Hi All, I started a project inspired by my knowledge in physics in software engineering.
I found one could find a framework based on convex analysis, optimization and duality theory to classify and diagonise programming languages performance qualitatively Below you find the abstract and link to the full article at researchgate.net I included python which is a beautiful coding language, highly convex in our terms besides other languages. Thanks in advance for suggestions and comments! The abstract is : Drawing inspiration from Dual-Space Engineering (DSE) in physical systems [1], we map the concepts of primal/dual spaces and topological invariants to the domain of software architecture. In this paper, we introduce a rigorous mathematical framework for software engineering by applying functional analysis, category theory, and algorithmic information theory. We formalize the relationship between the imperative Primal Space X and the declarative Dual Space Y via categorical adjunctions, and introduce the Stepanov Regularity Condition based on Stepanov's algebraic foundations of programming [2, 3]. We define the Semantic Duality Gap as a natural transformation between monadic embeddings, and establish that strong static type systems act as a form of topological protection via Homotopy Type Theory (HoTT). We argue that the space of imperative programs is fundamentally non-convex due to state entanglement, whereas the space of Stepanov-regular, purely functional programs exhibits a convex-like structure. We define the Software Compressibility Paradox, demonstrating that highly organized code possesses high Duality Richness (C D) and minimal Kolmogorov complexity. Finally, we present the Proximal Dual-Space Refactoring (PDSR) algorithm, provide a rigorous computational complexity analysis, and conduct a comprehensive topological analysis of modern and historical programming languages, positioning DSE as a unifying theory for software aesthetics and formal methods. The full paper is here https://www.researchgate.net/publication/408133115_Dual-Space_Software_Engineering Best Wishes, Walid -- https://mail.python.org/mailman3//lists/python-list.python.org
