Formal foundations for hybrid effect analysis

Type-and-effect systems are a powerful tool for program construction and verification. Type-andeffect systems are useful because it help reduce bugs in computer programs, enable compiler optimizations and provide program documentation. As software systems increasingly embrace dynamic features and complex modes of compilation, static effect systems have to reconcile over competing goals such as precision, soundness, modularity, and programmer productivity. In this thesis, we propose the idea of combining static and dynamic analysis for effect systems to improve precision and flexibility. We describe intensional effect polymorphism, a new foundation for effect systems that integrates static and dynamic effect checking. Our system allows the effect of polymorphic code to be intensionally inspected. It supports a highly precise notion of effect polymorphism through a lightweight notion of dynamic typing. When coupled with parametric polymorphism, the powerful system utilizes runtime information to enable precise effect reasoning, while at the same time retains strong type safety guarantees. The technical innovations of our design include a relational notion of effect checking, the use of bounded existential types to capture the subtle interactions between static typing and dynamic typing, and a differential alignment strategy to achieve efficiency in dynamic typing. We introduce the idea of first-class effects, where the computational effect of an expression can be programmatically reflected, passed around as values, and analyzed at run time. A broad range of designs “hard-coded" in existing effect-guided analyses can be supported through intuitive programming abstractions. The core technical development is a type system with a couple of features. Our type system provides static guarantees to application-specific effect management properties through refinement types, promoting “correct-by-design" effect-guided programming. Also, our type system computes not only the over-approximation of effects, but also their under-approximation. The duality unifies the common theme of permission vs. obligation in effect reasoning. Finally, we show the potential benefit of intensional effects by applying it to an event-driven system to obtain safe concurrency. The technical innovations of our system include a novel effect system to