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Re: Representing Types in the Catalog (was Re: Distributed foreign keys)

From: Paul Vernon <paul.vernon_at_ukk.ibmm.comm>
Date: Tue, 8 Jul 2003 19:50:38 +0100
Message-ID: <bef3uj$1vlg$1@gazette.almaden.ibm.com>


"Bob Badour" <bbadour_at_golden.net> wrote in message news:1_DOa.435$%R5.65300577_at_mantis.golden.net...
> A type declaration comprises possible representations and constraints. One
> can derive the relation literal as a cartesian product of the components of
> a possible representation restricted by the constraints.
>
>
> > So it's both the components and the constraints on them that we need.
>
> Yes, I agree. The question is how best to represent components and how best
> to represent constraints in the catalog.

OK, although I think we are suggesting roughly equivalent representations. I guess I am bundling the components and the constraints into one relational expression. You suggest holding the components separately from the constraints, then if we want a literal, building a single RE by cross producing the components and restricting the result with the constraint. Sounds OK for simple types, but how would you define how two poss reps for a single type equate?

E.g. the boolean type poss rep literal (and, in this case it's defining RE) could look like

VAR Boolean CONST RELATION
{ Boolean Boolean SELF_REF // I *think* we need this self referencing attribute
, Bit_Rep BIT_1
, Eng_String_Rep STRING_5
}
= RELATION { // I ignore the self ref'ed column here..

    TUPLE ( Bit_Rep BIT_1('0'), Eng_String_Rep('False') } , TUPLE ( Bit_Rep BIT_1('1'), Eng_String_Rep('True') } }

If BIT_1 and STRING_5 are noted separately as components of poss reps of Boolean, how do we link 'False' to '0' and 'True' to '1'. In which pos rep's constraint do we make this link?

[snip]
>. That there is an equivalence between pos
> > rep values (none of this where one POINT type has cartesiaon and polar
> > poss reps that cannot be equivalent using RATIONAL numbers).
>
> Possible representation literals won't prevent that.

See above. If a type has more than one poss rep, then the values of those poss reps need to be explicitly linked (in the current scheme by sharing the same tuple in the type literal)

> > We also get to formalise the "THE_" operators (aka. GET & SET) of poss
> > representations, because these just become the relation attributes of the
> > pos rep literal.
>
> The "THE_" operators are already formalized without setting anything. If a
> variable's declared type has a possible representation, P1, with A and B
> components, the "THE_" operator to the left of the assignment operator is
> just a shorthand for another assignment:
>
> THE_A(var1) := "NewAValue";
>
> is a shorthand for
>
> var1 := P1( A := "NewAValue", B := THE_B( var1 ) );

Maybe, but I want to see the P1() function above be cast in purely relational terms. Functions are just shorthand for some <COMPOSE> with a relation literal. In this case, the relation literal for the function is the poss rep literal for the type.

And why don't I like functions? Well it's just that they are one extra concept that (at the level of abstraction for that I'm talking about here) are not needed IMO.

> > Non-canonical representations (i.e. multiple poss rep values mapping to
> one
> > type value) would, I guess, be held in a separate catalog literal that
> maps to
> > the canonical form for the particular poss rep.
>
> Catalog literals seem like a dead end to me. The catalog needs to represent
> the type, and from this representation the dbms can derive a literal as
> necessary.

In my scheme the literal is derived from a relational expression. The ER defines the type. What is it about types that you think cannot be defined by a (set of) REs?

> It does not seem feasible to parameterize catalog literals, but it is easy
> enough to parameterize other representations of a type. Using the
> parameterized representation, the dbms can instantiate a literal when
> provided arguments for the parameters.

Agreed and I suggest "parameterized" REs as such an representation. (Well, OK, I've not yet defined what the basic RE type looks like, never mind parameterized REs, but that's to-do next).

> > All in all, it looks to me like a type system that does have some useful
> > properties, and solves some of the problems that I am (and I think that
> > databases are) interested it.
>
> I am less interested in some of the properties you want, but I agree a
> relation literal can represent the set of values of a possible
> representation easily enough. However, I do not think a relation literal is
> the appropriate way to represent a type in the catalog.

Again, the literal is (most times) derived. From REs such as:

"SELECT i.i as Bound_Lower, j.i as Bound_Upper FROM INTEGERS_0-2^32 i, INTEGERS_0-2^32 j WHERE i.i <= j.i"

> The catalog representation must suffice to derive the appropriate relation
> literal, of course.

Agreed. Including the rule that each poss rep for a type has the same number of values, and has one value per type value.

> > [snip]
> > > I suggest changing the focus from using expressions to define the set of
> > > values as a relational literal to using expressions to describe the
> possible
> > > representations etc.
> >
> > Same thing (if the expressions are non "parameterized")
> >
> > > From a description of the possible representations, one
> > > can derive or generate an expression to define the set of values. A
> > > parameterized type would use a parameterized expression for the possible
> > > representation etc.
> >
> > Sounds reasonable. What we need is the definition of a Relational
> Expression
> > as a data type. What are some plausible possible representations of
> Relational
> > Expressions? Are parameterised REs a super-type of a REs?
>
> Parameterised REs are types with operations that result in REs.

Agreed.

[snip]
> > Agreed. I wonder if <TCLOSE> should be replaced with generalised
> recursion?
>
> TTM has recursion as a relational prescription.

True. Which must therefore be an extension of their algebra (assuming that <TCLOSE> cannot be used to do generalised recursion), unless they say that D does the recursion rather than the algebra. Even more reason to replace <TCLOSE> with generalised recursion.

Regards
Paul Vernon
Business Intelligence, IBM Global Services Received on Tue Jul 08 2003 - 13:50:38 CDT

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