English

$\varphi$-Calculus: Object-Oriented Formalism

Programming Languages 2026-01-08 v9

Abstract

Object-oriented programming (OOP) is one of the most popular paradigms used for building software systems. However, despite its industrial and academic popularity, OOP is still missing a formal apparatus similar to λ\lambda-calculus, which functional programming is based on. A number of attempts were made to formalize OOP, but none of them managed to cover all the features available in modern OO programming languages, such as C++ or Java. We have made yet another attempt and created φ\varphi-calculus. This paper does not demonstrate the practical use or effect of \varphivarphi but merely explains it.

Keywords

Cite

@article{arxiv.2111.13384,
  title  = {$\varphi$-Calculus: Object-Oriented Formalism},
  author = {Yegor Bugayenko and Maxim Trunnikov},
  journal= {arXiv preprint arXiv:2111.13384},
  year   = {2026}
}