[PL-sem-jr] 9/29 seminar: solving recursive equations

[Dale Vaillancourt]

I've added some references for today's material to the Wiki for those
interested in following up.  Let me know if you run into problems or
questions.

-Dale

On Wed, 28 Sep 2005, Dale Vaillancourt wrote:

> Here is a short abstract of what we will discuss during Thursday's
> seminar.
> -Dale
>
> Recursive equations are a compact formalism for specifying entities such
> as functions, data types, and semantic domains.  We are all (more or less)
> familiar with equations such as these:
>
> (1) f = (lambda (x) (if (zero? x) 1 (* x (f (- x 1)))))
> (2) L = nil + cons(int, L)
> (3) D = [D -> D]
>
> Despite that each equation specifies a different kind of structure (a
> function, a set, and a partially-ordered set), there are common structures
> lurking that explain both the existence of solutions and how to calculate
> them.  These common structures are called complete partial-orders (cpos).
> We will review cpos and how to use them to solve equations like (1) and
> (2).  And more interestingly, we will see that we can actually use cpos to
> solve equations like (3) which *itself* specifies a cpo!
>
>
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