UML class diagram association properties {subsets < Association end > } | {union} | {redefines} - uml

I don't quite understand what {subset} stands for when it comes to the association between class diagrams in UML. I've found this PDF that talks about it on page 4: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.138.5537&rep=rep1&type=pdf.
Here is the diagram & text that you can also find on page 4:
I read this and I'm not 100% about what {subsets < class > } is about.
It says that "The slot representing d will be a subset of the slot representing b. Elements of type B can be inserted into slot b and elements of type D can be inserted into slots b and d."
So, is {subset} some kind of polymorphism ? I think that thorugh "slot" they mean like the argument of a method that is of type B. And because D subsets b that means that D is like the sub-class of b so it can be passed down as "b" in arguments because of Polymorphism.
So the question is :
What is {subsets < class > } exactly, is it representing a sub class ?
On top of that I have other questions:
What are {union}, {redefines < class > }, {nonunique} & {sequence}. What do does stand for ?
Some examples in code would make it easier to understand.

So the question is : What is {subsets < class > } exactly, is it representing a sub class ?
It is not {subsets < class >} but {subsets < property name >}
In the given diagram D is the only visible class specializing B, and if they are no other classes specializing B then all the instances of B are instances of D and then {subset b} is equal to b.
But having at least :
all the instances of B are not necessary instances of D (including of classes specializing D), this is why d only concerns a subset of the instances of B concerned by b.
In your diagram and mine the subsets are not really useful, but there are for instance in case of redefinition e.g. {subsets a, redefines a} {subsets b, redefines b}
What are {union}, {redefines < class > }, {nonunique} & {sequence}
referring to formal/2017-12-05 ยง9.5.4 page 113 and 114 :
union means that the property is a derived union of its subsets.
nonunique: means that there may be duplicates in a multi-valued property. This is the opposite of unique meaning there is no possible duplicates. For instance supposing b is {nonunique} then some instances of B can be present several times in b. If the property is implemented in C++ by a std::set it is {unique}.
sequence means that the property represents an ordered bag, this is a shortcut of {nonunique, ordered}. This is the case of std::vector and std::list in C++.
{redefines < property-name > } (not {redefines < class >}) means that the property redefines an inherited property identified by < property-name >. If in your diagram the {subsets b} is replaced by {redefines b} then the classes C only has the slot (e.g. attribute in C++ etc) d. This is not like having b private so not accessible from C, that really means d is a redefinition of b.

Related

Is "set" the default multiplicity?

Are these two equivalent:
r: A -> B
r: A set -> set B
That is, is set the default multiplicity?
If yes, then I will quibble with the definition of the arrow operator in the Software Abstractions book. The book says on page 55:
The arrow product (or just product) p->q of two relations p and q is
the relation you get by taking every combination of a tuple from p and
a tuple from q and concatenating them.
I interpret that definition to mean the only valid instance for p->q is one that has every possible combination of tuples from p with tuples from q. But that's not right (I think). Any instance containing mappings between p and q is valid. For example, on page 56 is this example,
Name = {(N0), (N1)}
Addr = {(D0), (D1)}
The book says this is a valid relation for Name->Addr
{(N0, D0), (N0, D1), (N1, D0), (N1, D1)}
But that's not the only valid relation, right? For example, this is a valid relation:
{(N0, D0), (N1, D1)}
Is that right?
The declaration r : A->B means r is a subset of A->B. The expression A->B has just one value, which is the cross product of A and B. The declaration results in a set of possible values for r, which would include both the example given in the book that you cite, and the example that you ask about.

Use functions of a class by after including third class

Sorry for the naming of the title because I don't know how to name this situation.
There are three classes A, B and C. Class A need the function of class C. Class B is an instance collection of class C. So the operation should be class A calls the static method of class B to get the instance of class C.
//in class A
Class C = B.getCInstance("[instance name]")
C.doSth();
Then what is the relationship between class A, B and C in UML? When I draw a UML class diagram, should I need to build all of the relationship between A, B and C? for example:
A class A uses a class B.
A class B has A class C.
A class A has A class C.
According the definition of the UML Usage dependency, I would say that class A uses both Class B and C and Class B uses Class C as depicted below
A Usage is a Dependency in which one NamedElement requires another NamedElement (or set of NamedElements) for its full
implementation or operation. The Usage does not specify how the client uses the supplier other than the fact that the supplier is used
by the definition or implementation of the client.

Alloy - Lone instance

I am writing a simple Alloy code but I cannot understand how can I say AT MOST one A has associate with p.D (so AT MOST would be One or Zero). So I wrote the below code but the assertion presents no counter-example with an instance of P1 without D. Could you help me how can I define my fact in terms of having AT MOST one instance for p.D where I can see a counter example that p has no connection for its D.
abstract sig A {}
sig A1,A2,A3 extends A{}
abstract sig P {}
sig P1 extends P {D: A}
fact
{
all p: P1 | lone (p.D & A)
}
assert asr
{no p: P1 | no (p.D & A)}
check asr for 5
Your specification (introduction of sig P1) says that for each p in P1 is always related by d to exactly one a in A. Your fact is redundant ("0 or 1" is implied by "always 1").
You could declare "sig P1 extends P (D : lone A}". (The fact would still be redundant.)
Also note that the "& A"s in your fact and assertion are redundant.
You might have meant the fact to be
fact {lone P1.D}
which says that all those instances of P1 which are related to an A are related to the same A.

Alloy: Int meaning of field

i saw the following Alloy definition:
one sig Number { i:Int[3]}
//what does Int[3] mean. I mean what is the meaning of the above field 'i'
It means i is a relation between the singleton set Number and the singleton subset of Int with the atom 3. In object notation it's like Number.i = 3

About casting and objects

it's simple, i just want a explanation about this:
internal class B { // Base class
}
internal class D : B { // Derived class
}
in other class I wrote:
B b3 = new Object(); //compilation time error!
why??? We suposse that all classes inherit from "object"
B is more specialized than Object, therefore you cannot assign an Object instance to a B reference. This is because not every Object is actually a B - only the opposite is true.
Let's assume that you have a field x in the class B. When you instantiate an Object, no memory is reserved for this field, and if you could assign it to a reference of type B, it would therefore try to read or write to unallocated memory, which is not allowed (or useful).
All classes are objects, but not all objects are {someclass}.
In a similar way, all buses are vehicles, but not all vehicles are buses.

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