On the Impossibility to Assure a Finite Software Concepts’ Catalog
Iaakov Exman
a
Software Engineering Dept., The Jerusalem College of Engineering - Azrieli, Jerusalem, Israel
Keywords: Knowledge Discovery, Concepts, Natural Language, Conceptual Integrity, Software Concepts’ Catalog,
Software Systems Theory.
Abstract: In recent times it has been recognized that Concepts play a central role within Software. This has been
expressed by Fred Brooks’ idea that “Conceptual Integrity is the most important consideration for software
system design”. However, concepts as human natural language words with assigned meaning by the Concepts’
relationships, evolve under continual dynamics of concepts discovery. This language dynamics has
consequences that cannot be ignored. This paper illustrates concepts discovery within design patterns, up to
very large-scale systems, highlighting intrinsic shortcomings of Concepts’ semantics as a solid basis for
Software Conceptual Integrity. Paradoxically, these shortcomings are the consequence of the very creative
process of Concepts Discovery from existing knowledge. Finally, one arrives at the paper’s main results: the
absolute Software Concepts freedom of choice, typical of natural languages, implies the impossibility to
assure a finite Software Concepts catalog. One finds oneself in an unending pursue of additional concepts to
achieve some kind of Integrity or completeness. Even deliberate finite catalogs cannot be definitive. But there
is no reason for despair. Finite Software Concepts’ catalogs, despite not definitive, are still very useful.
1 INTRODUCTION
The language of software design is any human natural
language, whose aim is to be understood by humans,
and eventually by Artificially Intelligent robots.
What tells apart the natural language of software
system design from lower levels of programming
languages? The latter usually have restricted and
static numbers of reserved words and syntax, whose
goal is to be actuators of computing machines.
Human live languages, in continual dynamics,
create new words, change and add word meanings,
and turn obsolete other words. This absolute
Concepts’ invention freedom, and naturally evolving
thesaurus, are a software design bonus, but incurs
limitations, the goal of this paper’s investigation.
1.1 Concepts’ Semantics are Part of the
Software Essence
Concepts are words of a human natural language, e.g.,
English, Mandarin Chinese, or Portuguese, with
assigned meaning by the Concepts’ relationships,
which are composable into software concept systems.
a
https://orcid.org/0000-0002-9917-3950
What are fundamental software concepts’ system
properties? Concepts’ semantics are part of the
software essence. But this is not the whole story.
Brooks’ Conceptual Integrity thought as “the
most important consideration for software system
design”, can be implemented from his principles
(Brooks, 2010): propriety – a software system should
have only concepts essential to its purpose and no
more; orthogonality – software system concepts
should be totally independent of one another.
1.2 Concept Discovery as Software
Liveness
Software system design liveness consists in
everlasting concepts discovery/invention, and
creation or modification of concepts relationships.
Concepts discovery refers to mutual concepts
adjustment to achieve Conceptual Integrity for a
given software system.
It also refers to variations of an original system
into a slightly different system. For instance, different
but similar car models have much in common, one for
Exman, I.
On the Impossibility to Assure a Finite Software Concepts’ Catalog.
DOI: 10.5220/0011553400003335
In Proceedings of the 14th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (IC3K 2022) - Volume 1: KDIR, pages 273-280
ISBN: 978-989-758-614-9; ISSN: 2184-3228
Copyright
c
 2022 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
273

regular family usage, and another station-wagon
model, with larger space for luggage.
1.3 Paper’s Focus and Organization
This paper focuses on the Concept discovery extreme
dynamics of natural languages, and how it affects
software semantics.
Section 2 illustrates software design pattern
concepts discovery. Section 3 deals with very large-
scale concepts’ systems. The main theoretical results
are formulated in section 4, the finite and definitive
concepts catalog impossibility theorems. The paper is
concluded with Related Work in Section 5, and a
Discussion in Section 6.
2 SOFTWARE DESIGN PATTERN
CONCEPTS DISCOVERY
Design Patterns are frequently used small software
sub-systems, defined in terms of natural language
concepts, whose purpose is to compose software
systems at the design level.
2.1 Software Design Patterns
Design Patterns are relevant to this paper since they
are abstractions of the small sub-systems they
represent. They are reusable by substituting the
abstractions by actual concepts of the specific
application being built.
