=Paper=
{{Paper
|id=Vol-2116/paper6
|storemode=property
|title=Visualizing and Analyzing Discrete Sets with a UML and OCL Software Design Tool
|pdfUrl=https://ceur-ws.org/Vol-2116/paper6.pdf
|volume=Vol-2116
|authors=Martin Gogolla,Khanh-Hoang Doan
|dblpUrl=https://dblp.org/rec/conf/diagrams/GogollaD18
}}
==Visualizing and Analyzing Discrete Sets with a UML and OCL Software Design Tool==
https://ceur-ws.org/Vol-2116/paper6.pdf
Visualizing and Analyzing Discrete Sets with a
UML and OCL Software Design Tool
Martin Gogolla and Khanh-Hoang Doan
Computer Science Department, University of Bremen, Bremen, Germany
{gogolla|doankh}@informatik.uni-bremen.de
Abstract. This contribution discusses the visualization of discrete sets.
With diagrams, we realize filtering set elements with particular proper-
ties, study set-theoretic operations, and exhibit set elements and their
internal relationships. These techniques allow software developers to ex-
plore crucial set properties diagramatically.
1 Introduction
Modelling languages like UML (Unified Modeling Language) [5, 2], which in-
cludes the OCL (Object Constraint Language) [7, 1], allow developers to repre-
sent discrete sets of objects with so-called object diagrams. In UML tools, one
can construct and manipulate such object diagrams and with this the underlying
object sets. In the context of our tool USE (Uml-based Specification Environ-
ment)1 , this paper studies set visualization and set property analysis by (a) OCL
queries in order to represent interesting subsets of a given set, (b) graphical rep-
resentation of set theoretic operations like union or intersection, and (c) associ-
ations for representing crucial relationships between set elements.
The rest of this contribution is structured as follows. Section 2 studies OCL
query selection. Section 3 focuses on set-theoretic operations. Section 4 treats
internal relationships in sets determined by derived associations. All presented
options are implemented in USE. Section 5 discusses very few related approaches.
Section 6 ends the paper with concluding remarks and future work.
2 Set Visualization through OCL Queries
Figure 1 presents a set of integers in form of 16 Int objects where each object
has an object identity (in the top of the object rectangle) and a unique attribute
val showing the represented integer. The integers are randomly chosen from the
interval 0..255 and are placed randomly in the object diagram. Such a situa-
tion, where an unknown set has to be traversed, occurs frequently in software
development. Systematic placement of elements will be discussed later. The pur-
pose of the following queries and selections is to explore this integer set and its
properties with diagrams, however considering the basic layout as fixed.
1
https://sourceforge.net/projects/useocl/
Y.Sato and Z.Shams (Eds.), SetVR 2018, pp. 76-83, 2018.
Visualizing and Analyzing Discrete Sets... Gogolla and Doan
Fig. 1. Example set of integers represented with objects.
Figure 2 explains how subsets of the underlying basic set can be investigated with
OCL queries and how the result can again be presented diagrammatically. The
last OCL query selects those integer values which possess neighbors (predecessor
and successor) in the underlying set. The result is presented in the object diagram
through the dark gray objects. In order to understand the result here in the
contribution better, we have indicated in the figure with light gray objects the
non-selected part as well (only dark gray objects are displayed in the tool). The
first two OCL queries in the right part of Fig. 2 show other OCL options, namely
simple retrievals for integers with enumerations (Set{2, 4, 8, 16, 32, 64,
128}) or for prime numbers. Figure 2 demonstrates that in our approach sets
can be selected and presented visually.
3 Set Visualization of Set-Theoretic Operations
Figure 3 shows how set-theoretic operations on the underlying set and its dia-
grammatic representation are achieved interactively. The first OCL query selects
integers divisible by 2, and the second OCL query identifies integers divisible
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Visualizing and Analyzing Discrete Sets... Gogolla and Doan
Fig. 2. Subset selection through an OCL query and its visualization.
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Visualizing and Analyzing Discrete Sets... Gogolla and Doan
Fig. 3. Example for visual representation of set-theoretic operation union.
