=Paper=
{{Paper
|id=Vol-3941/BENEVOL2024_NICE_paper3
|storemode=property
|title=Rethinking Paradigmatic Collaboration: New Metrics
for Inter-language Synergy in Software Engineering
|pdfUrl=https://ceur-ws.org/Vol-3941/BENEVOL2024_NICE_paper3.pdf
|volume=Vol-3941
|authors=Mikel Vandeloise,Gonzague Yernaux,Wim Vanhoof
|dblpUrl=https://dblp.org/rec/conf/benevol/VandeloiseYV24
}}
==Rethinking Paradigmatic Collaboration: New Metrics
for Inter-language Synergy in Software Engineering==
https://ceur-ws.org/Vol-3941/BENEVOL2024_NICE_paper3.pdf
Rethinking paradigmatic collaboration: new metrics for
inter-language synergy in software engineering
Mikel Vandeloise1 , Gonzague Yernaux2 and Wim Vanhoof3
Faculty of Computer Science, University of Namur, Rue Grandgagnage 21, 5000 Namur, Belgium
Abstract
This paper introduces two novel metrics for assessing collaboration potential between programming paradigms
and languages, offering a fresh approach to evaluating inter-paradigm interactions. The quantitative framework
introduced challenges traditional methods by highlighting both the opportunities and the challenges of integrating
paradigms with varying characteristics. Initial findings suggest that the metric effectively captures collaboration
within similar paradigms, with functional paradigms demonstrating particularly strong collaboration potential.
However, it also underscores the complexity of unifying divergent paradigms. The goal of this paper is to
provoke discussion and foster further research, such as the refinement of metrics to obtain useful measurements
in technology selection steps and interdisciplinary software development.
Keywords
Programming paradigms, Collaboration metrics, Interoperability, Languages integration
1. Introduction
Programming paradigms are fundamental frameworks that guide the conceptualisation, implementation,
and evolution of software systems. These paradigms, ranging from simple declarative structures
to complex procedural and concurrent constructs, must be carefully selected to meet the evolving
challenges of software projects [1]. Often, a hybrid approach becomes necessary. However, integrating
multiple paradigms increases complexity, particularly in terms of interoperability and maintainability,
which are crucial for long-term software evolution [2, 3]. Effectively managing these complexities is
key to the success and sustainability of evolving software systems. To clarify our approach, we define
inter-paradigmatic collaboration as follows.
Definition 1.1 Collaboration between programming paradigms (or inter-paradigmatic collaboration)
refers to the complementary potential of two paradigms to work together effectively at the abstract and
conceptual level. This potential is considered the inverse of the effort required to align and integrate
their conceptual frameworks. The collaboration relies on the balance of two key dimensions, each
displaying an inherent tension:
• Conceptual complementarity is the extent to which the core concepts and strengths of one paradigm
complement and reinforce those of another, mitigating each other’s weaknesses and resulting in
a more robust and versatile combined framework.
• Abstract interoperability is the ease with which different paradigms can conceptually interoperate
and integrate their theoretical constructs, rewarding seamless integration while penalising the
cognitive and structural effort required to combine them.
With most existing research on interoperability between programming languages focusing on the
technical and syntactic aspects of the question [4, 5], there is still a lack of quantitative tools capable of
encapsulating the notion at the level of programming paradigms. Our research aims to address this gap.
The key contributions of this paper are threefold.
BENEVOL24: The 23rd Belgium-Netherlands Software Evolution Workshop, November 21-22, Namur, Belgium
Envelope-Open mikel.vandeloise@unamur.be (M. Vandeloise); gonzague.yernaux@unamur.be (G. Yernaux); wim.vanhoof@unamur.be
(W. Vanhoof)
Orcid 0009-0002-0858-471X (M. Vandeloise); 0000-0001-6430-8168 (G. Yernaux); 0000-0003-3769-6294 (W. Vanhoof)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
1. We adapt an existing taxonomy of paradigms to allow for a rigorous formulation of the concept
of paradigm.
