Re: about inheritance of subtypes and entities (such as constants) related to a type in the same package

["Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>]

On 2018-05-31 11:10 PM, Dan'l Miller wrote:
> On Thursday, May 31, 2018 at 2:59:48 PM UTC-5, Dmitry A. Kazakov wrote:
>> On 2018-05-31 20:53, Dan'l Miller wrote:
>>> On Thursday, May 31, 2018 at 12:37:07 PM UTC-5, Dmitry A. Kazakov wrote:
>>>> On 2018-05-31 04:29 PM, Dan'l Miller wrote:
>>>>> Conversely, subtyping in Ada does none of that type-extension stuff:  no
>>>>>    additional data/cardinality-of-the-members-of-the-set, no additional
>>>>    > routines/behavior, no arbitrary refinement of behavior of overridden/copied
>>>>>    routines/operations.  Instead, subtyping in Ada is strictly subjecting the
>>>>>    parent type to an additional membership-narrowing predicate, such as subset
>>>>    > in set theory.  Randy likewise spoke of membership on other branches of this
>>>>    > thread.
>>>>
>>>> Untrue. Ada 83 subtyping extends the supertype (base type), because it
>>>> exports operations defined on the subtype to the base type. Ada 83
>>>> subtyping introduces an equivalent type, which is both sub- and
>>>> supertype of the base.
>>>
>>> If Ada83 untagged subtyping is type extension, please provide even a single characteristic that was extended/added/supplemented instead of contracted/subtracted/elided by the predicate.
>>
>> Elementary:
>>
>>      subtype Extension is Integer;
>>      procedure Extended_Operation (X : Extension) is null;
>>      X : Integer;
>>      Y : Extension;
>> begin
>>      Extended_Operation (X); -- See #1
>>      Extended_Operation (Y); -- See #2
> 
> There is exactly one procedure Extended_Operation, which despite its cleverly-deceptive name is not a demonstration of type extension:  We start with having a single procedure that takes X as a parameter and that is precisely where we end:  no new procedure for Y, no additional storage for Y beyond Y's Xness, no new outcome in the execution of that procedure when passed a Y (except enforcement of the [unfortunately-missing] predicate as a post-condition).

Interface was extended. Implementation details as to how many bodies 
there will be used are irrelevant.

> Or in fewer words:  nothing about Y is X-plus-more.  There is no "more" there.
> (not even a predicate to enforce, which would have made this example a tad juicier).
> 
>> The subtype Extension extends Integer with Extended_Operation, which has
>> two separate meanings:
>>
>> 1. The base type Integer has now a new operation:
>>
>>      new Integer interface = old Integer interface + Extended_Operation
>>
>> 2. The subtype Extension extends inherited Integer's set of operations:
>>
>>      Extended interface = old Integer interface + Extended_Operation
> 
> Invoking the same subprogram

Same to what? The interface of Integer as defined by the standard does 
not have Extended_Operation. How is it same?

> Y merely copied some characteristics (but not others, depending on the would-be predicate) from a prior exemplar named X.

You seems confuse:

1. a type with a set of values. Type = set of values + operations. 
Extension of a type, logically, is about adding something to any of these.

2. an extension of a type with a tagged record extension. A record 
extension is an extension but the reverse is wrong.

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