Abstract
This paper is based on an experience in teaching functional programming to mathematics students. This experience had two objectives. The first one was to help the student assimilate some mathematical concepts by putting them to practical use in programs. The second one was to give them a good start in programming by emphasizing the fact that abstraction, which is so useful in mathematics, is equally useful in programming and allows for more powerful and more easily extensible programs. The mathematical domain used here is geometry and more precisely geometrical transformations, and their group structure. The programming projects are oriented towards 2D tilings, both Euclidean and hyperbolic.
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References
G. Cousineau and M. Mauny. Approche fonctionnelle de la programmation. Ediscience, 1995. English version to be published by Cambridge University Press in september 97.
H.S.M. Coxeter. Introduction to geometry. John Wiley and sons, 1980.
H.S.M. Coxeter and W.O.J. Mauser. Generators and relations for discrete groups. Ergenisse der Mathematik und ihrer Grenzgebiete, 14, 1965.
Ph. Lechenadec. Canonical forms in finitely presented algebras. Pitman, 1986.
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© 1997 Springer-Verlag Berlin Heidelberg
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Cousineau, G. (1997). Functional programming and geometry. In: Glaser, H., Hartel, P., Kuchen, H. (eds) Programming Languages: Implementations, Logics, and Programs. PLILP 1997. Lecture Notes in Computer Science, vol 1292. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0033852
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DOI: https://doi.org/10.1007/BFb0033852
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