The software composition design process is
creative in two senses. One sense is planning an
overall software architecture. The other is naming
specific structures and functions. The concept
discovery naming activity is done either by choice of
existing or modified suitable concepts, or by
inventing new words and/or meanings.
The two design patterns analysed in this section,
illustrate and explain the nature of the concept
discovery process. They were taken from the well-
known Design Patterns GoF book. GoF means “Gang
of Four”, a humorous reference to its four authors
(Gamma et al., 1995).
2.2 The Composite Pattern
Composite is a design pattern – (Gamma et al., 1995)
page 163 – which composes objects into tree graphs
representing part-whole hierarchies. Individual
objects and their composites are treated uniformly
with respect to certain specific operations.
The abstract concepts of the Composite design
pattern are shown in Fig. 1.
Figure 1: Composite Design Pattern: Abstract Concepts –
This pattern is a single Module, whose building blocks are
Components. It contains 2 structure types: A composite and
a leaf. A composite may add/remove components, or get a
child name. Specific operations can be done on any
composite child or on a leaf. (Figures in color online).
A specific example of the Composite Design
Pattern is the FaceComponent shown in Fig. 2. This
is just one application example of the abstract Design
Pattern. Many different applications are possible.
Figure 2: Composite Design Pattern: FaceComponent – It
has 3 “leaves” (Face Contour, Eye and Mouth), and 1
Composite, the FacePicture, composed of 4 children (a Face
Contour circle, one mouth and 2 eyes). The vertical arrow
with a triangle arrowhead means that the 3 leaves and the
Composite inherit FaceComponent functions. Draw is the
specific operation of this Design Pattern. This figure is an
inverted tree with a top root and 3 leaves at the bottom.
This design pattern special idea is that individual
leaves and composites are components, treated in the
same way: one can add any component to an existing
composite. A composite’s children can be leaves and
internal composites. A leaf cannot have children.
The Draw function of the leaves is the same as the
generic composite function ForAllChildrenDoDraw,
assuming the number of children of a leaf to be zero.
A few notes analysing this pattern concepts are:
 Concepts are natural language words – (Face,
Eye, Mouth, Child, Leaf, Draw, Composite, Add,
Remove). But one readily perceives that these are
metaphors: a face in Fig. 2 is not a realistic face.
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 Necessarily the system is incomplete – one can
easily add concepts absent in this example
(moustache, ears, nose, hair, shadows, etc.).
 New concepts are continually created – language
dynamics causes relevant concepts discovery or
invention, e.g., by technology advances.
Some recent examples of newly created concepts
are emoticon – short for "emotion icon", text-based
symbols such as :-) replacing language – and emoji –
a word of Japanese origin with ‘e’ meaning ‘picture’
and ‘moji’ meaning ‘character’ – used for facial
expressions, and to reveal emotions.
2.3 The Observer Pattern
Observer is a design pattern – (Gamma et al., 1995)
page 293 – that formally defines a one-to-many
dependency between objects: when one is changed,
all the others are notified and updated. The abstract
concepts of the Observer design pattern are in Fig. 3.
Figure 3: Observer Design Pattern: Abstract Concepts –
The Observer Pattern is a single Module. It contains two
types of structures: A subject and an observer. A subject
attaches/detaches observers, notify observers that it has
changed, and enables setting/getting its state. Any observer
updates its state according to the current subject state.
A concrete example of the Observer Design Pattern is
a school with different floors, and many classrooms,
each of them with a wall-clock. If a seasons’
transition occurs, from wintertime to summertime for
daylight saving, one has to adjust all classroom clocks
one-by-one. With a central clock linked to all other
school clocks, it would be enough to adjust only the
central clock, as shown in Fig. 4.
Figure 4: Observer Design Pattern: A system of clocks –
The central clock is the subject (of Fig. 3) and the classroom
clocks are the observers. The central clock notifies all the
classroom clocks, which get the Central Clock state and
each one of the classroom clocks updates itself.
The analysis of the Observer Design pattern is
similar to the Composite pattern:
 Concepts are natural language words – (clock,
central, classroom, notify, attach, detach, state,
update).
 Necessarily the system is incomplete – many
possible concepts can be added to such a system
(digital vs. analog clocks, season, summertime,
time-zone, etc.).
 New concepts are continually created – language
dynamics together with technology advances
cause concepts discovery or invention.
Some recent examples of new concepts are UTC
– Coordinated Universal Time, a standard reference
to the British Greenwich Mean Time (GMT), serving
as the offset basis for time-zones – atomic clocks
made of Cesium, the most precise clocks, certainly
not necessary in a secondary school – GPS – Global
Positioning System – a global satellite system, also a
precise source of time and location. A very popular
application for everyday life is a handheld GPS watch
used as a bracelet for sports and fitness. A GPS watch
may also be a smartwatch.
3 VERY LARGE-SCALE SYSTEM
CONCEPTS DISCOVERY
Here we jump up from small-scale modules to Very
Large-Scale Systems, examining concepts discovery.
We begin displaying empirical data on the
significant increase of vocabulary of natural
languages. Then we deal with examples of
astronomic objects and electronic VLSI (Very Large
Scale Integrated) circuits.
3.1 Empirical Data and Graph
A representative snapshot of the dynamics of natural
language is given by data about the English language,
from a paper which analysed a huge quantity of
digitized books (Michel et al., 2011).
The referred paper’s estimate of the number of
words in the English vocabulary along the time axis
is: 544 kilowords in the year 1900, 597 kilowords in
1950 and 1022 kilowords in the year 2000.
These data are shown in Fig. 5. One clearly
perceives an acceleration of the net increase of words
along the years 1950 to 2000.
The referred paper
estimated the English net increase rate of number of
words, eliminating obsolete word spelling and usage,
from 1950 to 2000, as about 8500 words per year.
On the Impossibility to Assure a Finite Software Concepts’ Catalog
275

Figure 5: Number of kilowords in the English vocabulary
along the years (blue dots) and exponential trendline (red).
We have mentioned creative mechanisms causing
natural language vocabulary increase, in section 2.
These mechanisms include technological advances
due to deep scientific theories – e.g., GPS needs
relativistic corrections – mixed with everyday life
activities such as sports and states of mind like
emotions.
In the next sub-sections, we encounter somewhat
different motivations for concepts discovery:
 to make more familiar very large natural
phenomena – stars and galaxies;
 to make sense of a multitude of very small
components, human made by nanotechnologies.
3.2 Astronomical Objects
Referring to astronomical objects in the Universe, one
should pay attention to two facts.
1
st
fact, the estimated number of astronomical
objects is huge. For instance, the estimated number of
galaxies in the Universe is between 2 trillion – e.g.
(Conselice, 2016) – and the more recent and modest
number of 200 billion. The estimated number of stars
per galaxy ranges from a few hundred million (10
8
)
stars to one hundred trillion (10
14
) stars. Multiplying
the number of galaxies by the number of stars one gets
by any estimate a giant number.
2
nd
fact, despite the huge numbers, human beings
throughout the History discovered/invented names
and assigned meanings to astronomical objects:
galaxies, stars, constellations, planets, lunar craters,
asteroids, and whatever; to organize knowledge, and
to make sense of the huge Universe for humans.
The milk root of the word “galaxy” and the name
of our own galaxy the “milky way” (Licquia, 2015) is
due to a perceived white smear in the night sky.
Constellation names are suggestive of ideas and
patterns recognized by humans, among them the
southern cross, appearing in the Australian, Brazilian
and New Zealand flags, which had a navigation role
in the southern hemisphere of planet Earth.
Zodiac, a very old notion – derived from the
Greek zoidion, “little animal” – is due to
constellations visualized as little animals. It is a belt-
shaped region of the sky that extends north or south
of the ecliptic – the plane of the orbit of the Earth
around the Sun. The zodiac concept is still used in
modern astronomy – see e.g., (Licquia, 2015), and
sub-section 5.5 of Related Work.
3.3 VLSI Objects
VLSI (Very Large Scale Integrated) circuits have
electronic components with a huge number of
transistors packed in a single chip. The current
(March 2022), system on a chip transistor count is of
the order of 114 billion transistors, as announced in a
consumer electronics press release (M1-Ultra, 2022).
Transistors’ count has a surprising quantitative
similarity to galaxies. The transistors count in a chip
is of the same order of magnitude of the galaxies
number in the Universe.
Is this a real surprise? Or is it an expected
consequence of the same scientific and engineering,
ideas and tools, being used by humans, despite so
different knowledge fields?
Digital electronic chips, with concepts as – logic
gates, capacitors, memory units – are nowadays
designed with software tools in which these concepts’
semantics play an essential role.
4 FINITE CONCEPTS CATALOG
IMPOSSIBILITY
This section states this paper’s theoretical results.
After some preliminary definitions, we summarize
the theorems motivation, then formulate and prove
the theorems.
4.1 Preliminary Definitions
The definitions are needed for the theorem statement.
Each definition depends on the preceding one.
Definition 1: Natural Language Word Meaning.
Meaning is assigned as a set of natural language
words, a set with at least one word, not including
the word whose meaning is being assigned.
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4.2 Theorems Motivation
The language of software is any human natural
language, constantly changing its vocabulary. This
occurs by adding words, deleting obsolete words, or
changing words meanings.
The natural languages’ concept extraordinary
dynamics is the theorems’ foundational assumption.
We see no reason for language dynamics weakening
in a foreseeable future.
4.3 Finite Catalog Impossibility
Theorem
The first theorem is in the textbox below:
Proof:
The proof idea is by construction. One obtains an
infinite Software Concepts’ System catalog, through
an infinite recursion of assigned meanings to words.
The words used in this proof are natural number
names in a chosen language. In English these would
be: zero, one, two, three, four, …, etc. Every natural
number in any natural language has its own specific
name, despite the infinite set of natural numbers.
By assumption (a) there is absolute freedom of
words choice and their respective assigned meanings.
We assign to each natural number as its meaning “any
of the successors of the current or the following
natural numbers”. For instance, the successor(three)
= four, and the successor(four) = five.
By assumption (b) meanings are transitive thus
the successors of three are four, and five, and so on.
By induction, any natural number has an infinite
number of successors.
There is no impediment to include natural
numbers in any Software Concepts’ System, thus it is
impossible to assure that a catalog remains finite. ⧠
Some comments on the Finite Concepts’ Catalog
Impossibility theorem are:
 The justification for the choice of the meanings of
the natural numbers is the Axioms of Peano. Thus,
the meaning of each natural number is given by
the whole set of Peano Axioms.
 We choose zero as the 1
st
natural number for
compatibility with the Peano Axioms.
 A transitivity example is: the result meaning is
assigned to consequence; the consequence
meaning is assigned to outcome; by transitivity
the result meaning is also outcome.
 Meaning is transitive, but it is not symmetric.
4.4 Definitive Catalog Impossibility
Theorem
We again need a preliminary definition:
Intuitively, the impossibility to assure definitive
Software Concepts’ Systems catalogs is even more
plausible than the impossibility to assure finite
catalogs. This is also due to natural language
dynamics – whether the system is finite or infinite –
as was argued in several ways in this paper’s sections.
The next theorem formalizes this intuition.
Definition 2: Software Concept System. Software
concept system at the design level is defined by its
concepts, which are natural language words with
their meanings.
Definition 3: Software Concept System Catalog. A
catalog is an organized structure of software
concepts’ system definitions, with explicitly stated,
not necessarily linear, organizing criteria.
Theorem 1: Finite Concepts’ Catalog
Impossibility
Assuming – the three preliminary definitions
and the two following assumptions:
a) Absolute freedom of meaning choice – natural
language freedom refers to the word whose meaning
is assigned and to the word set assigned as meaning;
a single word may have an unrestricted number of
assigned meanings.
b) Meaning is a transitive relation – The meaning
of a meaning of a word is also a meaning of the
original word.
Then –
It is impossible to assure that a Software Concepts’
Systems Catalog remains finite.
Definition 4: Definitive Catalog. A software
concepts’ systems catalog is definitive, if after
reaching a stable definition of all its software
concepts’ systems, as decided by their inventors, it
will not change anymore.
Theorem 2: Definitive Concepts’ Catalog
Impossibility
Assuming –
a) Theorem 1 – its assumptions and its conclusion,
viz. the impossibility to assure that a Software
Concepts’ Systems Catalog remains finite.
Then –
It is impossible to assure that a Software Concepts’
Systems Catalog remains definitive.
