Nested Refinements for Dynamic Languages

Programs written in dynamic languages make heavy use of features— run-time type tests, value-indexed dictionaries, polymorphism,and higher-order functions — that are beyond the reach of type sys-tems that employ either purely syntactic or purely semantic reason-ing. We present a core calculus, System D, that merges these twomodes of reasoning into a single powerful mechanism of nested re-finement types wherein the typing relation is itself a predicate in therefinement logic. System D coordinates SMT-based logical impli-cation and syntactic subtyping to automatically typecheck sophisti-cated dynamic language programs. By coupling nested refinementswith McCarthy’s theory of finite maps, System D can precisely rea-son about the interaction of higher-order functions, polymorphism,and dictionaries. The addition of type predicates to the refinementlogic creates a circularity that leads to unique technical challengesin the metatheory, which we solve with a novel stratification ap-proach that we use to prove the soundness of System D.