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From: Niklas Holsti <niklas.holsti@tidorum.invalid>
Newsgroups: comp.lang.ada
Subject: Re: Preventing type extensions
Date: Fri, 24 Sep 2010 16:30:29 +0300
Organization: Tidorum Ltd
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Date: 2010-09-24T16:30:29+03:00
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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. I don't think such 
properties have any role in LSP substitutability, as such properties 
often will be different for the whole set and for a proper subset.

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.

-- 
Niklas Holsti
Tidorum Ltd
niklas holsti tidorum fi
       .      @       .