Semantic-Type-Guided Bug Finding
Kelvin Qian, Scott Smith, Brandon Stride, Shiwei Weng, Ke Wu
TL;DR
A semantic type refuter is defined which refutes semantic typings for a simple functional language and is proved to be co-recursively enumerable, and that it is sound and complete with respect to a semantic typing notion.
Abstract
In recent years, there has been an increased interest in tools that establish \emph{incorrectness} rather than correctness of program properties. In this work we build on this approach by developing a novel methodology to prove incorrectness of \emph{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.