Property-based testing uses randomly generated inputs to validate high-level program specifications. It can be shockingly effective at finding bugs, but it often requires generating a very large number of inputs to do so. In this paper, we apply ideas from combinatorial testing, a powerful and widely studied testing methodology, to modify the distributions of our random generators so as to find bugs with fewer tests. The key concept is combinatorial coverage, which measures the degree to which a given set of tests exercises every possible choice of values for every small combination of input features. In its “classical” form, combinatorial coverage only applies to programs whose inputs have a very particular shape—essentially, a Cartesian product of finite sets. We generalize combinatorial coverage to the richer world of algebraic data types by formalizing a class of sparse test descriptions based on regular tree expressions. This new definition of coverage inspires a novel combinatorial thinning algorithm for improving the coverage of random test generators, requiring many fewer tests to catch bugs. We evaluate this algorithm on two case studies, a typed evaluator for System F terms and a Haskell compiler, showing significant improvements in both
