lambda. 2.2 Visualizing Witnesses. We have described how to reliably find witnesses to type errors in OCAML, but this do
Dynamic Witnesses for Static Type Errors ∗ (or, Ill-Typed Programs Usually Go Wrong) Eric L. Seidel
Ranjit Jhala
Westley Weimer
UC San Diego, USA
University of Virginia, USA
{eseidel,jhala}@cs.ucsd.edu
[email protected]
Abstract Static type errors are a common stumbling block for newcomers to typed functional languages. We present a dynamic approach to explaining type errors by generating counterexample witness inputs that illustrate how an ill-typed program goes wrong. First, given an ill-typed function, we symbolically execute the body to synthesize witness values that make the program go wrong. We prove that our procedure synthesizes general witnesses in that if a witness is found, then for all inhabited input types, there exist values that can make the function go wrong. Second, we show how to extend the above procedure to produce a reduction graph that can be used to interactively visualize and debug witness executions. Third, we evaluate the coverage of our approach on two data sets comprising over 4,500 ill-typed student programs. Our technique is able to generate witnesses for 88% of the programs, and our reduction graph yields small counterexamples for 81% of the witnesses. Finally, we evaluate whether our witnesses help students understand and fix type errors, and find that students presented with our witnesses show a greater understanding of type errors than those presented with a standard error message.
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Categories and Subject Descriptors D.3.2 [Programming Languages]: Language Classifications—Applicative (functional) languages; D.3.4 [Programming Languages]: Processors—Debuggers; F.3.3 [Logics and Meanings of Programs]: Studies of Program Constructs—Type structure
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