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From: "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>
Newsgroups: comp.lang.ada
Subject: Re: Seeking for papers about tagged types vs access to subprograms
Date: Sun, 12 May 2013 08:02:16 +0200
Organization: cbb software GmbH
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Date: 2013-05-12T08:02:16+02:00
List-Id: <comp.lang.ada>

On Sat, 11 May 2013 18:51:27 -0400, Robert A Duff wrote:

> "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> writes:
> 
>> The condition is moved to the post-condition. E.g.
>>
>> # require X >= 0.0
>>    function sqrt (X : Float) return Float;
>> # ensure sqrt (X)**2 = X
>>
>> is replaced with
>>
>> # require true
>>    function sqrt (X : Float) return Float;
>> # ensure sqrt (X)**2 = X or else Constraint_Error raised
> 
> It seems to me that this replacement loses information (the info that 
> X is "supposed to be nonnegative").

# ensure
    (X >= 0.0 and then sqrt (X)**2 = X)
or else
    (X < 0.0 and then Constraint_Error raised)

> For example, a body of sqrt that says "return X / 0.0;" obeys the second
> contract but not the first above.  But that's obviously wrong to anyone
> who thinks that "sqrt" means "approximate square root of X".

As "approximate square root" any implementation is OK. A more realistic
contract that defines accuracy of the result could be like:

   sqrt (X)**2 in Float'Max (0.0, X'Pred)..Float'Min (Float'Last, X'Succ)

[It was just an illustration of the idea how preconditions of operations
are relaxed.]
 
> (Never mind the accuracy issues -- sqrt(X) might not be representable as
> a Float. ;-) )

No, because sqrt(X) < X, if X > 0.

But considering mathematical sqrt, yes, it is not even complex-valued. sqrt
is a multi-valued complex function. If we are lucky one value of sqrt(X)
might have zero imaginary part.

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