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Functional Geometry

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Higher-Order and Symbolic Computation

Abstract

An algebra of pictures is described that is sufficiently powerful to denote the structure of a well-known Escher woodcut, Square Limit. A decomposition of the picture that is reasonably faithful to Escher's original design is given. This illustrates how a suitably chosen algebraic specification can be both a clear description and a practical implementation method. It also allows us to address some of the criteria that make a good algebraic description.

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References

  1. Abelson, H. and Sussman, G.J. with Sussman, J. Structure and Interpretation of Computer Programs. Cambridge, Massachusetts, The MIT Press, 1985.

    Google Scholar 

  2. Chailloux, E. and Cousineau, G. Programming images in ML. In ACM SIGPLAN Workshop on ML and its Applications, P. Lee (Ed.). San Francisco, California, 1992, pp. 119–133.

  3. Elliott, C. and Hudak, P. Functional reactive animation. In Proceedings of the 1997 ACM SIGPLAN International Conference on Functional Programming, M. Tofte (Ed.). Amsterdam, The Netherlands, ACM Press, 1997, pp. 263–273.

    Google Scholar 

  4. Finne, S. and Peyton-Jones, S. Pictures: A simple structured graphics model. In Functional Programming, Glasgow 1995. Ullapool, Scotland, Springer-Verlag, 1995.

    Google Scholar 

  5. Henderson, P. Functional geometry. In Conference Record of the 1982ACMSymposium on Lisp and Functional Programming, D.P. Friedman and D.S.Wise (Eds.). Pittsburgh, Pennsylvania, ACM Press, 1982, pp. 179–187. See http://www.ecs.soton.ac.uk/~ph/funcgeo.pdf.

    Google Scholar 

  6. Hudak, P. Modular domain specific languages and tools. In Proceedings: Fifth International Conference on Software Reuse, P. Devanbu and J. Poulin (Eds.). IEEE Computer Society Press, 1998, pp. 134–142.

  7. Hudak, P., Makucevich, T., Gadde, S., and Whong, B. Haskore music notation-An algebra of music. Journal of Functional Programming, 9(4) (1999) 355–372.

    Google Scholar 

  8. Kay, A. XSLT Programmer's Reference, 2nd Edition. Wrox Press Ltd., 2001. ISBN: 1861005067.

  9. Locher, J. (Ed.). The World of M. C. Escher. Harry N. Abrahams Inc., New York, 1971. ISBN 810901012.

    Google Scholar 

  10. Thompson, S. A functional reactive animation of lift using Fran. Journal of Functional Programming, 10(3) (2000) 245–268.

    Google Scholar 

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Authors and Affiliations

  1. Department of Electronics and Computer Science, University of Southampton, Southampton, SO17 1BJ, UK

    Peter Henderson

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  1. Peter Henderson
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Henderson, P. Functional Geometry. Higher-Order and Symbolic Computation 15, 349–365 (2002). https://doi.org/10.1023/A:1022986521797

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  • DOI: https://doi.org/10.1023/A:1022986521797

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