preprint

[Dusko Pavlovic <dusko@kestrel.edu>]

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

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    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.