2. We develop a metric tailored to assess the potential for collaboration between different paradigms.
The metric is designed to allow for a certain (parametric) flexibility, that can be fine-tuned based
on research objectives.
3. We extend this metric to evaluate the potential for collaboration between different languages,
focusing on their underlying paradigms.
2. Towards a refined taxonomy of programming paradigms
In 2009, Van Roy’s foundational work [6] set the stage for a comprehensive classification of
programming paradigms. In this section, we extend and refine his seminal taxonomy through the
somewhat specific lens of inter-language synergies and collaborations. The theoretical foundations of
interest in this pursuit have, in fact, been little investigated in the past; the main sources that we have
collected and selected through an extensive literature review are [7, 1, 8, 9].
Our taxonomy is essentially embodied by an acyclic directed graph where each node corresponds to a
distinct paradigm (Figure 1a), and each edge signifies the acquisition of a concept (Figure 1b) that makes
a paradigm evolve into a more specialised form. We call the acquisition of specific concepts through such
evolutionary paths conceptual hierarchy. The resulting structure allows incorporating the paradigms’
inherent concepts as well as their computable attributes such as Turing completeness (Figure 1c) and
non-determinism observability (Figure 1d). These attributes allow categorising the paradigms into
broader groups known as meta-paradigms (Figure 1e), which help to provide a macroscopic view of
their relationships, according to the following definition.
Definition 2.1 A meta-paradigm is a collection of core concepts, attributes, and principles shared
by multiple paradigms. It conceptually regroups features that influence the models, design, and
implementation of groups of paradigms. Transitions between meta-paradigms result from acquiring
specific concepts, leading to shifts in focus and application.
An interesting case arises when distinct paradigms present similar (yet separated) conceptual hier-
archies, which can in some cases influence their compatibility predispositions. We call this specific
relation propagation; see Figure 1f for concrete examples.
Definition 2.2 Propagation is a relationship that occurs between two paradigms that share a same
set of concepts, but acquired in different orders.
(a) (b) (c) (d) (e) (f)
Figure 1: Fragments of the taxonomy. The grey-to-yellow gradient in (Figure 1c) indicates the shift from
paradigms limited to data structures to those enabling Turing completeness.
In total, our proposed taxonomy includes 28 distinct paradigms defined by 17 key concepts and 2
observable binary characteristics and organised into 11 meta-paradigms. The whole graph is depicted
in Appendix A’s Figure 4, along with an exhaustive enumeration of the different constitutive sets
and an illustration of our approach (Table 1) in which we instantiate our framework on the so-called
”deterministic logic” paradigm. More information on the array of paradigms considered can also be
found online in the form of a poster [10].
3. A measure for paradigmatic collaboration
Based on our taxonomy, we can formulate a definition of the very notion of a paradigm.
Definition 3.1 A programming paradigm, often denoted 𝑃, is formally defined as a 6-tuple, i.e.
𝑃 = (𝐶, 𝐹 , 𝑆, 𝑇 , 𝑂, 𝑀), where each element represents a specific dimension of the paradigm:
• 𝐶 (⊆ Concepts) is the non-empty set of key concepts that define the paradigm.
• 𝐹 (⊆ Paradigms) is the parent paradigms from which 𝑃 evolved.
• 𝑆 (⊆ Paradigms) is the child paradigms descended from 𝑃.
• 𝑇 (∈ {0, 1}) is a Boolean indicating if all languages using 𝑃 can be Turing-complete.
• 𝑂 (∈ {0, 1}) is a Boolean indicating if 𝑃 permits observable non-determinism.
• 𝑀 (∈ Meta-paradigms) is the associated meta-paradigm.
Now, to assess the compatibility and collaboration potential between paradigms, we developed a
metric that considers their structure, relationships, and key properties.
Definition 3.2 The Inter-Paradigm Collaboration Metric (PCM) ∶ Paradigms × Paradigms ↦ [0, 1] is
defined, for 𝑃1 = (𝐶1 , 𝐹1 , 𝑆1 , 𝑇1 , 𝑂1 , 𝑀1 ) and 𝑃2 = (𝐶2 , 𝐹2 , 𝑆2 , 𝑇2 , 𝑂2 , 𝑀2 ), as
PCM(𝑃1 , 𝑃2 ) = 𝛼 × 𝐼 𝐶(𝐶1 , 𝐶2 ) + 𝛽 × 𝐾 𝑅(𝐹1 , 𝑆2 ) + 𝛾 × 𝐾 𝑅(𝐹2 , 𝑆1 )
+ 𝛿 × MP(𝑀1 , 𝑀2 ) + 𝜖 × 𝑇 𝐶(𝑇1 , 𝑇2 ) + 𝜁 × 𝑂𝑁 𝐷(𝑂1 , 𝑂2 )
where 𝛼, 𝛽, 𝛾 , 𝛿, 𝜖, 𝜁 ∈ [0, 1] ∧ 𝛼 + 𝛽 + 𝛾 + 𝛿 + 𝜖 + 𝜁 = 1 ∧ 𝛽 = 𝛾
The parametric coefficients 𝛼, 𝛽, 𝛾, 𝛿, 𝜖, and 𝜁 are called the collaboration weights. In this initial study,
each weight is set to 16 to ensure equal contribution from the six factors, although future research may
adjust these values based on specific requirements.
The first component of the metric is the intersection of concepts, calculated as the ratio of
shared concepts to the total number of concepts, and incarnated in the definition by the function
|𝐶 ∩𝐶 |
IC ∶ 𝒫 (Concepts) × 𝒫 (Concepts) → ℝ defined by IC(𝐶1 , 𝐶2 ) = |𝐶1 ∪𝐶2 | . This ratio helps determine how
1 2
well paradigms complement each other.
Next, we check for kinship relationships by evaluating whether there is overlap between the
parent paradigms of one and the child paradigms of the other. The notion is formalised by the function
KR ∶ 𝒫 (Paradigms) × 𝒫 (Paradigms) ↦ {0, 1} where KR(𝐹 , 𝑆) = 1 if and only if 𝐹 ∩ 𝑆 ≠ ∅. Although
KR is asymmetric, using both 𝐾 𝑅(𝐹1 , 𝑆2 ) and 𝐾 𝑅(𝐹2 , 𝑆1 ) in 𝑃𝐶𝑀 ensures symmetry in the overall metric,
thus preventing PCM from requiring symmetry in each of its components.
The compatibility of meta-paradigms is determined by a function MP ∶ Meta-paradigms ×
Meta-paradigms ↦ {0, 1} such that MP(𝑀1 , 𝑀2 ) = 1 ⇔ 𝑀1 = 𝑀2 .
We also check for Turing completeness with TC ∶ {0, 1}2 ↦ {0, 1} where TC(𝑇1 , 𝑇2 ) = 𝑇1 ∧ 𝑇2 .
Finally, we similarly analyse observable non-determinism by determining whether both paradigms
permit it, formally using the function OND ∶ {0, 1}2 ↦ {0, 1} such that OND(𝑂1 , 𝑂2 ) = 𝑂1 ∧ 𝑂2 .
These metrics provide a systematic evaluation of compatibility and collaboration potential, fo-
cusing on conceptual and computational alignment [11, 12]. We applied this approach to 28 paradigms,
with notable examples including the functional, imperative, and deterministic logic paradigms.
The complete results are available in [13], and a focus on three paradigms is presented in Figure 2.
Interestingly, the functional paradigm (Figure 2a) demonstrates a high level of collaboration potential
with many pairs, suggesting strong compatibility and deep integration possibilities. In contrast, the
imperative paradigm (Figure 2b) shows more variability, with a balanced distribution between low
and moderate collaboration potential, this time hinting that specialised approaches may be needed
to achieve effective integration. As a last remark in this non-exhaustive analysis, we noticed that
the deterministic logic paradigm (Figure 2c) shows strong collaboration potential within its own
meta-paradigm (”constraints and logic”), but generally moderate compatibility outside of it, indicating a
more selective capacity for integration. The whole dataset, modelled using Haskell, is accessible in an
online repository1 .
