[Haskell-cafe] Re: Laws and partial values
conal at conal.net
Sun Jan 25 13:09:24 EST 2009
On Sun, Jan 25, 2009 at 9:17 AM, Jonathan Cast <jonathanccast at fastmail.fm>wrote:
> On Sun, 2009-01-25 at 09:04 -0800, Conal Elliott wrote:
> > On Sun, Jan 25, 2009 at 7:11 AM, Jonathan Cast
> > <jonathanccast at fastmail.fm> wrote:
> > On Sun, 2009-01-25 at 10:46 +0100, Thomas Davie wrote:
> > > On 25 Jan 2009, at 10:08, Daniel Fischer wrote:
> > >
> > > > Am Sonntag, 25. Januar 2009 00:55 schrieb Conal Elliott:
> > > >>> It's obvious because () is a defined value, while bottom
> > is not -
> > > >>> per
> > > >>> definitionem.
> > > >>
> > > >> I wonder if this argument is circular.
> > > >>
> > > >> I'm not aware of "defined" and "not defined" as more than
> > informal
> > > >> terms.
> > > >
> > > > They are informal. I could've written one is a terminating
> > > > computation while
> > > > the other is not.
> > >
> > > Is that a problem when trying to find the least defined
> > element of a
> > > set of terminating computations?
> > Yes. If you've got a set of terminating computations, and it
> > has
> > multiple distinct elements, it generally doesn't *have* a
> > least element.
> > The P in CPO stands for Partial.
> > jcc
> > and this concern does not apply to () .
> And? () behaves in exactly the same fashion as every other Haskell data
> type in existence, and in consequence we're having an extended, not
> entirely coherent, discussion of how wonderful it would be if it was a
> quite inconsistent special case instead? Why?
The discussion so far had mostly been about whether *necessarily* () /= _|_,
i.e., whether a choice of () == _|_ contradicts domain theory.
I think you're now switching to a different question (contributing to the
"not entirely coherent" aspect of the discussion): which semantics is
*preferable* for what reasons (merits). On that question, I'm inclined to
agree with you, because I like consistency.
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