Polymorphic Iterable Sequential Effect Systems

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