(a) 𝑃𝐶𝑀 for Functional (b) 𝑃𝐶𝑀 for Imperative (c) 𝑃𝐶𝑀 for Deterministic Logic
Figure 2: PCM comparisons for three different programming paradigms
4. Extending the collaboration metric to programming languages
To integrate the results obtained for each constitutive paradigm of a language, we can now define a
programming language as follows.
Definition 4.1 A programming language is a set of multiple programming paradigms that collectively
define its capabilities and behavioural characteristics. For a language named 𝐿, the corresponding set is
denoted by 𝑃𝐿 = {𝑃1 , 𝑃2 , … , 𝑃𝑛 }, where each 𝑃𝑖 (𝑖 ∈ 1..𝑛) is a distinct paradigm (represented by its tuple)
contributing to the language’s comprehensive functionality.
Detailed descriptions of the paradigmatic structures of individual languages are available in [10]. Given
the definition above, we can now define a new metric LCM, which captures paradigmatic compatibility
as well, but this time across languages. This metric operates on the combined paradigm sets of the
languages while preserving the integrity of each paradigm, even if it appears in both sets. Definition 4.2
below formalises this approach. It uses an ordering relation, denoted by >, to compare the paradigms
that are represented within the taxonomy. The first incarnation of the relation can be defined as follows.
For two paradigms 𝑐 and 𝑐 ′ , represented as tuples 𝑐 = (𝑥0 , 𝑥1 , … , 𝑥𝑚−1 ) and 𝑐 ′ = (𝑦0 , 𝑦1 , … , 𝑦𝑛−1 ), we
define the order as
𝑐 ′ > 𝑐 ⇔ (∃𝑘 ∈ {0, 1, … , min(𝑚, 𝑛) − 1} |𝑥𝑖 = 𝑦𝑖 ∀𝑖 < 𝑘 ∧ 𝑥𝑘 < 𝑦𝑘 ) ∨ (𝑚 < 𝑛 ∧ 𝑥𝑖 = 𝑦𝑖 ∀𝑖 < 𝑚)
1
See https://github.com/Vdloisem/MCC.
Definition 4.2 Let 𝑃𝐿𝐴 and 𝑃𝐿𝐵 be the sets of programming paradigms associated, respectively, with
the programming languages named 𝐿𝐴 and 𝐿𝐵 . Let 𝐶 be the multiset 𝑃𝐿𝐴 ⊕ 𝑃𝐿𝐵 , i.e. the ordered
concatenation of 𝑃𝐿𝐴 and 𝑃𝐿𝐵 using the relation > defined above. The Inter-Language Collaboration
Metric (LCM) between 𝐿𝐴 and 𝐿𝐵 is then calculated as
1
LCM(𝑃𝐿𝐴 , 𝑃𝐿𝐵 ) = ∑ PCM(𝑐, 𝑐 ′ )
(2𝑛) (𝑐,𝑐 ′ )∈𝑅
where 𝑅 = {(𝑐, 𝑐 ′ )|𝑐, 𝑐 ′ ∈ 𝐶, 𝑐 ′ > 𝑐} and 𝑛 = |𝐶|.
The process described in Definition 4.2 provides a structured framework to analyse collaboration
between 𝐿𝐴 and 𝐿𝐵 , offering preliminary insights into language selection, comparative analysis, and
paradigm interaction (see Figure 3). The dotted lines (also present in Figure 2) mark a notion of
”collaboration levels”, based on confidence intervals derived from the distribution of collaboration
scores. For a more comprehensive overview, including a more thorough explanation regarding the
collaboration levels, see [14].
