Some Quasi-Varieties of Iteration Theories

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. This article appeared in the Proceedings of Mathematical Foundations of Programming Semantics 1993, Lecture Notes in Computer Science, volume 802, 378–409.

• Type: Conference
• Year: 1993
• Where: MFPS
• Authors: Stephen L. Bloom, Zoltán Ésik
• Keywords: General Equational Theory, Laws Defining Iteration, MFPS 1993, Programming Languages, fixed Point