Re: The wisdom of the object mentors (Was: Searching OO Associations with RDBMS Persistence Models)

Dmitry A. Kazakov 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.

> 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.

> 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.

> 4. Copy (for marshaling, closures etc)
>
> := : f -> f

Copying is not a logical operation. 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.

> 6. Extension
>
> and so on

What is extension?

> >> 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.

> Don't you see any difference between mathematical constructs and
> programming language objects?

Yes. Programming language objects are bastardized counterparts of mathematical constructs. Received on Thu Jun 01 2006 - 15:07:49 CDT