Type Inheritance and Relational Theory

Chapter 20

Tuple / Relation Variables with Inheritance

Q: What type of inheritance do you hope for from your relations? A: Variable—it depends on how those relations change.

—Tinley Roquot(with apologies to Ambrose Bierce)

We saw in Chapter 15 that scalar values, at least, always have a unique most specific type, even with multiple inheritance. And the same goes for tuple and relation values as well, though once again the details are a little more complicated than they are in the scalar case. Such matters are the principal focus of this chapter.

IM PRESCRIPTION 27: TUPLE / RELATION MOST SPECIFIC TYPES

Let H be a heading defined as follows:

{ <A1,T1> , <A2,T2> , ... , <An,Tn> }

Then:

1. If t is a tuple of type TUPLE H, meaning t shall take the form

   TUPLE { <A1,MST1,v1> , <A2,MST2,v2> , ... , <An,MSTn,vn> }

   where, for all j (j = 1, 2, ..., n), type MSTj is a subtype of type Tj and is the most specific type of value vj, then the most specific type of t shall be

   TUPLE { <A1,MST1> , <A2,MST2> , ... , <An,MSTn> }

2. If r is a relation of type RELATION H, let the body of r consist of tuples t1, t2, ..., tm (m ≥0). Tuple ti (i = 1, 2, ..., m) shall take the form

   TUPLE { <A1,MSTi1,vi1> , <A2,MSTi2,vi2> , ... , <An,MSTin,vin> }

   where, for all j (j = 1, 2, ..., n), type MSTij is a subtype of type Tj and is the most specific type of value vij (note that MSTij is different for different tuples ti, in general). Then the most specific type of r shall be

   RELATION { <A1,MST1> , <A2,MST2> , ... , <An,MSTn> ...