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.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.