You are to collect yourselves into groups (already done) and have each
group pick an example property to prove via structural induction (from
the list mentioned in class today, except for #1, which we already did).
Next week, you will make presentations of the proofs, with each member 
of each group taking part of the presentation.


It is desirable, but not required, that the groups do different
proofs. If any group finds their proof too easy, they are welcome to
show off with a "stunt proof" involving a different set of axioms, but
_ONLY_ after everyone in the group is really confident about the basic
proof (see my note below about educating each other).

Each group should meet before lab to make a basic plan for how they'll
do the proof; this would be a good time to come up with axioms for any
terms used in the statement of the property (such as "mirror_image" or
"balanced").

During lab on Friday, each group should put together the outline of
their proof, and get into as much detail as they can, and start to make
a plan for who will present what.

Over the weekend and following week, you can meet again to organize
the presentation and practice.


Your presentations should be at the "middle level" of formality, where
you go through things in fairly detailed steps, but you don't have to
state exactly which axiom you use for each substitution. HOWEVER, each
person doing a presetation should be ready to tell me which axiom is
involved in any step I ask about (as I did in lecture today when asked
how I got from line 2 to line 3 of my inductive case proof). SO ... it
might be a good idea to write these things out if you aren't really
confident, so you can look back at them if I ask.


It is my hope that this will be much more fun, and at least as valuable
educationally, as making each of you try to do a structural induction
proof on your own. Keep in mind, as you work, that each of you will
need to present/explain part of the proof (e.g. what axioms you
created, the base case and one of the inductive cases; several similar
inductive cases; whatever), and each of you should be preparing to
answer questions that could, in principle, appear on the final exam.

To emphasize the educational aspect of this, and my hopes that you'll
be teaching each other, I'm planning to give one bonus point on the
final exam to every member of each group for which all members get at
least 85% of the points on any structural induction question that might
appear on the final. So you'll benefit from helping your group-mates,
but missing the one bonus point because a friend slips up won't kill
you.