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Visualizing and Analyzing Discrete Sets... Gogolla and Doan
by 3. The union of these two sets is graphically constructed by (a) clearing the
object diagram (pushing button Hide All in the first OCL window), (b) show-
ing the integers divisible by 2 (pushing button Evaluate with option Show acti-
vated), and (c) adding the integers divisible by 3 (pushing button Evaluate also
with option Show activated in the second OCL window). The result of the dia-
grammatically achieved result can be checked against the third OCL expression
that computes the union by means of a logical disjunction. Analogously, other
set-theoretic operations like intersection or difference can be performed (by ac-
tivating other options like Crop or Hide).
4 Set Visualization through Derived Links
Figure 4 pictures how an internal structure of a set can be used for its diagram-
matic arrangement, and a systematic object placement can be achieved. The
employed internal structure of the set is in this case automatically determined
by a computed, derived association between the set elements. For the previ-
ously used example integer set, the derived association identifies the neighbors
Fig. 4. Example for internal set element structure represented with derived links.
of a given integer, i.e., its predecessor and successor. Of course, other derived
associations could be defined. This derived association divides the previously un-
connected elements into components. In the example, there are six components.
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Visualizing and Analyzing Discrete Sets... Gogolla and Doan
Each single component constitutes a connected subset. Unconnected components
have disjoint predecessors and successors.
Up to now we have considered integer sets. Similar techniques as discussed above
can be applied however to sets of strings. Figure 5 is based on the titles of the
papers at the Diagrams 2016 conference. It shows a weighted word cloud of the
28 words appearing in at least two different titles. In our view such a word cloud
is also a diagrammatic representation of a set of strings. However, we will explore
an alternative representation revealing more information.
Fig. 5. Example for representing a word set (Diagrams 2016) with a word cloud.
Analogously to establishing a structure in a set of integers through its prede-
cessors or successors, one can introduce an internal structure on a string set,
e.g., through the common use of the word in different titles. Figure 6 shows the
28 words (each word appearing in at least two different titles) where a connection
in form of a derived link is established, if the two words have a title in common.
These links now classify the word set basically into four different components:
(1) the top left Spontaneous-Instruction component, (2) the isolated Visual com-
ponent, (3) the top right Perception-Reasoning component, and (4) the bottom
Drawings-Understand component. This internal structure reveals more informa-
tion than the word cloud in that it shows that certain words occur together
in groups of titles. This structure indicates strong and weak connections in the
word set: within one component, words have a strong connection, whereas words
from different components have a weaker connection. These components could
be shown also as a linear or an Euler diagram (see Fig. 72 ).
To understand the shown derived links, the right bottom part of Fig. 6 shows
how the Perception-Clutter-Diagrams triangle (the relation between “Perception”,
“Diagrams” and “Clutter”) from the upper right is built. Here, all words occur
in a single title.
The technical definition for the derived, reflexive association on class Word looks
as follows. A link indicates that the two words have a title in common. The link
goes from a lexicographically lower string (role fst) to a lexicographically higher
string (role lst).
association WordWord between
Word [0..*] role fst -- first
Word [0..*] role lst -- last
derived = self.t.w->select(e | self.WasSet()
end
2
https://www.cs.kent.ac.uk/people/staff/pjr/linear/, http://www.eulerdiagrams.org/inductivecircles.html
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Visualizing and Analyzing Discrete Sets... Gogolla and Doan
Fig. 6. Example for representing a set of words with derived links.
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Visualizing and Analyzing Discrete Sets... Gogolla and Doan
Fig. 7. Representing the word set components as a linear and as an Euler diagram.
5 Related Work
Due to space limitations we only mention very few approaches. In previous own
work [3] we have discussed different options in our tool with emphasis on meta-
models. Here we focus on set representations. The work in [4] discusses linear
diagrams that could be derived from our objects diagrams with components.
The work in [6] also applies UML diagrams focusing on ontology representation.
6 Conclusion
The problem discussed in this contribution has been to offer good diagrammatic
representations for discrete, finite sets. We have shown how to use a software de-
sign tool to represent finite sets with UML object diagrams. Future work includes
finding a general way to determine for a given set crucial internal relationships,
i.e., associations, that can be applied to guide the process leading from the set
to a diagram representing the set and displaying with the diagram layout mean-
ingful relationships between set elements. Furthermore, finding a systematic way
to go from the component representation to linear and Euler diagrams seems to
be promising for string sets. Last but not least, larger case studies and examples
should check the applicability and usefulness of the proposed techniques.
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