A wide range of gradual type systems have been proposed, providing many languages with the ability to mix typed and untyped code. However, hiding under language details, these gradual type systems embody fundamentally different ideas of what it means to be well-typed. In this paper, we show that four of the most common gradual type systems provide distinct guarantees, and we give a formal framework for comparing gradual type systems for object-oriented languages. First, we show that the different gradual type systems are practically distinguishable via a three-part litmus test. We present a formal framework for defining and comparing gradual type systems. Within this framework, different gradual type systems become translations between a common source and target language, allowing for direct comparison of semantics and guarantees.

The Java language lacks the important notions of ownership (an object owns its representation to prevent unwanted aliasing) and immutability (the division into mutable, immutable, and readonly data and references). Programmers are prone to design errors, such as representation exposure or violation of immutability contracts. This paper presents Ownership Immutability Generic Java (OIGJ), a backward-compatible purely-static language extension supporting ownership and immutability. We formally defined a core calculus for OIGJ, based on Featherweight Java, and proved it sound. We also implemented OIGJ and performed case studies on 33,000 lines of code.