Formalizing $φ$-calculus: a purely object-oriented calculus of decorated objects

Abstract

Many calculi exist for modelling various features of object-oriented languages. Many of them are based on -calculus and focus either on statically typed class-based languages or dynamic prototype-based languages.We formalize untyped calculus of decorated objects, informally presented by Bugayenko, which is defined in terms of objects and relies on decoration as a primary mechanism of object extension. It is not based on -calculus, yet with only four basic syntactic constructions is just as complete. We prove the calculus is confluent (i.e. possesses Church-Rosser property), and introduce an abstract machine for call-by-name evaluation. Finally, we provide a sound translation to -calculus with records.

On the Origins of Objects by Means of Careful Selection

“…As a humble attempt to create such a common ground for the world of objects, we suggest our own taxonomy of objects for EO 1 , a strictly formal (Kudasov et al, 2022) object-oriented programming language with an intentionally reduced feature set (Bugayenko, 2021). All objects are grouped as such:…”