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Electronic category theory

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 88))

Abstract

This paper describes some experiments in using algebraic and categorical ideas to write programs. In particular a program to compute colimits in a category given coproducts and coequalisers has been written, also one to ‘lift’ such colimits to comma categories. The discussion is informal and aims to show how categorical concepts can be painlessly realised in computational practice.

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References

  • Arbib, M. and Manes, E. (1975) Arrows, Structures and Functors. Academic Press: New York.

    Google Scholar 

  • Backus, J. (1978) Can programming be liberated from the von Neumann style? A functional style and its algebra of programs. CACM, 21, 8, 613–641.

    Google Scholar 

  • Barrow, H., Ambler, A.P. and Burstall, R.M. (1972) Some techniques for recognising structures in pictures. Proc. of the International Conference on Frontiers of Pattern Recognition (ed. S. Watanabe), Honolulu, Hawaii. Academic Press: New York, pp. 1–29.

    Google Scholar 

  • Burstall, R.M. (1977) Design considerations for a functional programming language, in Proc. of Infotech State of the Art Conference “The Software Revolution”, Copenhagen, pp. 45–57.

    Google Scholar 

  • Burstall, R.M., Collins, J.S. and Popplestone, R.J. (1971) Programming in POP-2. (A revision of POP-2 Papers, Edinburgh: University Press, 1968.) Edinburgh: University Press.

    Google Scholar 

  • Burstall, R.M. and Goguen, J.A. (1977) Putting theories together to make specifications, in Proc. of Fifth International Joint Conference on Artificial Intelligence, Boston, pp. 1045–1058. (From Comp. Sci.Dept., Carnegie-Mellon Univ.)

    Google Scholar 

  • Burstall, R.M. and Goguen, J.A. (1980) The semantics of CLEAR, a specification language, in Proc. of Advanced Course on Abstract Software Specifications, Copenhagen (1970). Lecture Notes in Computer Science. Berlin: Springer-Verlag (in press).

    Google Scholar 

  • Burstall, R.M. and Landin, P.J. (1969) Programs and their proofs: an algebraic approach. Machine Intelligence 4 (eds. B. Meltzer and D. Michie) Edinburgh: University Press, pp. 17–44.

    Google Scholar 

  • Burstall, R.M., MacQueen, D.B. and Sannella, D.T. (1980) HOPE: an experimental applicative language. Research Report, Dept. of Computer Science, University of Edinburgh.

    Google Scholar 

  • Ehrig, H., Kreowski, H-J., Maggiolo-Schettini, A., Rosen, B. and Winkowski, J. (1977) Deriving structures from structures. Research Report, IBM Research Center, Computer Sc ence Dept., Yorktown Heights, N.Y.

    Google Scholar 

  • Ehrig, H., Pfender, M. and Schneider, H. (1973) Graph grammars: an algebraic approach. Proc. 14th Ann. IEEE Symp. on Switching and Automata Theory, pp. 167–180.

    Google Scholar 

  • Goguen, J.A. and Burstall, R.M. (1978) Some fundamental properties of algebraic theories: a tool for semantics of computation. DAI Research Report No. 53, Dept. of Artificial Intelligence, University of Edinburgh. (Revised version to appear shortly from Edinburgh University Computer Science Dept.)

    Google Scholar 

  • Goguen, J.A. and Ginali, S. (1978) A categorical approach to general systems. In Applied General Systems Research (ed. G. Klir) Plenum, pp. 257–270.

    Google Scholar 

  • Klaeren, H. (1980) An abstract software specification technique based on structural recursion. SIGPLAN Notices, 15, 3, 28–34.

    Google Scholar 

  • MacLane, S. (1971) Categories for the Working Mathematician. Springer-Verlag.

    Google Scholar 

  • Perryman, G. (1970) Discovering the structure of an automaton from partial information. M.Sc. thesis. Dept. of Artificial Intelligence, University of Edinburgh.

    Google Scholar 

  • Thatcher, J., Wagner, E. and Wright, J. (1979) More advice on structuring compilers and proving them correct. Research Report RC 7588, IBM Research Center, Computer Science Dept., Yorktown Heights, N.Y.

    Google Scholar 

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P. Dembiński

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© 1980 Springer-Verlag Berlin Heidelberg

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Burstall, R.M. (1980). Electronic category theory. In: Dembiński, P. (eds) Mathematical Foundations of Computer Science 1980. MFCS 1980. Lecture Notes in Computer Science, vol 88. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022493

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  • DOI: https://doi.org/10.1007/BFb0022493

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10027-0

  • Online ISBN: 978-3-540-38194-5

  • eBook Packages: Springer Book Archive

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