Re: Storing data and code in a Db with LISP-like interface

From: Dmitry A. Kazakov <mailbox_at_dmitry-kazakov.de>
Date: Sat, 6 May 2006 11:35:56 +0200
Message-ID: <12fmfcmqb8931$.j61vu4c49qt1$.dlg@40tude.net>

On 5 May 2006 15:34:48 -0700, Mikito Harakiri wrote:

> Dmitry A. Kazakov wrote:

>> I am free to consider integers a subtype of rationals regardless their
>> construction (=representation.) Important here is only that integer
>> inherits +, -, * which I wish to reuse as well as the programs written for
>> rationals in terms of these operations.

>
> How does integer "inherits" arithmetic operations? You need a covariant
> return type:
>
> +(rational, rational) returns rational
> +(integer, integer) returns integer

Right, (though inheritance is specific to individual argument/result. You can inherit in one argument and don't in another. I.e. if the result were contravariant it would still be an inherited operation in covariant arguments.)

> But then, you have to redefine arithmetic operations for integers
> anyway.

That depends on what you understand under "redefine." In strict sense each inherited operation is always redefined just because types are different. But for a subtype like integer it can be done automatically using the composition:

Integer."+" ::=

Integer_From_Rational o Rational."+" o Rationals_From_Integers

Because + is closed in integer, Integer_From_Rational will never fail on integer arguments of the composition. I.e. integer is substitutable in rational's +. But direct substitution is a brain damage, what I keep on trying to convince people from both camps.

> So what is the point of inheritance, then?

Modeling is-a: integers might be not rationals, but one might wish to treat them as if they were, to simplify, reuse, generalize things etc.

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

Received on Sat May 06 2006 - 04:35:56 CDT