Towards a unified framework for programming paradigms: A systematic review of classification formalisms and methodological foundations

TL;DR

This paper systematically reviews classification formalisms of programming paradigms, highlighting limitations of current taxonomies and advocating for a formal, compositional framework based on mathematical primitives like type and category theory.

Contribution

It identifies the shift from traditional taxonomies to formal, reconstructive frameworks using minimal primitives and mathematical theories for better paradigm classification.

Findings

Existing taxonomies lack granularity and struggle with hybrid languages.

A convergence towards a compositional reconstruction approach is observed.

Mathematical frameworks like Type theory and Category theory are central to this approach.

Abstract

The rise of multi-paradigm languages challenges traditional classification methods, leading to practical software engineering issues like interoperability defects. This systematic literature review (SLR) maps the formal foundations of programming paradigms. Our objective is twofold: (1) to assess the state of the art of classification formalisms and their limitations, and (2) to identify the conceptual primitives and mathematical frameworks for a more powerful, reconstructive approach. Based on a synthesis of 74 primary studies, we find that existing taxonomies lack conceptual granularity, a unified formal basis, and struggle with hybrid languages. In response, our analysis reveals a strong convergence toward a compositional reconstruction of paradigms. This approach identifies a minimal set of orthogonal, atomic primitives and leverages mathematical frameworks, predominantly Type theory, Category theory and Unifying Theories of Programming (UTP), to formally guarantee their compositional properties. We conclude that the literature reflects a significant intellectual shift away from classification towards these promising formal, reconstructive frameworks. This review provides a map of this evolution and proposes a research agenda for their unification.