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From: Julio Mariņo <jmarino_at_fi.upm.es>

Date: Thu, 16 Dec 2010 15:42:10 +0100

On Thu, Dec 16, 2010 at 2:59 PM, Sebastian Fischer

<sebf_at_informatik.uni-kiel.de> wrote:

*> On Thu, 2010-12-16 at 20:22 +0900, Sebastian Fischer wrote:
*

*>> It is an equivalence class of pairs of (multi-)sets for the
*

*>> equivalence relation
*

*>>
*

*>> (A,X) ~ (B,Y) := A \union Y = X \union B
*

*>
*

*> This was incorrect. The correct definition is (writing u for union)
*

*>
*

*> (A,X) ~ (B,Y) := exists S : A u Y u S = X u B u S
*

*>
*

*> As a consequence, if we use sets and not multisets, then every element
*

*> is equivalent to failure. Writing E for empty set:
*

*>
*

*> (A,X) ~ (E,E) because for S = A u X : A u E u S = S = X u E u S
*

*>
*

*> So, for this construction to be useful, one should consider
*

*> multiplicities of results such that (a ? a) is different from a.
*

*>
*

*> We can also show that every element equals failure if (?) is idempotent
*

*> using the laws:
*

*>
*

*> a = a ? failure
*

*> = a ? (a ? anti a)
*

*> = (a ? a) ? anti a
*

*> = a ? anti a
*

*> = failure
*

Hmmm, that looks different from the typical constructive negation

interpretation... negation would subtract a given amount of copies of

positive results...

7 ? 7 ? inv 7 = 7 = 7 ? inv 7 ? 7

IMHO this makes it more interesting mathematically, but less

attractive as a programming tool.

Julio

*> Sebastian
*

*>
*

*> _______________________________________________
*

*> curry mailing list
*

*> curry_at_lists.RWTH-Aachen.DE
*

*> http://MailMan.RWTH-Aachen.DE/mailman/listinfo/curry
*

*>
*

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Received on Thu Dec 16 2010 - 16:50:47 CET

Date: Thu, 16 Dec 2010 15:42:10 +0100

On Thu, Dec 16, 2010 at 2:59 PM, Sebastian Fischer

<sebf_at_informatik.uni-kiel.de> wrote:

Hmmm, that looks different from the typical constructive negation

interpretation... negation would subtract a given amount of copies of

positive results...

7 ? 7 ? inv 7 = 7 = 7 ? inv 7 ? 7

IMHO this makes it more interesting mathematically, but less

attractive as a programming tool.

Julio

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Received on Thu Dec 16 2010 - 16:50:47 CET

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