Essential AOP: The A Calculus

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, e.g. 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.