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  1. Sound gradual types come in many forms and offer varying levels of soundness. Two extremes are deep types and shal- low 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 com- plete monitoring guarantee and shallow types satisfy a first- order 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 dis- tinct 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. 
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