On Mon, Jan 4, 2010 at 4:15 PM, Paul Brauner
I wonder why this isn't some "classic" category theory result (maybe it is ?)
It doesn't hold in category theory in general. Haskell (or at least a certain subset) is special - many things that just *look* category theoretical turn out to actually *be* category theoretical. That's quite a strong statement. So, for example, functions that have the type signature of a natural transformation are in fact natural transformations (which tells you non-trivial facts about the function). And you've found that things that are only half-defined functors are actually full-blown functors (subject to someone providing a rigorous proof of this...). This is useful. If you're using QuickCheck to convince yourself you've implemented a functor correctly, you only need to test it on id. -- Dan