Nested refinements: a logic for duck typing

  • Authors:

  • Ravi Chugh;Patrick M. Rondon;Ranjit Jhala

  • Affiliations:

  • University of California, San Diego, La Jolla, CA, USA;University of California, San Diego, La Jolla, CA, USA;University of California, San Diego, La Jolla, CA, USA

  • Venue:
  • POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
  • Year:
  • 2012

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Abstract

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 refinement 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.