From: "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>
Subject: Re: Preventing type extensions
Date: Fri, 24 Sep 2010 18:27:46 +0200
Date: 2010-09-24T18:27:44+02:00 [thread overview]
Message-ID: <9d1804mxit9j$.wyo5zgwjxh71.dlg@40tude.net> (raw)
In-Reply-To: 8g3nflFnruU1@mid.individual.net
On Fri, 24 Sep 2010 16:30:29 +0300, Niklas Holsti wrote:
> Dmitry A. Kazakov wrote:
>> On Tue, 21 Sep 2010 19:11:33 +0200, Georg Bauhaus wrote:
>>
>>> On 21.09.10 18:25, Dmitry A. Kazakov wrote:
>>>
>>>> horse /= animal
>>> It will help immensely, I think, at least those of us who do
>>> not do type theory on an every day basis, if we had a glossary
>>> of terms for interpreting expression like "horse /= animal".
>>
>> Gosh, it was no more than just this: if horse is an animal that does not
>> imply they are interchangeable. Compare: "all horses have hoofs" and "all
>> animals have hoofs."
>>
>> is-a /= is
>> member /= set
>>
>> Moreover:
>>
>> is-a /= substitutable (greeting to the LSP!)
>>
>> Compare: "some animals have tentacles" and "some horses have tentacles."
>
> Those are not properties of "horses" and "animals", but properties of
> the *set* of horses and the *set* of animals.
horses is set of horses.
> The property "all horses have hooves" expresses a universal property of
> horses: if X is a horse, then X has hooves. The statement "some horses
> have tentacles" says nothing about any given horse X.
Both are predicates:
forall x in horses, x has hooves
exists x in animals, x has tentacles
[ if you dropped existential quantification, you would not be able to
describe functions returning values ]
--
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de
next prev parent reply other threads:[~2010-09-24 16:27 UTC|newest]
Thread overview: 107+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-09-12 10:18 Preventing type extensions Florian Weimer
2010-09-12 11:59 ` Ludovic Brenta
2010-09-12 12:53 ` Florian Weimer
2010-09-12 21:23 ` Maciej Sobczak
2010-09-13 5:32 ` Florian Weimer
2010-09-13 7:13 ` Dmitry A. Kazakov
2010-09-13 9:19 ` Georg Bauhaus
2010-09-13 9:42 ` Dmitry A. Kazakov
2010-09-13 10:23 ` Niklas Holsti
2010-09-13 12:55 ` Cyrille
2010-09-13 13:55 ` Dmitry A. Kazakov
2010-09-13 21:13 ` J-P. Rosen
2010-09-21 13:57 ` Cyrille
2010-09-21 14:19 ` Dmitry A. Kazakov
2010-09-21 14:44 ` Cyrille
2010-09-21 16:25 ` Dmitry A. Kazakov
2010-09-21 17:11 ` Georg Bauhaus
2010-09-21 18:11 ` Dmitry A. Kazakov
2010-09-23 20:00 ` Simon Wright
2010-09-23 20:49 ` Dmitry A. Kazakov
2010-09-24 9:10 ` Georg Bauhaus
2010-09-24 10:24 ` Dmitry A. Kazakov
2010-09-24 13:30 ` Niklas Holsti
2010-09-24 16:27 ` Dmitry A. Kazakov [this message]
2010-09-24 17:47 ` Niklas Holsti
2010-09-24 19:42 ` Dmitry A. Kazakov
2010-09-21 14:32 ` J-P. Rosen
