A Glimpse at SETS Automated Reification
[ Back to SETS ]

SETS can be shown to supersede the standard relational database calculus. As a matter of fact, it has been taught to Minho's undergrads, for several years now, as a ``do it by calculation'' alternative to conventional database design.

This alternative is illustrated below by ``animating'' a small subset of SETS which leads naturally to 3NF data models. This animation is carried out in the CAMILA rapid-prototyping environment. The laws included in this prototype are numbered according to the lecture notes (Postscript) of a crash course on SETS technology (UNU/IIST, May 97) which the reader may want to have a look at for many details missing here.

The source code of this naive SETS animator (setsan.cam) can be obtained from J.N. Oliveira. Readers interested in a fully general SETS animator implemented on top of genetic algorithm based term-rewriting should get in touch with F.L. Neves.

A SETS refinement target: the relational database model

A SETS-specification data model is said to be compliant with the relational database model if it is a finitary product of expressions of the following kind:


An example: the PPD ``toy'' production database

Consider the following SETS data model for a ``toy factory'' production database:

The overall formal model is
so that a production tree exists for each equipment which may involve individual components and/or other production sub-trees.

Automatic calculation of a relational implementation of PPD

We start by loading our CAMILA prototype of a susbset of SETS:

[jno@camila-mobile]$ camila setsan.cam

UM-XMETOO version 1.10.DLL.COMM.USERTYPE (aap/pem/cjr/jj  97/02/26 )

First, we check for the laws which have been included in the prototype:

?- laws();
( 96) -- A*1 == A
(101) -- A*(B+C) == (A*B)+(A*C)
(110) -- A->B == (B+1)^A
(124) -- (A+B)->C <= (A->C)*(B->C)
(128) -- A->B->C <= (A->1)*(B->C)
(129) -- A->D*(B->C) <= (A->D)*((A*B)->C)
(130) -- A->B+C <= (A->B)*(A->C)
(134) -- A-seq <= |N->A

Now load the ppd SETS expression:

?- ld(ppd);

We just have to apply the ``step-by-step'' method step, which will re-write this expression while telling us which laws have been applied at each step:

?- step();
Law (124)
Law ( 96)
?- step();
Law (129)
?- step();
Law (101)
?- step();
Law (124)

We stop here because the resulting SETS expression already specifies a 3NF relational data-model - we have obtained 6 tables as a relational implementation of ppd:

component stock-level table C->|N
equipment stock-level table E->|N
component cost table C->$
table storing equipments with no production tree yet E->1
equipment-into-component decomposition table (E*C)->|N
equipment-into-(sub)equipment decomposition table (E*E)->|N


Jose Nuno Oliveira
Wed Jul 9 10:57:06 WET DST 1997