Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T00:31:48.778Z Has data issue: false hasContentIssue false
  • English
  • Français

Fixed Points as Equations and Solutions

Published online by Cambridge University Press:  20 November 2018

Jiří Adámek  and
Wolfgang Merzenich
Jiří Adámek
Affiliation:
Technical University Prague, Praha, Czechoslovakia
Wolfgang Merzenich
Affiliation:
Universität Dortmund, Dortmund, Germany
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In the literature about the definition of data types there exist many approaches using some concept of fixed point. Wand [13] and Lehmann, Smyth [9] e.g. constructed data types as least fixed points of functors F:K → K. Arbib and Manes [3] showed that some data types turn out to be the greatest fixed points of such endofunctors. In this paper we regard least and greatest fixed points that have a given property.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 36 , Issue 3 , 01 June 1984 , pp. 495 - 519
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Adámek, J., Free algebras and automata realization in the language of categories, Comment. Math. Univ. Carolinae 75 (1974), 589–602.Google Scholar
2. Arbib, M. A. and Manes, E. G., Machines in a category, SIAM Rev. 16 (1974), 136–192.Google Scholar
3. Arbib, M. A. and Manes, E. G., The greatest fixpoint approach to data types, Proc. of 3rd workshop: Categorical and Algebraic Methods in Computer Science and System Theory, Forschungsbericht 113, Universitàt Dortmund, (1980), 2–12.Google Scholar
4. Barr, M., Coequalizers and free triples, Math. Zeit. 116 (1970), 307–322.Google Scholar
5. Herrlich, H. and Strecker, G., Category theory (Alleyn and Bacon, Boston, 1973).Google Scholar
6. Koubek, V., Set functors, Comment. Math. Univ. Carolinae 12 (1971), 175–195.Google Scholar
7. Kůrková-Pohlová, V. and Koubek, V., When a generalized algebraic category is monadic, Comment. Math. Univ. Carolinae 15 (1975), 577–587.Google Scholar
8. Koubek, V. and Reiterman, J., Categorical constructions of free algebras, colimits and completions of partial algebras, J. of Pure and Appl. Algebra 14 (1979), 195–231.Google Scholar
9. Lehmann, D. and Smyth, M. B., Data types, Univ. of Warwick, Theory of Comp. Rep. 19 (1977).Google Scholar
10. Manes, E. G., Free algebraic theories, Proceedings of Universal algebra (Esztergom, North-Holland Verlag, 1977), 507–513.Google Scholar
11. Merzenich, W., Allgemeine Operatornetze als Fixpunktgleichungen, Forschungsbericht 97, Universitàt Dortmund, (1980).Google Scholar
12. Trnková, V., Adámek, J., Koubek, V. and Reiterman, J., Free algebras, input processes and free monads, Comment. Math. Univ. Carolinae 16 (1975), 339–351.Google Scholar
13. Wand, M., Fixed point constructions in order enriched categories, Th. Comp. Sci. 8 (1979), 13–30.Google Scholar