Re: [Haskell-cafe] is proof by testing possible?

I'm making the same mistake repeatedly. In both my mails there are places where I said (a,b) or (b,a) when I meant (a,a). -- Dan On Mon, Oct 12, 2009 at 11:09 AM, Dan Piponi wrote:

Joe,

...

On Mon, Oct 12, 2009 at 11:03 AM, Joe Fredette wrote: I completely forgot about free theorems! Do you have some links to resources -- I tried learning about them a while ago, but couldn't get a grasp on them... Thanks.

There is Wadler's paper but I do find it tricky: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.38.9875

You can play with the generator here: http://linux.tcs.inf.tu-dresden.de/~voigt/ft/ The results can look unreadable at first, but I find that if I copy them onto paper and do all of the remaining substitutions manually (like I had to do with (a,b) -> (b,a)) you end up with something readable. If you keep doing this you'll get a good intuition for what the free theorem for a type will look like. -- Dan