Re: The wisdom of the object mentors (Was: Searching OO Associations with RDBMS Persistence Models)
Date: Thu, 1 Jun 2006 22:57:25 +0200
Message-ID: <6bxw3slwltut.1hp76mukduj5i$.dlg_at_40tude.net>
On 1 Jun 2006 13:07:49 -0700, Mikito Harakiri wrote:
>> Operations on functions (subprograms):
>
> These are easily defined in the realtional world (where we consider a
> function as a relation)
>
>> 1. Mapping (call to) the tuple of arguments to the tuple of results >> >> Map : f x x1 x x2 x ... x xN -> y1 x y2 x ... x yN
>
> Calling a function f(x,y) with two arguments x=1 and y=2 is relational
> join of three relations:
>
> 'z=f(x,y)' /\ `x=1` /\ `y=2`
>
> projected to attribute z.
Where you get z for all possible x and y? Another problem is that this is untyped. You should add some constrains on x and y. You can do it externally, but it should be a function property. The third problem is that you need "=" for all things as well as literals for all things. It is a can of worms. Especially function literals aren't easy. What is a literal of sine?
>> 2. Composition: >> >> o : f1 x f2 -> f1 (f2 (x))
>
> Composition of y=f(x) and z=g(y) is relational join
>
> 'y=f(x)' /\ 'z=g(y)'
>
> projected to attributes x and z.
Same problem as before.
>> 3. Comparison >> >> = : f1 x f2 -> Boolean
>
> Comparison is the symmetric difference of the two relations. It is a
> relation, not boolena value. Empty result means that the relations are
> identical.
This is non-constructive. Are you going to compare all inputs and outputs? Even if they model uncountable sets?
>> 4. Copy (for marshaling, closures etc) >> >> := : f -> f
>
> Copying is not a logical operation.
It is. You should consider the computational state as an additional parameter:
":=" : f x S -> f x S
> Yet it corresponds to a trivial
> relational query that outputs the same relation.
>
>> 5. Convolution >> >> * : f1 x f2 x sum x prod x inv -> sum (prod (f(x), g(inv (x)))
>
> In your description I don't see how convolution is different from
> composition.
You have some free arguments and some bound arguments. Bound arguments run through some set. It can be specified through relations, of course. Anything can be.
>> 6. Extension >> >> and so on
>
> What is extension?
This is when you add some prologue and/or epilogue to a subprogram. It is especially important in generic programming and for things like constructors and destructors. In general, when you want to enforce some semantics on the resulting function.
>>>> But that is rather trivial and uninteresting. >>> >>> Well, it's hardly trivial for numbers, why it suddenly becomes trivial >>> for functions? >> >> Because in this particular case function is a value and values are outside >> the language scope. Somewhere in the application domain exists 2. So there >> does sine. You don't care what they are. You only need some object to >> represent them. Let the bit pattern 0x1 represent 2 and 0x2 do sine. End of >> story.
>
> I don't understand this gibberish.
Would "sin" be better?
>> Don't you see any difference between mathematical constructs and >> programming language objects?
>
> Yes. Programming language objects are bastardized counterparts of
> mathematical constructs.
Right. The problem is that mathematical constructs modeled in a computational framework might be too large for any finite state machine. So an uncountable set of real numbers is replaced by a finite set of intervals. That's the gibberish in which I am talking. We can't have all the table of real-valued functions. The size of this table is aleph-2! Where you find a hard disk of this size? Fortunately, from all this table, today, I need only sine. So I say let sine be denoted as 0x2.
-- Regards, Dmitry A. Kazakov http://www.dmitry-kazakov.deReceived on Thu Jun 01 2006 - 22:57:25 CEST