Unit testing Agda code, redux

[pozorvlak]

My post about unit-testing Agda code using elisp was posted to the dependent types subreddit (of which I was previously unaware). There, the commenter stevana pointed out that you could achieve the same effect using the following Agda code:

test1 : 2 + 1 == 3
test1 = refl

test2 : 3 + 0 == 3
test2 = refl

If your test fails, you'll get a compile-time error on that line. Aaaaaaaargh. I do wish someone had told me that before I spent a week mucking about with elisp. Well, that's not quite true - I learned a lot about Emacs, I had some fun writing the code, I learned some things about Agda that I might otherwise not have done, I got some code-review from aaroncrane, and I had a chance to try out using darcs and patch-tag for a collaborative project (the experience, I'm afraid, didn't measure up well against git and GitHub).

What I'd failed to realise, of course, is that the == type constructor describes computable equality: a == b is inhabited if the compiler can compute a proof that a is equal to b. "They both normalise to the same thing" is such a proof, and obviously one that the compiler's smart enough to look for on its own.

Ordinarily, a testcase is better than a compile-time assertion with the same meaning, because you can attach a debugger to a failing test and investigate exactly how your code is broken. This doesn't mean that types are stupid - types draw their power from their ability to summarise many different testcases. But in this case, I don't think there's much reason to prefer our approach to stevena's: the slight increase in concision that agda-test allows is balanced out by its inability to coerce both expressions to the same type, which often means the user has to type a lot more code. Stevena's approach does not suffer from this problem.

This also makes me more positive about dependent typing: if simple testcases can be incorporated into your type-system so easily, then maybe the "types are composable tests" slogan has some truth to it.

But seriously, guys, macros.