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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.doi:10.4230/lipics.fscd.2018.5 dblp:conf/rta/AlvesB18 fatcat:a5f5vez3inbgjo5qnsi6iad7da