On 27 Dec 2007, at 12:20 PM, Achim Schneider wrote:
Jonathan Cast <[EMAIL PROTECTED]> wrote:
On 27 Dec 2007, at 10:44 AM, Achim Schneider wrote:
Wolfgang Jeltsch <[EMAIL PROTECTED]> wrote:
Am Donnerstag, 27. Dezember 2007 16:34 schrieb Cristian Baboi:
I'll have to trust you, because I cannot test it.
let x=(1:x); y=(1:y) in x==y .
I also cannot test this:
let x=(1:x); y=1:1:y in x==y
In these examples, x and y denote the same value but the result of
x == y is _|_ (undefined) in both cases. So (==) is not really
equality in Haskell but a kind of weak equality: If x doesn’t equal
y, x == y is False, but if x equals y, x == y might be True or
undefined.
[1..] == [1..] certainly isn't undefined, it always evaluates to
True,
If something happens, it does eventually happen.
More importantly, we can prove that [1..] == [1..] = _|_, since
[1..] == [1..]
= LUB (n >= 1) [1..n] ++ _|_ == [1..n] ++ _|_
= LUB (n >= 1) _|_
= _|_
As far as I understand
http://www.haskell.org/haskellwiki/Bottom
, only computations which cannot be successful are bottom, not those
that can be successful, but aren't.
Um, no. Haskell has no formal denotational semantics, but everyone
knows what it should be. And _|_ is a polymorphic value in that
domain. _|_ is the denotation of every Haskell expression whose
denotation is _|_.
Kind of idealizing reality, that is.
Confusion of computations vs. reductions
In Haskell, these are the same thing (modulo IO).
and whether time exists or
not is included for free here. Actually, modulo mere words, I accept
both your and my argument as true
Huh?
, but prefer mine.
Preference doesn't come into it. By definition, the denotations of
Haskell functions are monotone continous functions on pointed
complete partial orders.
You _do_ accept that you won't ever see Prelude.undefined in ghci
when evaluating
let x=(1:x); y=(1:y) in x==y
Huh?
, and there won't ever be a False in the chain of &&'s, don't you?
Huh?
The question arises, which value is left from the possible values of
Bool when you take away False and _|_?
Why take away _|_?
And now don't you dare to say that _|_ /= undefined.
undefined is one of many Haskell expressions that has _|_ as a
denotation. It is not a normal form, certainly, but that's ok.
You seem to think that _|_ is defined in terms of operational
semantics. Haskell hasn't got an operational semantics, just a
denotational semantics that implementations must produce an
operational semantics to match with. _|_ is a denotational idea,
defined in terms of partial orders and least upper bounds. An
infinite list is the least upper bound of an infinite set of partial
lists, and the value of any function (such as \x -> x == x) applied
to it is the least upper bound of the values of that function applied
to those partial lists.
By definition.
jcc
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