Nested Refinements for Dynamic Languages

TL;DR

This paper introduces System D, a core calculus that combines syntactic and semantic reasoning through nested refinement types, enabling precise typechecking of complex dynamic language features.

Contribution

It presents System D, a novel type system merging syntactic and semantic reasoning with nested refinements, and introduces a stratification approach to prove its soundness.

Findings

System D can automatically typecheck sophisticated dynamic language programs.

Nested refinements enable precise reasoning about higher-order functions and dictionaries.

The stratification approach addresses circularity in the type system's metatheory.

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.