A key challenge when statically typing so-called dynamic languages is the ubiquity of value-based overloading, where a given function can dynamically reflect upon and behave according to the types of its arguments. Thus, to establish basic types, the analysis must reason precisely about values, but in the presence of higher-order functions and polymorphism, this reasoning itself can require basic types. We address this chicken-and-egg problem by introducing the framework of two-phased typing. The first “trust” phase performs classical, i.e. flow-, path- and value-insensitive type checking to assign basic types to various program expressions. When the check inevitably runs into “errors” due to value-insensitivity, it wraps problematic expressions with DEAD-casts, which explicate the trust obligations that must be discharged by the second phase. The second phase uses refinement typing, a flow- and path-sensitive analysis, that decorates the first phase’s types with logical predicates to track value relationships and thereby verify the casts and establish other correctness properties. First, we empirically demonstrate the ubiquity of value-based overloading. Next, we distill it into a core source language with union and intersection types. We formalize the trust phase as an elaboration to a simply typed target language without overloading, but with DEAD-casts and formalize the second phase that discharges the casts via classical refinement typing. Finally, we prove the equivalence of source and target to establish the end-to-end soundness of two-phase typing, thereby providing a new foundation for building static analyses for dynamic languages.
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