Date and Darwen have proposed a theory of types, the latter forms the basis of a detailed presentation of a panoply of simple and complex types. However, this proposal has not been structured in a formal system. Specifically, Date and Darwen haven't indicated the formalism of the type system that corresponds to the type theory established. In this paper, we propose a pseudo-algorithmic and grammatical description of a system of types for Date and Darwen's model. Our type system is supposed take into account null values; for such intention, we introduce a particular type noted #, which expresses one or more occurrences of incomplete information in a database. Our algebraic grammar describes in detail the complete specification of an inheritance model and the subryping relation induced, thus the different definitions of related concepts.