Space-Efficient Blame Tracking for Gradual Types

Static and dynamic type systems have well-known strengths and weaknesses. Gradual typing provides the benefits of both in a single language by giving the programmer control over which portions of the program are statically typed and which portions are dynamically checked based on the presence or absence of type annotations. A compiler for a gradually typed language infers where the dynamic checks are needed and inserts casts into the intermediate language to perform these checks. Herman, Tomb, and Flanagan noticed that casts in higher-order languages can cause space leaks proportional to the execution time of the program. They developed a solution that merges sequences of casts. On a separate front, Findler and Wadler developed blame tracking for a language similar to the intermediate language of gradual typing. Blame tracking solves the problem of tracing a run-time cast failure back to the source of the error. Findler and Wadler proved that well-typed portions of a program can’t be blamed. Blame tracking requires extra information to be stored in casts and whether this information can be merged to obtain space efficiency is an open question. This paper answers the question in the affirmative by developing a dynamic semantics for gradual types that is both space efficient and tracks blame. This paper also improves the precision of blame tracking by reporting what part of the cast caused the error.