Homework H3: Refactorings

Due Thursday, October 6th, 8pm

ER diagrams predate UML class diagrams.  They are still popular in the database community.  An typical ER diagram is shown below.  Boxes represent entities and diamonds connect 2 or more boxes to define a relationship among them.  Bubbles are attributes.  So each student has a name and a utid.  A course offering has a title, location, time, and unique#.  Takes is a relationship that pairs a student with a course offering.  (There can be many such pairings -- a student could take many courses, and a course could be taken by many students).  Cardinalities are not relevant for this problem.  One last thing is that relationships, like entities, can have attributes.  In this case, the relationship of (student, course offering) has the grade attribute: the grade that the student received in that course.

Two UML class diagrams were proposed as their meta-models, shown below.

Question: are they equivalent?  To answer this, you need to show a sequence of refactorings (equivalence transformations) that maps diagram (a) to diagram (b). If you can't find such a sequence, then they may not be equivalent.  If the sequence is reversible, then you have shown that the above diagrams are the same.

Be careful in your reasoning.