the second-order lambda calculus. Annals of Pure and Applied Logic, 51, 1991.

    Google Scholar 

  22. E. Meijer, M. Fokkinga, and R. Paterson. Functional programming with bananas, lenses, envelopes and barbed wire. In J. Hughes, editor, Procceding of the 5th ACM Conference on Functional Programming and Compter Architecture, volume 523 of LNCS, pages 124–44. Springer Verlag, 1991.

    Google Scholar 

  23. E. Meijer and G. Hutton. Bananas in space: extending fold and unfold to exponential types. In Procedings 7th International Conference on Functional Programming and Computer Architecture, San Diego, California, June 1995. ACM Press, 1995.

    Google Scholar 

  24. R. Milner. A theory of type polymorphism in programming. JCSS, 17, 1978.

    Google Scholar 

  25. S. Peyton Jones. Unboxed values as first-class citizens. In Functional Programming and Computer Architecture, volume 523 of LNCS, 1991.

    Google Scholar 

  26. J. Reynolds and G.D. Plotkin. On functors expressible in polymorphic lambda-calculus. In G. Huet, editor, Logical Foundations of Functional Programming. Addison-Wesley, 1990.

    Google Scholar 

  27. M. Tofte. Operational Semantics and Polymorphic Type Inference. PhD thesis, University of Edinburgh, 1988. available as CST-52-88.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. SOCS - Univ. of Tech. Sydney, P.O. Box 123, 2007, Broadway, Australia

    C. B. Jay

  2. DISI - Univ. di Genova, via Dodecaneso 35, 16146, Genova, Italy

    G. Bellè & E. Moggi

Authors
  1. G. Bellè
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. B. Jay
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. Moggi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Herbert Kuchen S. Doaitse Swierstra

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bellè, G., Jay, C.B., Moggi, E. (1996). Functorial ML. In: Kuchen, H., Doaitse Swierstra, S. (eds) Programming Languages: Implementations, Logics, and Programs. PLILP 1996. Lecture Notes in Computer Science, vol 1140. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61756-6_75

Download citation

  • DOI: https://doi.org/10.1007/3-540-61756-6_75

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61756-3

  • Online ISBN: 978-3-540-70654-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation