In recent years, there has been an increased interest in tools that establish incorrectness rather than correctness of program properties. In this work we build on this approach by developing a novel methodology to prove incorrectness of semantic typing properties of functional programs, extending the incorrectness approach to the model theory of functional program typing. We define a semantic type refuter which refutes semantic typings for a simple functional language. We prove our refuter is co-recursively enumerable, and that it is sound and complete with respect to a semantic typing notion. An initial implementation is described which uses symbolic evaluation to efficiently find type errors over a functional language with a rich type system.

@article{abs-2409-13896,
  title = {Semantic-Type-Guided Bug Finding},
  author = {Kelvin Qian and Scott Smith and Brandon Stride and Shiwei Weng and Ke Wu},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {8},
  number = {OOPSLA2},
  year = {2024},
  doi = {10.1145/3689788}
}