Unlike traditional static type checking, the type system in the Dart programming language is unsound by design, even for fully annotated programs. The rationale has been that this allows compile-time detection of likely errors and enables code completion in integrated development environments, without being restrictive on programmers. Despite unsoundness, judicious use of type annotations can ensure useful properties of the runtime behavior of Dart programs. We present a formal model of a core of Dart with a focus on its type system, which allows us to elucidate the causes of unsoundness. Our main contribution is a characterization of message-safe programs and a theorem stating that such programs will never encounter ‘message-not-understood’ errors at runtime. Message safety is less restrictive than traditional type soundness, and we argue that it forms a natural intermediate point between dynamically typed and statically typed Dart programs.

Unlike traditional static type checking, the type system in the Dart programming language is unsound by design, even for fully annotated programs. The rationale has been that this allows compile-time detection of likely errors and enables code completion in integrated development environments, without being restrictive on programmers. Despite unsoundness, judicious use of type annotations can ensure useful properties of the runtime behavior of Dart programs. We present a formal model of a core of Dart with a focus on its type system, which allows us to elucidate the causes of unsoundness. Our main contribution is a characterization of message-safe programs and a theorem stating that such programs will never encounter 'message not understood' errors at runtime. Message safety is less restrictive than traditional type soundness, and we argue that it forms a natural intermediate point between dynamically typed and statically typed Dart programs.

Aspect-oriented programming (AOP) has produced interesting language designs, but also ad hoc semantics that needs clarification. We contribute to this clarification with a calculus that models essential AOP, both simpler and more general than existing formalizations. In AOP, advice may intercept method invocations, and proceed executes the suspended call. Proceed is an ad hoc mechanism, only usable inside advice bodies. Many pointcut mechanisms, for example, wildcards, also lack regularity. We model proceed using first-class closures, and shift complexity from pointcuts to ordinary object-oriented code. Two well-known pointcut categories, call and execution , are commonly considered similar. We formally expose their differences, and resolve the associated soundness problem. Our calculus includes type ranges , an intuitive and concise alternative to explicit type variables that allows advice to be polymorphic over intercepted methods. We use calculus parameters to cover type safety for a wide design space of other features. Type soundness is verified in Coq.

Virtual classes are class-valued attributes of objects. Like virtual methods, virtual classes are defined in an object's class and may be redefined within subclasses. They resemble inner classes, which are also defined within a class, but virtual classes are accessed through object instances, not as static components of a class. When used as types, virtual classes depend upon object identity -- each object instance introduces a new family of virtual class types. Virtual classes support large-scale program composition techniques, including higher-order hierarchies and family polymorphism. The original definition of virtual classes in BETA left open the question of static type safety, since some type errors were not caught until runtime. Later the languages Caesar and gbeta have used a more strict static analysis in order to ensure static type safety. However, the existence of a sound, statically typed model for virtual classes has been a long-standing open question. This paper presents a virtual class calculus, VC, that captures the essence of virtual classes in these full-fledged programming languages. The key contributions of the paper are a formalization of the dynamic and static semantics of VC and a proof of the soundness of VC.