* David Barbour
`undefined` is not a value in any domain. It isn't a value at all. It's certainly not part of my monad language or algebra. Up to the semantic level of comparing observable and legally defined behaviors, we can have the identity law. That's sufficient for the letter of the law, even if not ideal from Haskell's operational perspective.
First, can we please agree on what kind of semantics we are discussing? In the beginning you are talking about domains, so it sounds like denotational semantics. But then you move to behaviours, and that sounds like operational semantics. If we are talking about the denotational semantics, then we choose a domain and need to map every legal Haskell expression to something in that domain. Now, 'undefined' is certainly a legal Haskell expression. If you don't like exceptions, let's define 'undefined' as (let x = x in x). Hence you need to have some element in your domain corresponding to 'undefined'. -- Roman I. Cheplyaka :: http://ro-che.info/