Re: Using the RM for ADTs

On 2 juil, 11:28, David BL <davi..._at_iinet.net.au> wrote:
> Consider a requirement to record electronic circuits in a relational
> database. Circuits are abstract mathematical objects (i.e. "values")
> independent of physical layout. There is no requirement to label
> individual components (e.g. all 1 ohm resistors are
> indistinguishable), nor any requirement to label circuit nodes.
>
> The reason for recording circuit values in a physical database is
> outside the scope of this discussion.
>
> Two circuits are equivalent if they are isomorphic. A model for a
> circuit value must define exactly when circuits are identical. Failure
> to do so would mean for example that a set of circuit values is ill-
> defined (e.g. one cannot determine the cardinality of the set).
>
> In principle a very large circuit can consist of thousands of
> components, wired up in a complex network. Recursive types cannot
> eliminate the need for abstract identifiers.
>
> One approach is to use abstract identifiers for the circuit nodes, and
> use relations such as:
>
>     resistor(N1,N2,R) :- there is a resistor of value R
>         connected between nodes N1,N2.
>
> This raises the question of whether the following symmetry
>
>         resistor(N1,N2,R) <=> resistor(N2,N1,R)
>
> should be an integrity constraint. If so then in the logical model
> information is represented twice and it complicates updates. If not
> then there are potential surprises when using the relation.  Do we
> take the union of the resistors connected from N1 to N2, and N2 to
> N1?
>
> Two or more resistors connected in parallel between a given pair of
> nodes are always equivalent to some single resistor value, so in
> theory we could make {N1,N2} the key.  If we want to model resistors
> in parallel then even if the key is {N1,N2,R} there cannot be multiple
> resistors of the same value.  To model that we could instead use:
>
>     resistor'(N1,N2,R,M) :- there are M resistors
>         of value R connected (in parallel) between
>         nodes N1,N2.
>
> I find it curious that we would only tend to record the tuples where
> M>0.  Normally under a closed world assumption one expects the set of
> tuples for a given relation to be uniquely defined.  However in this
> case, under CWA, a tuple with M=0 can be removed without changing the
> circuit value.  Note as well that a similar issue would occur in the
> relation
>
>     resistor''(N1,N2,C) :- there is a resistor with
>        conductance C (in siemens) connected between
>        nodes N1,N2.
>
> because resistors with zero conductance are equivalent to no resistor
> at all. I find this interesting because it complicates the definition
> of circuit identity. One could apply the integrity constraint C>0,
> however that somehow seems artificial in a logical model, and more
> like a rule an implementation would impose.
>
> I'd like to know whether circuit identity can be implicit in the
> database schema by treating abstract identifiers specially. If there's
> still ambiguity in the model then a comparison operator must be
> separately and explicitly defined. Is that acceptable given that
> C.Date says the relations *are* the logical model?
>
> Tuples have a well defined definition of equality (they must have the
> same attribute names and values), and so also for relations which are
> sets of tuples.  One can't mess with these definitions! It follows
> that a tuple with relation valued attributes cannot really be used to
> define a possrep for a circuit if it fails to define logical
> equivalence as we would like. The missing concept seems to be
> encapsulation in the sense used for an ADT defined in terms of a
> private implementation.

The definition of an entity relation according to its properties or to a specific context is not a relational definition. Received on Thu Jul 02 2009 - 12:58:17 CEST