We describe a natural language parser that uses type information to determine the grammatical structure of simple sentences and phrases. This stands in contrast to studies of type inference where types and grammatical structure play opposite roles, the former being determined by the latter. Our parser is implemented in Haskell and is based on a linguistic theory called applicative universal grammar (AUG). Our results should be interesting to computer scientists in the way in which AUG relates to types and combinatory calculus, and to linguists in the way in which a very simple, brute force parsing strategy performs surprisingly well in both performance and accuracy.