1. Do exercise 2.3.2 of Winskel at the end of Chapter 2, that is prove
   that the function f_b,c in the definition of the denotational
   semantics of while B do C is continuous.

2. Suppose that the domain D has "no infinite ascending chains", that
   is, if d_0 <= d_1 <= d_2 <= is a chain then
       d_n = d_{n+1} = d_{n+2} = ... for some n.
   (Every chain eventually becomes constant.)
   Show that every monotone f : D -> D is continuous

3. Let D be the set of finite and infinite sequences over Sigma :=
   {a,b} with c= the prefix ordering.
   a. Verify that this is a domain
   b. Which of the following functions f:D->D is monotone / continuous?
      (i)   f(s) = s with all a's removed
      (ii)  f(s) = abba if s is finite; f(s) = s if s is infinite
      (iii) f(s) = abbas
      (iv)  f(s) = a if s contains finitely many b's; f(s) = b if s contains infinitely many b's
   c. Compute the least fixed point of the f in (b) that are continuous.

4. Define the "binary sum of domains", that is, given domains D and E, define
   - the set D+E
   - the ordering <= on D+E and prove it is a po
   - a bottom element
   - for (d_i) a chain in D+E the lub of (d_i) and show it is the least upperbound
   - injections inl : D -> D+E and inr : E -> D+E that are continuous.