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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 present discriminative 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 

Abstract Gradual typing allows programs to enjoy the benefits of both static typing and dynamic typing. While it is often desirable to migrate a program from more dynamically typed to more statically typed or vice versa, gradual typing itself does not provide a way to facilitate this migration. This places the burden on programmers who have to manually add or remove type annotations. Besides the general challenge of adding type annotations to dynamically typed code, there are subtle interactions between these annotations in gradually typed code that exacerbate the situation. For example, to migrate a program to be as static as possible, in general, all possible combinations of adding or removing type annotations from parameters must be tried out and compared. In this paper, we address this problem by developing migrational typing , which efficiently types all possible ways of replacing dynamic types with fully static types for a gradually typed program. The typing result supports automatically migrating a program to be as static as possible or introducing the least number of dynamic types necessary to remove a type error. The approach can be extended to support user-defined criteria about which annotations to modify. We have implemented migrational typing and evaluated it on large programs. The results show that migrational typing scales linearly with the size of the program and takes only 2–4 times longer than plain gradual typing.