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Not AvailableActor systems are a flexible model of concurrent and distributed programming, which are efficiently implementable, and avoid many classic concurrency bugs by construction. However they must still deal with the challenge of messages arriving in unexpected orders. We describe an approach to restricting the orders in which actors send messages to each other, by equipping actor references—the handle used to address another actor—with a protocol restricting which message types can be sent to another actor and in which order using that particular actor reference. This endows the actor references with the properties of (flow-sensitive) static capabilities, which we call actor capabilities. By sending other actors only restricted actor references, actors may control which messages are sent in which orders by other actors. Rules for duplicating (splitting) actor references ensure that these restrictions apply even in the presence of delegation. The capabilities themselves restrict message send ordering, which may form the foundation for stronger forms of reasoning. We demonstrate this by layering an effect system over the base type system, where the relationships enforced between the actor capabilities and the effects of an actor’s behaviour ensure that an actor’s behaviour is always prepared to handle any message that may arrive. 

We describe a new concrete approach to giving predictable error locations for sequential (flow-sensitive) effect systems. Prior implementations of sequential effect systems rely on either computing a bottom-up effect and comparing it to a declaration (e.g., method annotation) or leaning on constraint-based type inference. These approaches do not necessarily report program locations that precisely indicate where a program may “go wrong” at runtime. Instead of relying on constraint solving, we draw on the notion of a residual from literature on ordered algebraic structures. Applying these to effect quantales (a large class of sequential effect systems) yields an implementation approach which accepts exactly the same program as an original effect quantale, but for effect-incorrect programs is guaranteed to fail type-checking with predictable error locations tied to evaluation order. We have implemented this idea in a generic effect system implementation framework for Java, and report on experiences applying effect systems from the literature and novel effect systems to Java programs. We find that the reported error locations with our technique are significantly closer to the program points that lead to failed effect checks. 

Effect systems are lightweight extensions to type systems that can verify a wide range of important properties with modest developer burden. But our general understanding of effect systems is limited primarily to systems where the order of effects is irrelevant. Understanding such systems in terms of a semilattice of effects grounds understanding of the essential issues and provides guidance when designing new effect systems. By contrast, sequential effect systems—where the order of effects is important—lack an established algebraic structure on effects. We present an abstract polymorphic effect system parameterized by an effect quantale—an algebraic structure with well-defined properties that can model the effects of a range of existing sequential effect systems. We define effect quantales, derive useful properties, and show how they cleanly model a variety of known sequential effect systems. We show that for most effect quantales, there is an induced notion of iterating a sequential effect; that for systems we consider the derived iteration agrees with the manually designed iteration operators in prior work; and that this induced notion of iteration is as precise as possible when defined. We also position effect quantales with respect to work on categorical semantics for sequential effect systems, clarifying the distinctions between these systems and our own in the course of giving a thorough survey of these frameworks. Our derived iteration construct should generalize to these semantic structures, addressing limitations of that work. Finally, we consider the relationship between sequential effects and Kleene Algebras, where the latter may be used as instances of the former.