On 24/07/12 14:39, Jonas Almström Duregård wrote:
Hi,
I suppose you need to define what commutativity means in the presence of undefined values. For instance if error "0" is different from error "1" then you do not have commutativity. Also nontermination needs to be considered, for instance "(fix $ \x->x) == undefined" typically fails to terminate but "undefined == (fix $ \x->x)" typically yields an error.
Regards, Jonas
In the usual Haskell semantics, all bottoms are considered to be the same. In other words, there is only one. You could implement this by setting undefined to nontermination, and error _ = undefined. In fact, the Haskell report does exactly this. Any error messages you get are only visible in IO land, where anything can happen anyway. So _|_ == x = _|_ holds for (almost) all types, except perhaps for (). Though in practice also undefined == () = undefined. Twan