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From: "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>
Subject: Re: Ada Interfaces and the Liskov Substitution Principle
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Date: Mon, 28 May 2007 13:50:17 +0200
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Date: 2007-05-28T13:50:06+02:00
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On Mon, 28 May 2007 11:52:22 +0200, Georg Bauhaus wrote:

> There is nothing wrong with a mathematically "beautiful"
> and simple solution. But when
> 
> (1) there is a perfectly simple, straight forward, working
>     solution,
> 
> (2) the solution matches the problem specification 1:1,
> 
> (3) the solution is partially incongruent with a mathematical
>     model,
> 
> (4) because of (3), the solution (1)+(2) is discarded,
> 
> there is something wrong.

Nothing is wrong except naive LSP. When understood naively it is
mathematically unsound. The problem of is that it tries to make very strong
statements about sets (of values) as whole rather than individual elements
of.

A mathematical interpretation of naive LSP is:

Any true proposition involving the name of the set T stays true when this
name is substituted by the name of another set S

This is extremely strong. Controversies like Circle-Ellipse are
predictable:

   forall X,Y exists Ellipse with the axis X,Y

"Circle" cannot substitute "Ellipse" in above. All usual ways to save LSP
are about limiting the substitution context and protecting some appearances
of the type from substitution (e.g. contravariance). 

> If I had the money, I'd put up a challange that triggers some
> programming oriented model research (as opposed to research that
> will move the focus of modelling to formal properties of models
> only.)

Difference?

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de