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 \(λ\)-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 \(\varphi\)-calculus. This paper does not demonstrate the practical use or effect of \\(varphi\) but merely explains it.

翻译：面向对象编程（OOP）是构建软件系统最流行的范式之一。然而，尽管在工业界和学术界广受欢迎，OOP 仍缺乏类似于函数式编程所基于的 λ-演算的形式化工具。已有多次尝试对 OOP 进行形式化，但均未能涵盖现代面向对象编程语言（如 C++ 或 Java）中的所有特性。我们进行了又一次尝试，创建了 φ-演算。本文并不展示 φ-演算的实际用途或效果，仅对其作出解释。