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Functional programming with bananas, lenses, envelopes and barbed wire

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Functional Programming Languages and Computer Architecture (FPCA 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 523))

Abstract

We develop a calculus for lazy functional programming based on recursion operators associated with data type definitions. For these operators we derive various algebraic laws that are useful in deriving and manipulating programs. We shall show that all example functions in Bird and Wadler's “Introduction to Functional Programming” can be expressed using these operators.

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References

  1. Roland Backhouse, Jaap van der Woude, Ed Voermans, and Grant Malcolm. A relational theory of types. Technical Report ??, TUE, 1991.

    Google Scholar 

  2. Rudolf Berghammer. On the use of composition in transformational programming. Technical Report TUM-18512, TU München, 1985.

    Google Scholar 

  3. R. Bird. An introduction to the theory of lists. In M. Broy, editor, Logic of Programming and Calculi of Discrete Design, pages 3–42. Springer Verlag, 1987. Also Technical Monograph PRG-56, Oxford University, October 1986.

    Google Scholar 

  4. Richard Bird. Constructive functional programming. In M. Broy, editor, Marktoberdorf International Summer school on Constructive Methods in Computer Science, NATO Advanced Science Institute Series. Springer Verlag, 1989.

    Google Scholar 

  5. Richard Bird and Phil Wadler. Introduction to Functional Programming. Prentice-Hall, 1988.

    Google Scholar 

  6. R. Bos and C. Hemerik. An introduction to the category-theoretic solution of recursive domain equations. Technical Report TRCSN 88/15, Eindhoven University of Technology, October 1988.

    Google Scholar 

  7. Manfred Broy. Transformation parallel ablaufender Programme. PhD thesis, TU München, München, 1980.

    Google Scholar 

  8. A. de Bruin and E.P. de Vink. Retractions in comparing Prolog semantics. In Computer Science in the Netherlands 1989, pages 71–90. SION, 1989.

    Google Scholar 

  9. Peter de Bruin. Naturalness of polymorphism. Technical Report CS 8916, RUG, 1989.

    Google Scholar 

  10. Maarten Fokkinga. Tupling and mutumorphisms. The Squiggolist, 1(4), 1989.

    Google Scholar 

  11. Maarten Fokkinga, Johan Jeuring, Lambert Meertens, and Erik Meijer. Translating attribute grammars into catamorphisms. The Squiggolist, 2(1), 1991.

    Google Scholar 

  12. Maarten Fokkinga and Erik Meijer. Program calculation properties of continuous algebras. Technical Report 91-4, CWI, 1991.

    Google Scholar 

  13. C. Gunter, P. Mosses, and D. Scott. Semantic domains and denotational semantics. In Marktoberdorf International Summer school on Logic, Algebra and Computation, 1989. to appear in: Handbook of Theoretical Computer Science, North Holland.

    Google Scholar 

  14. Tasuya Hagino. Codatatypes in ML. Journal of Symbolic Computation, 8:629–650, 1989.

    Google Scholar 

  15. J. Arsac and Y Kodratoff. Some techniques for recursion removal. ACM Toplas, 4(2):295–322, 1982.

    Google Scholar 

  16. D.J. Lehmann and M.B. Smyth. Algebraic specification of data types: a synthetic approach. Math. Systems Theory, 14:97–139, 1981.

    Google Scholar 

  17. Grant Malcolm. Algebraic Types and Program Transformation. PhD thesis, University of Groningen, The Netherlands, 1990.

    Google Scholar 

  18. Lambert Meertens. Algorithmics — towards programming as a mathematical activity. In Proceedings of the CWI symposium on Mathematics and Computer Science, pages 289–334. North-Holland, 1986.

    Google Scholar 

  19. Lambert Meertens. Paramorphisms. To appear in Formal Aspects of Computing, 1990.

    Google Scholar 

  20. John-Jules Ch. Meyer. Programming calculi based on fixed point transformations: semantics and applications. PhD thesis, Vrije Universiteit, Amsterdam, 1985.

    Google Scholar 

  21. Ross Paterson. Reasoning about Functional Programs. PhD thesis, University of Queensland, Brisbane, 1988.

    Google Scholar 

  22. John C. Reynolds. Types abstraction and parametric polymorphism. In Information Processing '83. North Holland, 1983.

    Google Scholar 

  23. David A. Schmidt. Denotational Semantics. Allyn and Bacon, 1986.

    Google Scholar 

  24. M.B. Smyth and G.D. Plotkin. The category-theoretic solution of recursive domain equations. SIAM Journal on Computing, 11(4):761–785, November 1982.

    Google Scholar 

  25. Joseph E. Stoy. Denotational Semantics, The Scott-Strachey Approach to Programming Language Theory. The MIT press, 1977.

    Google Scholar 

  26. Nico Verwer. Homomorphisms, factorisation and promotion. The Squiggolist, 1(3), 1990. Also technical report RUU-CS-90-5, Utrecht University, 1990.

    Google Scholar 

  27. Phil Wadler. Views: A way for pattern matching to cohabit with data abstraction. Technical Report 34, Programming Methodology Group, University of Göteborg and Chalmers University of Technology, March 1987.

    Google Scholar 

  28. Philip Wadler. Theorems for free ! In Proc. 1989 ACM Conference on Lisp and Functional Programming, pages 347–359, 1989.

    Google Scholar 

  29. Philip Wadler. Comprehending monads. In Proc. 1990 ACM Conference on Lisp and Functional Programming, 1990.

    Google Scholar 

  30. M. Wand. Fixed point constructions in order enriched categories. Theoretical Computer Science, 8, 1979.

    Google Scholar 

  31. Hans Zierer. Programmierung mit funktionsobjecten: Konstruktive erzeugung semantische bereiche und anwendung auf die partielle auswertung. Technical Report TUM-18803, TU München, 1988.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Informatics, University of Nijmegen, Toernooiveld, 6525 ED, Nijmegen

    Erik Meijer

  2. CWI, Amsterdam & University of Twente, The Netherlands

    Maarten Fokkinga

  3. Imperial College, London

    Ross Paterson

Authors
  1. Erik Meijer
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  2. Maarten Fokkinga
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  3. Ross Paterson
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Editor information

John Hughes

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© 1991 Springer-Verlag Berlin Heidelberg

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Meijer, E., Fokkinga, M., Paterson, R. (1991). Functional programming with bananas, lenses, envelopes and barbed wire. In: Hughes, J. (eds) Functional Programming Languages and Computer Architecture. FPCA 1991. Lecture Notes in Computer Science, vol 523. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3540543961_7

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  • DOI: https://doi.org/10.1007/3540543961_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54396-1

  • Online ISBN: 978-3-540-47599-6

  • eBook Packages: Springer Book Archive

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