UJ: Type Soundness for Universe Types

Universe types characterise aliasing in object oriented programming languages andare used to reason modularly about programs. In this report we formalise prior work byMüller and Poetzsch-Heffter, who designed the Universe Type System for a core subsetof Java. We present our work in two steps. We first give a Topological Universe TypeSystem and show subject reduction to a small-step dynamic semantics for our language.Motivated by concerns of Modular verification, we then give an Encapsulation UniverseType System (based on the owner-as-modifier principle), prove subject reduction withrespect to the former small-step semantics, and show how the type system can be usedfor modular verification.