Nested Refinements: A Logic For Duck Typing

Ravi Chugh, Patrick Rondon, and, Ranjit Jhala.

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 systems that employ either purely syntactic or purely semantic reasoning. We present a core calculus, System D, that merges these two modes of reasoning into a single powerful mechanism of nested re- finement types wherein the typing relation is itself a predicate in the refinement logic. System D coordinates SMT-based logical implication and syntactic subtyping to automatically typecheck sophisticated dynamic language programs. By coupling nested refinements with McCarthy’s theory of finite maps, System D can precisely reason about the interaction of higher-order functions, polymorphism, and dictionaries. The addition of type predicates to the refinement logic creates a circularity that leads to unique technical challenges in the metatheory, which we solve with a novel stratification approach that we use to prove the soundness of System D.

In the Proceedings of the 39th ACM Symposium on Principles of Programming Languages, 2012. (POPL 2012).

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© 2012.