On the Impossibility to Assure a Finite Software Concepts’ Catalog
277

Proof:
Even if one decides to limit the catalog size to an
arbitrarily chosen maximal integer, it is a trivial
corollary of Theorem 1 that such a catalog can be
extended as far as one wishes. Thus, the conclusion
of Theorem 2 is proven. ⧠
Some comments on the Definitive Concepts’ Catalog
Impossibility theorem are:
 The importance of Theorem 1 is to serve the proof
of Theorem 2.
 Finite catalogs are more important in practice than
infinite ones, even though both theorems have
significant implications (see section 6).
5 RELATED WORK
We have chosen a few deeper topics for a concise set
of references to relevant literature.
5.1 Conceptual Integrity
Conceptual Integrity is Frederick Brooks’ idea of the
most important consideration for software system
design, which at first sight is not so obvious. It has
been first proposed and developed in his two well-
known books: “The Mythical Man-Month” (Brooks,
1995) and “The Design of Design” (Brooks, 2010).
Brooks also offered principles to be followed in
order to attain Conceptual Integrity: propriety and
orthogonality. Various authors adopted Brooks’
Conceptual Integrity ideas.
It is remarkable that the Conceptual Integrity
constructive and convincing idea, solidified after a
previous rather pessimistic viewpoint published in
Brooks’ paper on “No Silver Bullet - Essence and
Accidents of Software Engineering” (Brooks, 1987).
It was disputed by David Harel in his reply paper
“Biting the Silver Bullet: Toward a Brighter Future of
System Development” (Harel, 1992).
5.2 Naming and Natural Numbers
Our Theorem 1 proof assumes that every natural
number in any natural language has its own specific
name, despite the infinite set of natural numbers.
A minimal symbol set to write the infinite natural
number names is {0, S}, zero and S i.e., Successor, in
the Peano Arithmetic (PA) language: 0, S0, SS0,
SSS0, …;
For instance, SS0 reads Successor(Successor(0))
is the number 2. In this notation the number of S
symbols tends to infinity. The paper (Horsten, 2005)
mentions PA language, and offers a framework to
investigate names canonicity and naming systems.
Shorter number names ask for word combinations
such as ‘one thousand three hundred’. This assumes
that a finite word set suffices to name infinite natural
numbers, with repeated use of the word set.
Different natural languages have semantically
different number names. For instance, 90 in English
is ‘ninety’ and in French it is ‘quatre-vingt-dix’
meaning “four times twenty plus ten”.
Referring to the Peano arithmetic axiomatization,
the mathematician Henri Poincare (Poincare, 1914)
claimed that arithmetic is a synthetic science whose
objects are not independent from human thought.
Naming in general, is a challenging philosophical
issue. It is discussed in a book “Naming, Necessity
and Natural Kinds” edited by Stephen Schwartz
(Schwartz, 1997), with chapters by several authors.
5.3 Infinite Catalogs
A paper by Allison-Cassin (Allison-Cassin, 2012)
referring to “The Possibility of the Infinite Library”
obviously demands infinite catalogs.
Allison-Cassin compares linear traditional library
catalogs, with the great expectations of the Internet
“infinite library”, with non-linear Hypertext links.
Concerning the term “bibliographic universe”
Allison-Cassin clearly highlights the problematics of
this universe, stressing that this “universe implies an
openness that is not fully accounted for by the idea of
totality”.
5.4 The Infinite Library of Babel
Nothing compares to literature in ideas expressivity,
such as infinity in a fascinating short story entitled
“The Library of Babel” by the fiction writer Jorge
Luis Borges (Borges, 1941).
The story tells us that “The Universe (which
others call the Library) is composed of an … infinite
number of hexagonal galleries”. As it continues “Like
all men of the Library, in my younger days … I have
journeyed in quest of a book, … the catalog of
catalogs.” Finally, one encounters “…thousands and
thousands of false catalogs, …, a proof of the falsity
of the true catalog…”
5.5 Catalogs of Virtually Unending
Stars
Many scientific papers describe how to estimate the
number of stars in the Milky Way and beyond. All
papers make inferences from star catalogs.
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Licquia et al. (Licquia, 2015) present a new
statistical method to determine photometric
properties of the Milky Way, allowing our Galaxy to
be compared to objects found in extragalactic
surveys. It mentions and uses catalogs.
Astraatmadja and Bailer-Jones (Astraatmadja,
2016) inferred distances for two million stars using
parallaxes published in the Gaia DR1 catalog from
the European Space Agency.
