1. MetaModeling the core of MDE and modeling in general UML
class diagrams
object diagrams and constraints
metamodeling
examples
MDE
the core of MDE and modeling in general
MetaModeling

2. Today’s Lecture
Recall this slide from the last lecture:

3. Today’s Lecture
Learn the importance of recursion

4. Terminology
model
meta-model
Let 𝑥 be a model and 𝑋 be a metamodel; 𝑥 belongs to the domain of 𝑋 iff
𝑥 is an instance of 𝑋 if objects & refs satisfy the class diagram of 𝑋
and
𝑥 conforms to 𝑋 if 𝑥 satisfies all metamodel constraints of X.
“Conforms to” is a much more difficult constraint to satisfy than “instance of”

5. Examples
A Java program that is syntactically-correct is an instance of a Java Language Metamodel if it is type-correct and it conforms to the Java Language Metamodel
Example: 2 instances and a model – only one instance conforms

6. Perspective Model to Instances
You create a model M:
age of every Employee > min age of department
And now you create instances m1 and m2 that conform to the model M m1 M
both conform. m2 m1 m2

7. Perspective Instances to Model
You have a collection of instances, such as m1 and m2
What is a model M to which m1 and m2 conform?
Called metamodeling m1 m2 M M m1 m2

8. MetaModels
Here are 2 instances of a “graph”, which contains nodes and edges
What is a class diagram of such graphs? n1 n2 g1 n6 n8 n9 g2

9. One Solution Model What is “normalized” database design?
What is a perfectly good Java representation of this meta model? note arrow ends added to meta model
class Node { private String Name;
private Set<Edge> edge; }
class Edge {
private node connects[2];

10. Fundamentals of MetaModeling
RULE: ANY graph can be viewed as an object diagram
Here are 2 instances of another kind of graph or object diagram called a UML Class Diagram
For simplicity, there are no methods and there are any # of attributes, no inheritance relationships
What is a UML class diagram to which these instances conform?

11. Hint... Think Visio Drawing Tool
Each “template” icon on left represents a class of objects
dragging icon onto canvas creates an instance of that class
so there are 2 classes of objects in a UML class diagram that we’re using
Determine attributes of each class
Determine relationships & constraints among classes
Fire up Visio!

12. Step 1. Identify Shapes Given instance:
What are the shapes that you can drag onto a canvas?
they are classes in your metamodel
I see boxes and lines. that’s really all that I see now.
(Of course, they each have attributes, and attributes
are something that will become objects that I can “drag” onto
my design canvas)

13. Step 2. Identify Attributes
Given instance:
What are the shapes that you can drag onto a canvas?
they are classes in your metamodel
I see boxes and lines. that’s really all that I see now.
(Of course, they each have attributes, and attributes
are something that will become objects that I can “drag” onto
my design canvas)

14. Step 3. Identify Associations
Look at model instance:
Here is its metamodel MM 1 3 2

15. Step 4. Beautify (Rename)
Rename elements, add names to roles, etc.
This is almost a metamodel of class diagrams!
what
is missing?

16. Step 5. Add Constraints
Association cardinalities usually turn into constraints
attribute-class: verify an Attribute tuple points to an existing Class tuple
assocEnd-class: verify an AssocEnd tuple points to an existing Class tuple
assocEnd-association: verify every AE points to an existing A tuple
association-assocEnd: every A must have 2 AEs
attribute-class
assocEnd-class
assocEnd-association
association-assocEnd
// every A must have 2 AEs
ErrorReport er = new ErrorReport();
er.printReport(System.out);
no two attributes of a class have the same name
Also no two anchor ends associated to the same class have the same name.
And no anchor end of a class has the same name as an attribute of the class.
association.stream()
.filter(t-> assocEnd.stream().
.filter(x->x.is(“aid”,t.get(“aid”))).count()!=2)
.forEach(t->er.add(t.get(“aid”) +
“ does not have 2 association ends”);

17. Note! Common for a metamodel to be an instance of itself!
model MM conforms to MM
Not an oddity! Requirement for advanced models
make sure that you understand what this slide says!
conforms to
or is an
instance of M M m1 m2

18. Diagram-2-Table Mapping Notes#
Table Attribute/Field
Class c#
name
Attribute
at#
visibility?
attrOf
AssocEnd
ae#
visible?
cardinality
anchoredAt
endOf
Association k#
Table #
Attribute
Class c#
name
at#
visibility?
attrOf
AssocEnd
ae#
visible?
cardinality
anchoredAt
endOf
Association
Table #
Attribute
Class c#
name
AssocEnd
Association
Table #
Attribute
Class
AssocEnd
Association
Table #
Attribute
Class c#
name
at#
visibility?
attrOf
AssocEnd
Association

19. Tabular Representation
Attribute 2
Class 1 a#
name
visibility
attrOf #
Name
Visibility
AttrOf a1
name - cl a2 at a3
visibility? a4 ae a5
visible? a6
cardinality #
Name cl
Class at
Attributes ae
AssociationEnd as
Association c#
name
AssocEnd
Association
ae#
name
vis?
card
anchAt
endof #
name
vis?
card
anchAt
endof
ae1
attrOf - 1 cl k1
ae2
hasAttr * at
ae3
anchoredAt k2
ae4
anchors ae
ae5 as k3
ae6
hasEnd 2 4
Create each table + attributes
Then fill in (as much as possible) Class and Attribute tables
Then AssocEnd and Association Table.
Filling in the attributes then becomes more like a puzzle. # k1 k2 k3 k# 3

20. Your Turn: Entity-Relationship Model precursor to UML Class Diagrams
Entity sets classes are boxes & have unique names
Attributes are bubbles; underlined attributes are keys
Relationships are diamonds with unique names connecting 2 or more boxes
Attributes are associated with only one Entity or one Relationship
Entity set must have 1+ key attribute; Relationships >0 or more attributes

21. A Solution
1st stab at a solution:
Constraints?
Problem:

22. A Solution Not Association Normalized 1st stab at a solution:
Constraints?
Problem:
Constraints (beyond cardinality constraints)
C1. Each Bubble belongs to a Box OR Diamond, but never both
C2. Each Box has at least 1 keyed attribute
C3. Each Diamond has 0+ attributes, 0+ keyed attributes
C4. Each Box has a unique name
C5. Each Diamond has a unique name
C6-7. Bubble names for each box (each diamond) are unique
Not Association Normalized

23. A Solution continued... Normalizing Box-Diamond association yields:
Tables?
Constraints (beyond cardinality constraints)
C1. Each Bubble belongs to a Box OR Diamond, but never both
C2. Each Box has at least 1 keyed attribute
C3. Each Diamond has 0+ attributes, 0+ keyed attributes
C4. Each Box has a unique name
C5. Each Diamond has a unique name
C6-7. Bubble names for each box (each diamond) are unique

24. A Database Diamond Box Bubble BoxDiamond b# name # name e Employee d1 2 b#
name #
name e
Employee d
Department u
University d#
name d#
name wi
worksin
dis
disciplines
Bubble 4
BoxDiamond a#
name
key?
belongsTo a#
name
key?
belongsTo a1
empNo
yes e a2
age no a3
deptName d a4
building a5
phone a6
address u a7 3
bd# e# r#
bd1 e wi
bd2 d
bd3
dis
bd4 u
bd# e# r#