Entity Modelling

www.entitymodelling.org - entity modelling introduced from first principles - relational database design theory and practice - dependent type theory

Recursive Composition

When the type of a part is identical to the type of the whole then the relationship must be looped around to renter the top after leaving the bottom: . This asserts that every type entity is composed of one or more type entities... each one of which, therefore, is itself composed of one more type entities ... and so on indefinitely.

The implied infinity in this model is a concern which is elaborated by Jonathon Swift for whom the type in question is the type flea:

Big fleas have little fleas,
Upon their backs to bite 'em,
And little fleas have lesser fleas,
and so, ad infinitum.

In fact, if we are to avoid asserting an infinity of parts of parts of parts then we must specify zero, one or more parts within the whole as here: . Further, if we are to avoid asserting an infinity of ever bigger conglomerates as concerned Augustus De Morgan in his rejoinder:

And the great fleas themselves, in turn, have greater fleas to go on,
While these again have greater still, and greater still, and so on
then we must specify that a part is optionally part of some other part as here: .

The example in figure 7 illustrates this looping in action; it is further developed in subsequent sections.

  • a folder is composed of zero, one or more folders and zero, one or more files
Figure 7
Describing the file system of a computer drive.