On Thursday 11 November 2010 12:34:21 pm John Lato wrote:
> I think the only way this would work would be if you consider functions to
> be equal only to themselves, i.e. "x+x" and "2*x" are not equal. That's
> not a trade-off I would be willing to make.

In general, it doesn't even have to be based on a mathematical identity. As
has been stated, this would in general simply break referential transparency.
Are these two functions equal:

f x = k (h x) (h x)
g x = let y = h x in k y y

Presumably, no, if serialize exists (and they may have different performance
characteristics).

You cannot factor out or inline subexpressions or without the difference being
observable (presumably) by serialize.

Yes, exactly. Thanks for this example, because it illustrates better how far-reaching this would be. And it's true not just when these transformations are manually performed, but also when they're performed by the compiler. Haskell without referential transparency simply wouldn't be Haskell any more. And any code that used a pure serialize may or may not work, depending on compiler magic.

Of course, this is presuming that serialize is pure. I suppose it might be possible for a serialize with type "a -> IO ByteString" to just dump stack+heap+whatever. You could use TH+Hint, LLVM, or likewise to get a similar effect now.

John