Laws and partial values (was: [Haskell-cafe] mapM_ -> Monoid.Monad.map)

[Jonathan Cast]

On Sat, 2009-01-24 at 03:08 -0700, Luke Palmer wrote:
> On Sat, Jan 24, 2009 at 2:40 AM, Ryan Ingram <ryani.spam at gmail.com>
> wrote:
>         On Fri, Jan 23, 2009 at 10:49 PM, Thomas Davie
>         <tom.davie at gmail.com> wrote:
>         > Isn't the point of bottom that it's the least defined
>         value.  Someone above
>         > made the assertion that for left identity to hold, _|_
>         `mappend` () must be
>         > _|_.  But, as there is only one value in the Unit type, all
>         values we have
>         > no information about must surely be that value, so this is
>         akin to saying ()
>         > `mappend` () must be (), which our definition gives us.
>         
>         
>         But _|_ is not ().
> 
> Correction: _|_ is not always ().

For example: in Haskell.

Prelude> () `seq` True
True
Prelude> (undefined `asTypeOf` ()) `seq` True
*** Exception: Prelude.undefined

jcc