Datatypes R2 Issue 83

Data Types Issue 83: Discrete and Continuous SET (DSET, QSET)

Introduction

Much angst and arguments about our stance on what a SET is. People know discrete enumerated sets, but they don't think that an interval is also a set, yet, interval of real numbers cannot be enumerated.

Issue

While implementing HL7 abstract data types in Java SIG, we find a use for distinguishing two kinds of sets,

• Discrete Set (DSET<T>) is a SET<T>
• Continuous Set (QSET<T specializes QTY>) is a SET<T>

Here would be SET (I'm copying from Java SIG code)

 SET<T specializes ANY> specializes ANY {
   BL      contains(T element);
   BL      isEmpty();
   BL      nonEmpty();
   BL      contains(SET<T> subset);
   INT     cardinality();
   SET<T>  union(SET<T> otherset);
   SET<T>  except(T element);
   SET<T>  except(SET<T> otherset);
   SET<T>  intersection(SET<T> otherset);
   T       any(); // this is another proposal
 }

Here is DSET in Java only right now:

 public interface DSET<T extends ANY> extends SET<T>, Iterable<T> {
   /** An iterator over this set. This is guaranteed to be an iterator of discrete T values. */
   Iterator<T> iterator();
 }

You see, that iterator does not exist in QSET. Not sure yet how to do this for HL7 abstract.

Now QSET:

 QSET<T specializes QTY> specializes SET<T> {
   QSET<T> union(QSET<T> otherset);
   QSET<T> except(T element);
   QSET<T> except(QSET<T> otherset);
   QSET<T> intersection(QSET<T> otherset);
   IVL<T>  hull();
   IVL<T>  nextTo(T element);
   IVL<T>  nextAfter(T element);
   QSET<T> periodicHull(QSET<T> otherset);
   BL      interleaves(QSET<T> otherset);
 };

Now with this we can assert:

• IVL<T> specializes QSET<T>
• PIVL<T> specializes QSET<T>
• EIVL<T specializes TS> specializes QSET<T>

And we still assert GTS == QSET<TS> (and nothing else.

Discussion

This distinction is not changing any semantics, it only helps clarifying that there are some things you can do with a DSET that you can't do with a QSET. A DSET can be implemented as a plain old naive so called "collection". But a QSET needs more. For QSET we'll have to make another proposal.

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