« Bracha on Monkey Patching | Main | A located lambda calculus »


It's customary to indicate the end of a proof with a little square (a "tombstone"), with "Q.E.D.," or elsewise. These marks almost never seem helpful to me, but there are other points where significant proof obligations are discharge, and I wish these were marked.

One instance is the end of a case, in a proof by cases. Each of these is a major branch of the proof, which dead-ends in the middle. Variables may be brought into scope, which evaporate when the case is completed, so it's important to know the bounds of that case.

My contribution, then, to the technique of proof-by-cases, is to introduce the marker "huzzah!" indicating the simple end of a case as well as one's excitement at having proven something—a miminal proof-unit, perhaps. Here it is in a screenshot:

Having trouble achieving this effect yourself? Here's a TeX macro:


Update: According to Wikipedia, "Paul Sally at the University of Chicago is known for ending proofs with a pirate face symbol." This doesn't seem to be true of the couple of books coauthored by Sally that I could get through Google Books.


Now, that's an inspiring idea. I would be motivated to complete the proof just for that... one... last... huzzah!. ;)

P.S. We could then add another usage category to Wikipedia's Huzzah!

Ay, one needs motivation. I daresay proving in Coq has led me to feel I'm playing a video game. Bob Atkey said that "Proof Completed" is more like "Level Completed." Perhaps "huzzah" would be more relevant.

In fact, I've wanted the same thing in Coq: an assertion that I've completed a case, so that it won't try applying the following tactics to the present case, if the case were not actually proven.

For amusement, try searching for "huzzah" and "huzza" at dictary.

Seems our use is already as good as those in the "Gaming" section on Wikipedia.

I felt the same way with Coq, though I've only gone through the POPL tutorial. It's rather anti-climactic when you resolve a cases in an inductive proof.

Old post, but I have a copy of Sally's book in which the pirate symbol is indeed used. Of course, the man does have an eye patch and he smokes a pipe.

Post a comment