Hi
I dont understand all this 'confusion'.
Example: monotonically increasing
( 1) should be #f or error, there is no increase, hence no comparison.
Logically, how can you ask:
- What is the difference? ()
- What is the difference between a frog? ( frog)
Neither of those make any sense.
On Oct 21, 2008, at 8:03 AM, Ken Dickey wrote:
Doesn't it make more sense to require existence for comparison?
Existence of one ordered pair does not matter much. You need
to either prove the existence of a counter example to produce
#f, or to prove universality (e.g., with for-all) to
On Tuesday 21 October 2008 05:03:07 Ken Dickey wrote:
1 * x = 1
Apologies. That should certainly be
1 * x = x
RWIM [Read What I Mean]
-KenD
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On Tuesday 21 October 2008 07:42:48 Abdulaziz Ghuloum wrote:
On Oct 21, 2008, at 8:03 AM, Ken Dickey wrote:
Doesn't it make more sense to require existence for comparison?
Existence of one ordered pair does not matter much. You need
to either prove the existence of a counter example to
On Oct 21, 2008, at 11:04 AM, Ken Dickey wrote:
No. Actually, I'd like a holds-for-all which returns #f as the
base case.
You can push it down, but you can't escape making these
exceptions.
Nonrecursive definitions:
for-all p? [a_i, ...] = (and (p? a_i) ...)
holds-for-all p? [] = #f
On Tuesday 21 October 2008 08:32:12 Abdulaziz Ghuloum wrote:
On Oct 21, 2008, at 11:04 AM, Ken Dickey wrote:
No. Actually, I'd like a holds-for-all which returns #f as the
base case.
You can push it down, but you can't escape making these
exceptions.
The law of the excluded third has a
Ken Dickey wrote:
Comparison is taught in kindergarden. Comparison is fundamental.
And in algebra. Things I didn't see taught in high school
were definitions for relation, transitive relation, reflexive
relation, symmetric relation, partial order, total order,
and equivalence along with
Thomas Lord scripsit:
For example, you know that if you raise a total
ordering of characters to a lexical ordering of strings that the
resulting lexical order is a total order.
Though not necessarily the correct total order.
--
By Elbereth and Luthien the Fair, you shall [EMAIL
Ken Dickey wrote:
On Tuesday 21 October 2008 08:32:12 Abdulaziz Ghuloum wrote:
On Oct 21, 2008, at 11:04 AM, Ken Dickey wrote:
No. Actually, I'd like a holds-for-all which returns #f as the
base case.
You can push it down, but you can't escape making these
exceptions.
John Cowan wrote:
Thomas Lord scripsit:
For example, you know that if you raise a total
ordering of characters to a lexical ordering of strings that the
resulting lexical order is a total order.
Though not necessarily the correct total order.
Yes, well, that's a whole other
On Tuesday 21 October 2008 12:53:32 Thomas Lord wrote:
Ken Dickey wrote:
Comparison is taught in kindergarden. Comparison is fundamental.
And in algebra. Things I didn't see taught in high school
were definitions for relation, transitive relation, reflexive
relation, symmetric relation,
On Tuesday 21 October 2008 12:53:32 Thomas Lord wrote:
Ken Dickey wrote:
Can't we just use comparison predicates to compare quantities?
A set of binary predicates makes sense to me.
The way the word is usually used, the consequent of the conditional
should return #t. (You're defining
Ken Dickey wrote:
I know (=) = #t looks normal _to you_. But I believe that you are a
specialist and I think that you are trying to inject a particular logic into
a basic literacy kind of usage.
Sorry to disturb an otherwise interesting discussion, but isn't all of
this much easier to
On Tuesday 21 October 2008 14:01:16 Egil Kvaleberg wrote:
Ken Dickey wrote:
I know (=) = #t looks normal _to you_. But I believe that you are a
specialist and I think that you are trying to inject a particular logic
into a basic literacy kind of usage.
Sorry to disturb an otherwise
John Cowan wrote:
Thomas Lord scripsit:
Asked to compute (= +inf.0 +inf.0) Scheme should dynamically raise
the question: Well, what do you mean exactly?
Why dynamically? Why isn't static override (i.e. replacing = with a
predicate that does what you want) good enough?
On Tuesday 21 October 2008 14:57:19 you wrote:
should read:
Ken's definition = a singleton or empty list is _not_ ordered.
And you should be saying monotonic or sorted as well.
Precisely. Something that cannot be compared with cannot be ordered or sorted
so cannot be monotonic
Ken Dickey wrote:
On Tuesday 21 October 2008 14:57:19 you wrote:
should read:
Ken's definition = a singleton or empty list is _not_ ordered.
And you should be saying monotonic or sorted as well.
Precisely. Something that cannot be compared with cannot be ordered or
On Tue, 21 Oct 2008, Ken Dickey wrote:
(sorted? a) = #f
(sorted?) = #f
I suspect that would come as a nasty surprise to a majority of users of such a
predicate.
Andre
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