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From: "G.B." <bauhaus@notmyhomepage.invalid>
Newsgroups: comp.lang.ada
Subject: Re: Ada 2012 Constraints (WRT an Ada IR)
Date: Wed, 14 Dec 2016 12:46:30 +0100
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Xref: news.eternal-september.org comp.lang.ada:32812
Date: 2016-12-14T12:46:30+01:00
List-Id: <comp.lang.ada>

On 13/12/2016 22:11, Dmitry A. Kazakov wrote:
>
> They are not, what was meant would be a predicate, spelled fully:
>
>    forall a > b, a in T, b in T  exist n in N
>    a = b * n + a rem b
>
> It is not a Boolean expression and it cannot be written or evaluated in Ada. Though it is possible to write a program in Ada that would perform calculus on such expressions, e.g. SPARK.

I'm not exactly sure which set you are referring to, and why.
A theory of remainder values is not identical with contracts,
being much more ambitious and being "meta" indeed.

It looks like rewriting something to do with McJones and Stepanov
and `remainder` in predicates only, possibly defining a result set,
where

   b in what you have written may be 0 in "a rem b",
      also negative.
   N, if the natural numbers, is from some other domain.

Whereas I mentioned the example only because they have stated

  // Precondition: a ≥ b > 0

to then show how their `requires(ArchimedianMonoid(T))`
together with this precondition will produce a terminating
algorithm that does what it is supposed to do. Provided that
b > 0, for example.

And that statement of a precondition is something a programmer
can work with in Ada, by deriving from it a Pre aspect for
a contract.