Abstract
A number of lattice-theoretic fixed point rules are generalised to category theory and applied to the construction of isomorphisms between list structures.
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R. C. Backhouse, M. Bijsterveld, R. van Geldrop, and J.C.S.P. van der Woude. Category theory as coherently constructive lattice theory. Department of Mathematics and Computing Science, Eindhoven University of Technology. 1995. Working document. Available via world-wide web at http://www.win.tue.nl/win/cs/wp/papers.
R.C. Backhouse and M. Bijsterveld. Category theory as coherently constructive lattice theory: an illustration. Technical report, Department of Computing Science, Eindhoven University of Technology, 1994. Available via world-wide web at http://www.win.tue.nl/win/cs/wp/papers.
H. Bekič. Programming Languages and Their Definition, volume 177 of LNCS. Springer-Verlag, 1984. Selected papers edited by C.B. Jones.
Patrick Cousot and Radhia Cousot. Systematic design of program analysis frameworks. In Conference Record of the Sixth Annual ACM Symposium on Principles of Programming Languages, pages 269–282, San Antonio, Texas, January 1979.
E.W. Dijkstra and C.S. Scholten. Predicate Calculus and Program Semantics. Springer-Verlag, Berlin, 1990.
Maarten M. Fokkinga. Calculate categorically! Formal Aspects of Computing, 4:673–692, 1992.
Peter Freyd. Algebraically complete categories. In G. Rosolini A. Carboni, M.C. Pedicchio, editor, Category Theory, Proceedings, Como 1990, volume 1488 of Lecture Notes in Mathematics, pages 95–104. Springer-Verlag, 1990.
P.J. Freyd and A. Scedrov. Categories, Allegories. North-Holland, 1990.
Claudio A. Hermida and Bart Jacobs. An algebraic view of structural induction. To appear. Conference Proceedings of Computer Science Logic, 1994.
J. Lambek. A fixpoint theorem for complete categories. Mathematische Zeitschrift, 103:151–161, 1968.
J. Lambek. Least fixpoints of endofunctors of cartesian closed categories. Mathematical Structures in Computer Science, 3:229–257, 1993.
J. Lambek and P.J. Scott. Introduction to Higher Order Categorical Logic, volume 7 of Studies in Advanced Mathematics. Cambridge University Press, 1986.
S. Mac Lane. Categories for the Working Mathematician, volume 5 of Graduate Texts in Mathematics. Springer-Verlag, 1971.
D.J. Lehman and M.B. Smyth. Algebraic specification of data types: A synthetic approach. Math. Syst. Theory, 14(2):97–140, 1981.
G. Malcolm. Algebraic data types and program transformation. PhD thesis, Groningen University, 1990.
G. Malcolm. Data structures and program transformation. Science of Computer Programming, 14(2–3):255–280, October 1990.
E.G. Manes and M.A. Arbib. Algebraic Approaches to Program Semantics. Texts and Monographs in Computer Science. Springer-Verlag, Berlin, 1986.
Eindhoven University of Technology Mathematics of Program Construction Group. Fixed point calculus. Information Processing Letters, 53(3):131–136, February 1995.
P. Wadler. Theorems for free! In 4'th Symposium on Functional Programming Languages and Computer Architecture, ACM, London, September 1989.
G. Winskel. The Formal Semantics of Porgramming Languages. MIT Press, 1993.
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Backhouse, R., Bijsterveld, M., van Geldrop, R., van der Woude, J. (1995). Categorical fixed point calculus. In: Pitt, D., Rydeheard, D.E., Johnstone, P. (eds) Category Theory and Computer Science. CTCS 1995. Lecture Notes in Computer Science, vol 953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60164-3_25
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DOI: https://doi.org/10.1007/3-540-60164-3_25
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