Dear All, As many of you know, December is the season of two column logic/CS related preprints. The title of mine is: Towards semantics of guarded induction and it is at the bottom of the page http://www.kestrel.edu/HTML/people/pavlovic/ Comments **most** welcome, esp. as I am still a bit in the darkness as to how to present some parts. This is still an extended abstract, but a bit more extended and less abstract than the version some of you have seen before. (Thanks again for the questions that helped me improve it!) With the very best wishes, -- Dusko ============================================================================== Towards semantics of guarded induction by Dusko Pavlovic Abstract. We analyze guarded induction, a coalgebraic method for implementing abstract data types with infinite elements (e.g. various dynamic systems, continuous or discrete). It is widely used not just in computation, but also, tacitly, in many basic constructions of differential calculus. However, while syntactic characterisations abound, only the very first steps towards a formal semantics have been made. A language independent analysis was recently initiated, but just special cases were covered so far. In the present paper, we propose a new approach, based on a somewhat unusual combination of monads and polynomial categories. The first result is what appears to be a precise semantic characterisation of guarded operators on arbitrary final coalgebras.