Deep and shallow types for gradual languages

Sound gradual types come in many forms and offer varying levels of soundness. Two extremes are deep types and shallow types. Deep types offer compositional guarantees but depend on expensive higher-order contracts. Shallow types enforce only local properties, but can be implemented with first-order checks. This paper presents a language design that supports both deep and shallow types to utilize their complementary strengths.

In the mixed language, deep types satisfy a strong complete monitoring guarantee and shallow types satisfy a firstorder notion of type soundness. The design serves as the blueprint for an implementation in which programmers can easily switch between deep and shallow to leverage their distinct advantages. On the GTP benchmark suite, the median worst-case overhead drops from several orders of magnitude down to 3x relative to untyped. Where an exhaustive search is feasible, 40% of all configurations run fastest with a mix of deep and shallow types.