Abstract
All known structures involving a constructively obtainable fixed point (or iteration) operation satisfy the equational laws defining iteration theories. Hence, there seems to be a general equational theory of iteration. This paper provides evidence that there is no general implicational theory of iteration. In particular, the quasi-variety generated by the continuous ordered theories, in which fixed point equations have least solutions, is incomparable with the quasi-variety generated by the pointed iterative theories, in which fixed point equations have unique solutions.
Partially supported by a joint grant from the NSF and the Hungarian Academy of Science
Partially supported by a grant from the National Foundation for Scientific Research of Hungary and a joint grant from the NSF and the Hungarian Academy of Science
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Bloom, S.L., Ésik, Z. (1994). Some quasi-varieties of iteration theories. In: Brookes, S., Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Semantics. MFPS 1993. Lecture Notes in Computer Science, vol 802. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58027-1_19
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DOI: https://doi.org/10.1007/3-540-58027-1_19
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