A Categorical Model of State Transformations in Programming Languages
M. Kohútová, W. Steingartner, S. Novotný · Journal of Applied Mathematics Statistics and Informatics · 2026
Abstract Formal semantics of programming languages represents a basic formal method connecting theoretical foundations of computer science with the development of reliable software. It allows for rigorous analysis of the correctness and properties of programs independently of the implementation. When formulating it, it is necessary to respect the principles of the programming paradigm, which determines the basic abstractions of the language. At the same time, there are unifying formalisms that allow for systematic comparison of semantic definitions across paradigms. Category theory represents one of the most important such approaches. We formalize this perspective by introducing a general categorical model of state transformations and show how different programming paradigms can be uniformly represented and related within this framework via structure-preserving mappings.