Abstract
We have presented an existence theorem and some important properties of Galois connections. We have also shown how data structures problems can be simplified and better understood when Galois insertions are used. In particular, the proof of correctness of an implementation follows simply from the construction of a Galois insertion. We plan further applications of Galois connections theory to computing-related problems.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
5. References
Birkhoff, G. Lattice Theory, 3rd ed. AMS Colloquium Publication, Rhode Island, 1967.
Blyth, T.S., and Janowitz, M.F. Residuation Theory. Pergamon Press, Oxford, 1972.
Gierz, G., et. al. A Compendium of Continuous Lattices. Springer-Verlag, Berlin, 1980.
Herrlich, H. and Husek, M. Galois connections, Proc. Math. Foundations of Prog. Semantics, Manhattan, KS, April, 1985, Springer-Verlag Lecture Notes in Computer Science, to appear.
Huet, G., and Oppen, D. Equations and rewrite rules: A survey. In R. Book (ed.), Formal Language Theory, Perspectives and Open Problems. Academic Press, New York, 1980, pp. 349–405.
McCarthy, J. Towards a mathematical science of computation, Proc. IFIP Congress 1963, pp. 21–28, North-Holland, Amsterdam, 1963.
Ore, O. Galois connexions, Trans. Amer. Math. Soc. 55 (1944) 493–513.
Pickert, G. Bemerkungen uber Galois-Verbingungen, Archiv. Math. 3 (1952) 285–289.
Schmidt, D. Denotational Semantics, Allyn and Bacon, Inc., Boston, 1986.
Schmidt, J. Beitrage fur Filtertheorie, II. Math. Nachr. 10(1953) 197–232.
Scott, D. Continuous Lattices, Springer-Verlag Lecture Notes in Math. 274 (1972), pp. 97–136.
Smyth, M. B. and Plotkin, G. D. The category-theoretic solution of recursive domain equations, SIAM Journal of Computing 11(1982) 761–783.
Wegner, P. Programming language semantics. In Formal Semantics of Programming Languages, R. Rustin, ed., Prentice-Hall, Englewood Cliffs, N.J., 1972, pp. 149–248.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Melton, A., Schmidt, D.A., Strecker, G.E. (1986). Galois connections and computer science applications. In: Pitt, D., Abramsky, S., Poigné, A., Rydeheard, D. (eds) Category Theory and Computer Programming. Lecture Notes in Computer Science, vol 240. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-17162-2_130
Download citation
DOI: https://doi.org/10.1007/3-540-17162-2_130
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17162-1
Online ISBN: 978-3-540-47213-1
eBook Packages: Springer Book Archive