2010-09-21 15:02 ` Cyrille
2010-09-21 15:26 ` J-P. Rosen
2010-09-21 16:18 ` Cyrille
2010-09-22 8:01 ` J-P. Rosen
2010-09-22 17:28 ` Cyrille
2010-09-22 19:30 ` Ludovic Brenta
2010-09-22 19:51 ` Florian Weimer
2010-09-22 20:14 ` Dmitry A. Kazakov
2010-09-22 20:25 ` Florian Weimer
2010-09-22 20:38 ` Dmitry A. Kazakov
2010-09-22 21:25 ` Vinzent Hoefler
2010-09-22 21:20 ` Georg Bauhaus
2010-09-22 20:16 ` Ludovic Brenta
2010-09-22 20:34 ` Florian Weimer
2010-09-22 22:45 ` Britt Snodgrass
2010-09-23 8:02 ` Ludovic Brenta
2010-09-23 16:51 ` Pascal Obry
2010-09-23 18:37 ` Florian Weimer
2010-09-23 18:55 ` Pascal Obry
2010-09-23 20:28 ` Ludovic Brenta
2010-09-24 9:20 ` Ludovic Brenta
2010-09-24 14:49 ` Simon Wright
2010-09-24 15:09 ` Ludovic Brenta
2010-09-24 16:21 ` Robert A Duff
2010-09-25 7:10 ` Pascal Obry
2010-09-25 12:03 ` Brian Drummond
2010-09-24 8:16 ` J-P. Rosen
2010-09-24 8:39 ` Cyrille
2010-09-24 9:27 ` Cyrille
2010-09-29 16:47 ` J-P. Rosen
2010-09-30 10:08 ` Cyrille
2010-10-05 17:02 ` J-P. Rosen
2010-10-08 7:50 ` Cyrille
2010-10-08 13:58 ` Cyrille
2010-10-08 20:12 ` Dmitry A. Kazakov
2010-10-11 7:57 ` Cyrille
2010-10-11 8:24 ` Dmitry A. Kazakov
2010-10-12 5:23 ` Shark8
2010-10-13 9:06 ` J-P. Rosen
2010-10-13 17:37 ` Cyrille
2010-10-13 18:50 ` Dmitry A. Kazakov
2010-09-21 14:50 ` (see below)
2010-09-21 17:37 ` Cyrille
2010-09-21 19:07 ` (see below)
2010-09-13 13:05 ` Dmitry A. Kazakov
2010-09-13 20:21 ` Niklas Holsti
2010-09-13 21:00 ` Dmitry A. Kazakov
2010-09-13 21:10 ` J-P. Rosen
2010-09-14 12:16 ` Niklas Holsti
2010-09-14 16:46 ` Dmitry A. Kazakov
2010-09-14 18:08 ` Niklas Holsti
2010-09-14 18:32 ` Niklas Holsti
2010-09-15 8:18 ` Dmitry A. Kazakov
2010-09-14 17:04 ` J-P. Rosen
2010-09-13 15:12 ` Securing type extensions (was: Preventing type extensions) Georg Bauhaus
2010-09-13 15:29 ` Securing type extensions Dmitry A. Kazakov
2010-09-13 17:23 ` Simon Wright
2010-09-13 20:22 ` Georg Bauhaus
2010-09-13 20:41 ` Dmitry A. Kazakov
2010-09-14 10:02 ` Georg Bauhaus
2010-09-14 12:22 ` Dmitry A. Kazakov
2010-09-14 21:18 ` Georg Bauhaus
2010-09-15 8:15 ` Dmitry A. Kazakov
2010-09-15 20:47 ` Georg Bauhaus
2010-09-16 7:47 ` Dmitry A. Kazakov
2010-09-16 11:52 ` Georg Bauhaus
2010-09-16 12:45 ` Dmitry A. Kazakov
2010-09-16 20:53 ` Georg Bauhaus
2010-09-16 21:37 ` Dmitry A. Kazakov
2010-09-17 8:45 ` Georg Bauhaus
2010-09-17 9:39 ` Dmitry A. Kazakov
2010-10-05 5:59 ` Randy Brukardt
2010-09-13 18:32 ` Preventing " Florian Weimer
2010-09-13 20:30 ` Dmitry A. Kazakov
2010-09-22 19:41 ` Florian Weimer
2010-09-22 20:34 ` Dmitry A. Kazakov
2010-09-22 21:10 ` Georg Bauhaus
2010-09-17 0:16 ` Shark8
2010-09-17 7:04 ` AdaMagica
2010-09-17 21:05 ` Shark8
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