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From: "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>
Newsgroups: comp.lang.ada
Subject: Re: Subtypes and type invariants in Ada2012
Date: Mon, 21 Aug 2017 18:52:16 +0200
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Xref: news.eternal-september.org comp.lang.ada:47770
Date: 2017-08-21T18:52:16+02:00
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On 2017-08-21 18:29, Victor Porton wrote:
> Dmitry A. Kazakov wrote:
> 
>> On 2017-08-21 17:38, Victor Porton wrote:
>>
>>> So, my question: Is it possible to restrict a subtype with something like
>>> a type invariant?
>>
>> Type invariant is not a restriction of public interface/properties, it
>> is an implementation detail. So it should never produce a [sub]type.
>>
>>> I want a subtype restricted by an arbitrary condition. Is it possible?
>>
>> Arbitrary condition breaks type operations. E.g. condition Is_Prime (X)
>> breaks more or less everything (assuming covariance). All restrictions
>> do. A few don't break much, e.g. range constraints.
> 
> I don't get. What do you mean saying "breaks"?

    Prime + Prime not in Prime

Properties of the set of prime numbers are not ones of the set of 
integer numbers.

> For me the condition Is_Prime added to a subtype of Natural seems quite
> natural.

The new set loses properties of Natural.

    Natural + 1 in Natural

is false for Prime.

> It is quite natural to have a variable which can hold only prime
> numbers. This may appear in some math software.

Subtyping is not about individual values it is about sets of values as a 
whole. Properties of prime numbers require a new type with other 
operations. E.g.

    Prime + Prime return Natural (contra-variant)

Then

    X : Prime := 13;
    Y : Prime := X + 1; -- Type error (not a subtype!)
    Z : Natural := X + 1; -- OK

> I would propose to add public subtype invariants (not only private tagged
> type invariants as now) to Ada2020. Anything particular against this?

It would not make sense.

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