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

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.