An MDELite Allegory Model

We recently made a connection between UML class diagrams and allegories -- categories that have power set domains. Here's the idea: a natural way to think about tuples in categories is by a domain of tuples. But what we really want in a relational database interpretation is a power set of tuples -- elements of this domain are sets of tuples -- i.e., relational tables. Arrows in this universe map tables-to-tables; this is exactly what relational algebra does.

Below is a UML class diagram that relates persons to the departments that they work in, departments to the divisions in which they reside, and persons with children (who are also persons):

An allegory (category) with power domains is shown below. Arrow traversals are rightSemiJoins. A database that encodes these relationships is shown below:

---column1---

---column2---

Given this, here are some queries (easily transformed into constraints) that one can express. Note how compact they are.

print all persons whose name begins with 'd' or 'p'
```
---two---
```

print all divisions in which don works
```
---three---
```

print all persons that work in the same department as priscila
```
---four---
```

who are the division colleagues of priscila
```
---five---
```

print the children of persons
```
---six---
```

are there children who work in the same department as their parent?
```
---seven---
```

The above program, and the hand-written Java class that implements these arrows is in MELite7/LectureExamples/allegory. The current version of the allegory program is shown below.

Please note that this source, which is in the LectureExamples directory of MDELite7, is a single file with nested classes. Study it in detail -- the main ideas are shown below.

---catdb---	class Department extends common<Department> { ---Department---
class Person extends common<Person> { ---Person---	abstract class common<T extends common> { ---commonT---
class Division extends common<Division> { ---Division---	class childrenOf_parentsOf extends common<childrenOf_parentsOf> { ---CP---
	class employs_worksin extends common<employs_worksin> { ---EW---

A Catalina (MDELite-bootstrapped) specification of this design is:

And a generated version of the above source is here.