[Haskell-cafe] Re: Laws and partial values
jonathanccast at fastmail.fm
Sun Jan 25 13:24:47 EST 2009
On Sun, 2009-01-25 at 10:09 -0800, Conal Elliott wrote:
> 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
> > > On 25 Jan 2009, at 10:08, Daniel Fischer wrote:
> > >
> > > > Am Sonntag, 25. Januar 2009 00:55 schrieb Conal
> > > >>> 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
> > > > computation while
> > > > the other is not.
> > >
> > > Is that a problem when trying to find the least
> > 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?
> Hi Jonathan,
> The discussion so far had mostly been about whether *necessarily*
> () /= _|_, i.e., whether a choice of () == _|_ contradicts domain
We started, I think, with the claim that () as implemented by GHC did in
fact satisfy the monoid laws, because () = _|_. This is false ---
Haskell as it exists does not satisfy that equation. The claim for this
was somewhat over-stated (it's not a law of domain theory that a domain
have two elements --- Haskell 98 even has a bottom-only type!) So we
got the question of whether it is such a law or not. But we started
with the question of whether () in the standard library is a monoid or
not --- with the claim that it is made on the basis of the idea that ()
`should' equal undefined :: (). Apparently on the basis of a belief
that that was the way Haskell works.
> 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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