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
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