Lauer et al. (Lauer, 2020) used images of NASA’s
New Horizons spacecraft cruising the most distant
solar planet Pluto to derive limits on the Cosmic
Optical Background (COB). Its basic insight is that
Universe formation and evolution comes from
knowing how dark the night sky is. COB is an integral
over the cosmological history of star formation
occurring in recognizable galaxies. Lauer’s paper
mentions the Gaia DR2 catalog, among others.
6 DISCUSSION
We discuss the importance of the Finite/Definitive
Impossibility Theorems. It is claimed that software
catalogs are not software theories, and one asks why
nonetheless they are useful. Finally, we state future
work and the main contribution of this paper.
6.1 Absolute Freedom of Meaning
Choice
The center of gravity of the Finite/Definitive
Impossibility Theorems is the natural language
assumption of Absolute freedom of meaning choice.
We took the liberty to represent any meaning
choice by the infinite set of integers – in fact the
Peano Axioms. This choice, rather than arbitrary, is
reasonable, since numbers are frequent participants of
software concept systems.
6.2 Importance of Finite/Definitive
Impossibility Theorems
If Concepts’ Catalog could be assured to be finite and
definitive, it would be a first step towards
formalization of software system Catalogs as theories
of Software as a whole, by themselves. But this would
sacrifice the assumption of Absolute freedom of
meaning choice.
Any organized concepts’ structure, analogous to a
catalog – e.g. taxonomy, dictionary, encyclopaedia –
is by itself neither a full-fledged software theory nor
a substitute for an autonomous agent evolving on its
own.
Concepts’ semantics are indeed an essential part
of software. Nevertheless, software theories should
have an algebraic theoretical component,
complementing the Conceptual aspect. But these
considerations are out of the scope of this paper, and
are dealt with elsewhere – see e.g., (Exman and
Sakhnini, 2018), (Exman and Wallach, 2020) and
(Exman and Shmilovitch, 2021).
6.3 The CYC Counterexample
A counterexample to Theorem 1 is Cyc, succinctly
described as an attempt to compose a finite catalog
about how the world works, doubtless a very
ambitious goal.
In neutral terms Cyc is a long-range Artificial
Intelligence (AI) project aiming at a comprehensive
ontology and knowledge base spanning concepts and
rules, to capture common sense knowledge.
It started in 1984 by Douglas Lenat (Lenat, 1990)
and still is under development. Its ontology, as of the
stable release of 2017, contains about 1,500,000 (one
million and a half) terms.
Criticism has stated the Cyc problems are
“unending amount of data required to produce any
viable results and the inability for Cyc to evolve on
its own”. The late Marvin Minsky, from the MIT AI
laboratory, said that "strategies most popular among
AI researchers in the 1980s reached a dead end."
6.4 Usefulness of Finite Catalogs
A widely known explicit finite catalog is the so-called
GoF book (Gamma et al., 1995) on software design
patterns. It contains 23 design patterns classified into
three categories: Creational, Structural and
Behavioral. It triggered publication of other catalogs,
on specific topics, such as Software Architecture
(Buschmann et al., 1996), Communications Software
(Rising, 2001), and Concurrent and Networked
Objects (Schmidt et al., 2000).
The GoF book was influenced by the architectural
book by Christopher Alexander (Alexander, 1977) on
pattern languages for towns and buildings.
The GoF patterns catalog is hard to formalize,
which is not unexpected according to the current
paper claims. Despite not being definitive, which fits
our Theorem 2, the GoF design patterns’ finite
catalog is useful and was influential, stimulating a
new way of thought about a higher abstraction level
of software design.
On the Impossibility to Assure a Finite Software Concepts’ Catalog
279

6.5 Future Work
There remain open issues of interest, deserving a
deeper investigation. An issue in need of a neat
resolution, is the apparent contradiction between:
a) Brooks’ propriety principle – a software system
should have only concepts essential to its purpose and
no more – apparently implying that software
concepts’ systems complying with Conceptual
Integrity should and can be finite;
b) Theorem 1 – which tells that it is impossible to
assure that a software concepts’ system catalog
remains finite.
6.6 Main Contribution
The main contributions of this paper are the
Impossibility Theorems to Assure a Finite and
Definitive Software Concepts’ Catalog. Nonetheless,
finite but not definitive catalogs can indeed be useful.
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