A Unifying Framework for Type Inhabitation

In this paper we define a framework to address different kinds of problems related to type inhabitation, such as type checking, the emptiness problem, generation of inhabitants and counting, in a uniform way. Our framework uses an alternative representation for types, called the pre-grammar of the type, on which different methods for these problems are based. Furthermore, we define a scheme for a decision algorithm that, for particular instantiations of the parameters, can be used to show different inhabitation related problems to be in PSPACE