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Gradual typing has emerged as a popular design point in programming languages, attracting significant interests from both academia and industry. Programmers in gradually typed languages are free to utilize static and dynamic typing as needed. To make such languages sound, runtime checks mediate the boundary of typed and untyped code. Unfortunately, such checks can incur significant runtime overhead on programs that heavily mix static and dynamic typing. To combat this overhead without necessitating changes to the underlying implementations of languages, we presentdiscriminative typing. Discriminative typing works by optimistically inferring types for functions and implementing an optimized version of the function based on this type. To preserve safety it also implements an un-optimized version of the function based purely on the provided annotations. With two versions of each function in hand, discriminative typing translates programs so that the optimized functions are called as frequently as possible while also preserving program behaviors. We have implemented discriminative typing in Reticulated Python and have evaluated its performance compared to guarded Reticulated Python. Our results show that discriminative typing improves the performance across 95% of tested programs, when compared to Reticulated, and achieves more than 4× speedup in more than 56% of these programs. We also compare its performance against a previous optimization approach and find that discriminative typing improved performance across 93% of tested programs, with 30% of these programs receiving speedups between 4 to 25 times. Finally, our evaluation shows that discriminative typing remarkably reduces the overhead of gradual typing on many mixed type configurations of programs. In addition, we have implemented discriminative typing in Grift and evaluated its performance. Our evaluation demonstrations that DT significantly improves performance of Grift. 

Gradual typing allows programmers to use both static and dynamic typing in a single program. However, a well-known problem with sound gradual typing is that the interactions between static and dynamic code can cause significant performance degradation. These performance pitfalls are hard to predict and resolve, and discourage users from using gradual typing features. For example, when migrating to a more statically typed program, often adding a type annotation will trigger a slowdown that can be resolved by adding more annotations elsewhere, but since it is not clear where the additional annotations must be added, the easier solution is to simply remove the annotation. To address these problems, we develop: (1) a static cost semantics that accurately predicts the overhead of static-dynamic interactions in a gradually typed program, (2) a technique for efficiently inferring such costs for all combinations of inferrable type assignments in a program, and (3) a method for translating the results of this analysis into specific recommendations and explanations that can help programmers understand, debug, and optimize the performance of gradually typed programs. We have implemented our approach in Herder, a tool for statically analyzing the performance of different typing configurations for Reticulated Python programs. An evaluation on 15 Python programs shows that Herder can use this analysis to accurately and efficiently recommend type assignments that optimize the performance of these programs without sacrificing the safety guarantees provided by static typing.