(a) Fuctional language (b) Imperative language (c) Deterministic Logic Language
Figure 3: LCM comparisons for three different programming languages
5. Conclusions and future work
This research has laid the groundwork for evaluating collaboration between programming paradigms
based on the adaptation of an existing taxonomy in that context. Our findings suggest that functional
paradigms and, by extension, the languages that incorporate them, show stronger indicators of col-
laboration potential. This kind of insight is especially valuable for software engineers that need to
make informed decisions during the architecture and design phases of system development, as it offers
a quantitative basis for selecting paradigms that can work together more effectively. Although the
metrics show promise, for now, they primarily focus on static characteristics and do not fully capture the
broader concerns of language interoperability as (complex) systems grow and evolve. Future work will
aim to explore deeper inter-paradigmatic interactions and refine the metrics, with a focus on expanding
the framework to support more languages and paradigms while assessing its practical relevance through
qualitative studies. These will examine developers’ language selection based on familiarity, community
support, and domain-specific constraints. Additionally, we plan to develop tools for multi-language
integration in development environments, potentially automating early-stage software decisions. To
enhance comprehensiveness, we will incorporate factors such as typing, compilation, and memory
management into our metrics. Real-world case studies will further refine these metrics, formalize
interoperability and collaboration, and help determine optimal collaboration weights depending on
application contexts. Finally, we will explore assigning weights to each paradigm within a language
and integrating them into LCM to better capture their relative influence. These efforts should refine our
proof of concept and support more complete and effective analyses of software development strategies
in various programming environments.
References
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13381795.
A. Appendix A
The following sets provide a detailed view of the refined taxonomy developed in this research.
This taxonomy categorises 28 distinct paradigms based on 17 key concepts and two observable binary
characteristics. These paradigms are further organised into 11 meta-paradigms, offering a comprehensive
framework for evaluating collaboration potential within and across programming languages.
descriptive declarative, first-order functional, functional, imperative, deterministic logic,
⎧ ⎫
⎪ lazy functional, continuation, adt functional, event loop, stateful functional, ⎪
⎪ guarded command, imperative search, sequential object oriented, relational and logic, ⎪
⎪ declarative concurrent, adt imperative, multi agent, active object, ⎪
Paradigms =
⎨ shared state concurrent, concurrent object oriented, constraint logic, ⎬
⎪ concurrent constraint, lazy declarative concurrent, nonmonotonic dataflow, ⎪
⎪ ⎪
⎪ multi agent dataflow, continuous synchronous, lazy concurrent constraint, ⎪
⎩ discrete synchronous ⎭
record, procedure, closure, unification, cell, search, solver, thread, by-need sync,
Concepts = { continuation, unforgeable constant, channel, single assign, nondet choice, }
sync on partial termination, clocked computation, local cell
Binary characteristics = { Turing completeness, observable non-determinism }
functional, shared state, logic and constraint, data abstraction, message passing,
Meta-paradigms = { concurrent dataflow, algorithmic search, constrained execution, reactive, }
dataflow and message passing, functional concurrent dataflow
The table below illustrates an example of the structure used in our taxonomy, specifically applied to
the deterministic logic paradigm. Details the core concepts, computational properties, and position of
the paradigm within the evolutionary path of the taxonomy, highlighting its relationships with related
paradigms.
Table 1
Example with the deterministic logic paradigm
Category Actual Value Figure
Paradigm deterministic logic programming (Figure 1a)
Concepts record, procedure, closure, unification (Figure 1b)
Turing completeness True (Figure 1c)
Non-determinism observability False (Figure 1d)
Meta-paradigm logic and constraint (Figure 1e)
Evolutionary path: parent functional programming (Figure 1b)
Evolutionary path: child relational and logic programming (Figure 1b)
Propagation False (Figure 1f)
Figure 4 shows an overview of all the paradigms that are (for now) included in our framework, in the
form of an acyclic directed graph as described in the paper.
Figure 4: Taxonomy of programming paradigms