22.02.2012, 11:20, wren ng thornton w...@freegeek.org:
On 2/22/12 1:45 AM, Miguel Mitrofanov wrote:
However, there is no free ordering on:
{ (a0,b) | b- B } \cup { (a,b0) | a- A }
What? By definition, since, a0= a and b0= b, we have (a0, b0)= (a0, b)
and (a0, b0)= (a0, b0), so,
On 2/22/12 2:20 AM, wren ng thornton wrote:
On 2/22/12 1:45 AM, Miguel Mitrofanov wrote:
However, there is no free ordering on:
{ (a0,b) | b - B } \cup { (a,b0) | a - A }
What? By definition, since, a0 = a and b0 = b, we have (a0, b0)
= (a0,b) and (a0, b0) = (a0, b0), so, (a0, b0) is clearly
On 2/22/12 2:37 AM, Dan Doel wrote:
unless I'm still sketchy on what you mean by domain. I don't think it
matters that we're only considering strict homomorphisms.
I think part of the problem is that there are many different ideas of
what exact properties a domain has. The one I'm most
On 2/21/12 10:44 AM, wren ng thornton wrote:
but domain products do not form domains! In order to
get a product which does form a domain, we'd need to use the smash
product[2] instead. Unfortunately we can't have our cake and eat it too
Bah, I don't know why my wires were crossed yesterday.
On 2/21/12 2:17 AM, Roman Cheplyaka wrote:
* Sebastian Fischerfisc...@nii.ac.jp [2012-02-21 00:28:13+0100]
On Mon, Feb 20, 2012 at 7:42 PM, Roman Cheplyakar...@ro-che.info wrote:
Is there any other interpretation in which the Reader monad obeys the
laws?
If selective strictness (the seq
Ehm... why exactly don't domain products form domains?
On 21 Feb 2012, at 19:44, wren ng thornton wrote:
On 2/21/12 2:17 AM, Roman Cheplyaka wrote:
* Sebastian Fischerfisc...@nii.ac.jp [2012-02-21 00:28:13+0100]
On Mon, Feb 20, 2012 at 7:42 PM, Roman Cheplyakar...@ro-che.info wrote:
Is
On Tue, Feb 21, 2012 at 10:44 AM, wren ng thornton w...@freegeek.org wrote:
That's a similar sort of issue, just about whether undefined ==
(undefined,undefined) or not. If the equality holds then tuples would be
domain products[1], but domain products do not form domains!
...
[1] Also a
On 2/21/12 11:27 AM, MigMit wrote:
Ehm... why exactly don't domain products form domains?
One important property of domains[1] is that they have a unique bottom
element. Given domains A and B, let us denote the domain product as:
(A,B) def= { (a,b) | a - A, b - B }
Which will inherit
On 2/21/12 11:54 AM, Dan Doel wrote:
On Tue, Feb 21, 2012 at 10:44 AM, wren ng thorntonw...@freegeek.org wrote:
That's a similar sort of issue, just about whether undefined ==
(undefined,undefined) or not. If the equality holds then tuples would be
domain products[1], but domain products do
22.02.2012, 09:30, wren ng thornton w...@freegeek.org:
On 2/21/12 11:27 AM, MigMit wrote:
Ehm... why exactly don't domain products form domains?
One important property of domains[1] is that they have a unique bottom
element. Given domains A and B, let us denote the domain product as:
On 2/21/12 11:54 AM, Dan Doel wrote:
You don't have to get rid of bottom entirely (I think). If you make
matches against products irrefutable, then you're again in the
situation of seq being the only thing able to distinguish between _|_
and (_|_, _|_), so we could keep the current
On 2/22/12 1:45 AM, Miguel Mitrofanov wrote:
However, there is no free ordering on:
{ (a0,b) | b- B } \cup { (a,b0) | a- A }
What? By definition, since, a0= a and b0= b, we have (a0, b0)= (a0, b) and (a0,
b0)= (a0, b0), so, (a0, b0) is clearly the bottom of A\times B.
Sorry, the
On Wed, Feb 22, 2012 at 1:40 AM, wren ng thornton w...@freegeek.org wrote:
It's a category-theoretic product, but not for the category of domains. Let
Set be the category of sets and set-theoretic functions. And let pDCPO be
the category of (pointed) domains and their homomorphisms.
The
I just realised that many common monads do not obey the monad laws when
it comes to bottoms.
E.g. for the Reader monad:
undefined = return /= undefined
return () = undefined /= undefined
return () = const undefined /= undefined
return undefined = \x - case x of () - return () /=
On Mon, Feb 20, 2012 at 7:42 PM, Roman Cheplyaka r...@ro-che.info wrote:
Is there any other interpretation in which the Reader monad obeys the
laws?
If selective strictness (the seq combinator) would exclude function
types, the difference between undefined and \_ - undefined could not
* Sebastian Fischer fisc...@nii.ac.jp [2012-02-21 00:28:13+0100]
On Mon, Feb 20, 2012 at 7:42 PM, Roman Cheplyaka r...@ro-che.info wrote:
Is there any other interpretation in which the Reader monad obeys the
laws?
If selective strictness (the seq combinator) would exclude function
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