On Sat, 24 Jun 2006, Paul Hudak [EMAIL PROTECTED] wrote:
Hmmm... never tried to write all this down in one place before, but I
think this covers all cases:
A partial list is one that ends in _|_.
A total list is one that ends in [].
A finite list is either partial or total.
Any other list
Stepan Golosunov wrote:
1:_|_ is certainly finite.
And what is length _|_ ?
_|_, of course!! :-)
The point being, length is well-defined only for total lists; it is
undefined for partial lists. But this doesn't mean that a partial list
isn't finite.
What is finite list then?
Is ones =
Paul Hudak wrote:
Actually Brian's intuition is right on target. One way to define an
infinite list is as the limit of an infinite chain of partial lists
(which, in domain theory, is essentially how all elements are defined).
as the answer to Brian Hulley conjecture criticized by myself:
Jerzy Karczmarczuk wrote:
OK, I think that this subject matured enough to rest in peace...
I would have to agree with that, although...
Couldn't an infinite list just be regarded as the maximum element of
the (infinite) set of all finite lists?
Perhaps his intuition is right, but there are
On Fri, 2006-06-23 at 09:38 -0400, Paul Hudak wrote:
. . .
But the limit of a chain IS the maximal element of the set of all
elements comprising the chain, since the LUB, in the case of a chain, is
unique, and thus we don't have to worry about choosing the least
element (i.e. it reduces
--- [EMAIL PROTECTED] wrote:
Jerzy Karczmarczuk wrote:
OK, I think
that this subject matured enough to rest in peace...
I would have to
agree with that, although...
Since the subject is not going to rest, why
not also jump in?
Well, each partial list is finite.
I think quite
a few
Bill Wood wrote:
On Fri, 2006-06-23 at 09:38 -0400, Paul Hudak wrote:
But the limit of a chain IS the maximal element of the set of all
elements comprising the chain, since the LUB, in the case of a chain, is
unique, and thus we don't have to worry about choosing the least
element (i.e. it
[EMAIL PROTECTED] wrote:
Well, each partial list is finite.
I think quite
a few people would agree that a finite list is one ending in []. So 1:_|_
is a partial list, but not a finite one. 1:[] is a finite list.
1:_|_ is certainly finite. In what sense is it not?
That doesn't quite make
--- [EMAIL PROTECTED] wrote:
[EMAIL PROTECTED] wrote:
1:_|_
is certainly finite. In what sense is it not?
I see that point. I have
been using finite as, by convention, equal to total and finite. And so
have others. As always with convention, one can argue. I won't, of course.
Sorry, see my
On Fri, Jun 23, 2006 at 10:57:48AM -0400, Paul Hudak wrote:
[EMAIL PROTECTED] wrote:
Well, each partial list is finite.
I think quite
a few people would agree that a finite list is one ending in []. So 1:_|_
is a partial list, but not a finite one. 1:[] is a finite list.
1:_|_ is
Stepan,
And what is length _|_ ?
_|_
Regards,
Stefan
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Stepan Golosunov wrote:
On Fri, Jun 23, 2006 at 10:57:48AM -0400, Paul Hudak wrote:
[EMAIL PROTECTED] wrote:
I think quite
a few people would agree that a finite list is one ending in []. So 1:_|_
is a partial list, but not a finite one. 1:[] is a finite list.
1:_|_ is certainly finite. In
On Fri, Jun 23, 2006 at 03:30:18PM -0400, Paul Hudak wrote:
Stepan Golosunov wrote:
On Fri, Jun 23, 2006 at 10:57:48AM -0400, Paul Hudak wrote:
[EMAIL PROTECTED] wrote:
I think quite
a few people would agree that a finite list is one ending in []. So 1:_|_
is a partial list, but not a
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