Benja Fallenstein wrote:
Not so fast :-)
Caveat one, there may be useful ways to for functions to implement Show that don't conflict with extensionality (i.e., the property that two functions are equal if they yield the same results for all inputs).
Sure, and I suppose one way to do this is to put the show function for functions into the IO monad -- then you can't inspect the results. But if you want to inspect the result, then I have no idea how to do this.
Caveat two, we generally assume extensionality when reasoning about Haskell, but it's entirely possible to give a semantics for Haskell that doesn't assume extensionality. IMHO, a good answer to the question why functions aren't showable in Haskell needs to explain why we prefer our semantics to be extensional, not say that by god-given fiat, Haskell is extensional, so we can't show functions.
Well, my caveat was that the Haskell designers wanted it this way. So you are essentially rejecting my caveat, rather than creating a new one. :-) -Paul