[Haskell-cafe] If you'd design a Haskell-like language, what would you do different?

[Alexander Solla]

On Tue, Dec 20, 2011 at 1:46 AM, Ben Lippmeier <benl at ouroborus.net> wrote:

>
> On 20/12/2011, at 6:06 PM, Roman Cheplyaka wrote:
>
> > * Alexander Solla <alex.solla at gmail.com> [2011-12-19 19:10:32-0800]
> >> * Documentation that discourages thinking about bottom as a 'value'.
>  It's
> >> not a value, and that is what defines it.
> >
> > In denotational semantics, every well-formed term in the language must
> > have a value. So, what is a value of "fix id"?
>
> There isn't one!
>
>
Indeed, that is my point.  "Bottom" is the representation of a computation
which cannot be computed.  It does not have a semantic in anything less
than the first infinite ordinal.  It should be treated as essentially
unique.  It exists as a syntactic construct, but it cannot be given an
interpretation in Haskell.

In particular, we cannot compare "distinct" (or even indistinct) bottoms,
because of the halting problem.  There is no consistent logic in which
(forall x, x = x) does not hold.  Treating bottom the same way we treat 1,
"abc", (Just 10), and the other (in principle) comparable values introduces
contradiction to Haskell, as a logic.  (That is why bottom has the
syntactic symbol _|_, the syntax for /the/ unique contradiction)

Denotational semantics is nice, but it goes way out of the realm of
realistic computation to deal with infinite ordinals just to have a
complete semantic.  (We can't run computations even up to the first
infinite ordinal in real life)

I would rather have an incomplete semantic, and have all the incomplete
parts collapsed into something we call "bottom".  We can then be smart and
stay within a total fragment of the language (where bottom is guaranteed to
not occur).  Or we may have to move into the non-total fragment of the
language for performance reasons.  That's fine, but we shouldn't treat
things like 'seq' as if they produce values.  'seq', 'unsafeCoerce', and
many others are literally compiler magic, and as such, should be used with
extreme care not warranted when dealing with "regular" values.

I have used the phrase "proto-value" for describing these magical objects.
 I just wish the documentation made the distinction between a "proto-value"
and a real value more clear.
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