Type checking and type inference are important concepts and methods of programming languages and software engineering. Type checking is a way to ensure some level of consistency, depending on the type system, in large programs and in complex assemblies of software components. Type inference provides powerful static analyses of pre-existing programs without types, and facilitates the use of type systems by freeing the user from entering type information. In this paper, we investigate the application of these concepts to systems biology. More specifically, we consider the Systems Biology Markup Language SBML and the Biochemical Abstract Machine BIOCHAM with their repositories of models of biochemical systems. We study three type systems: one for checking or inferring the functions of proteins in a reaction model, one for checking or inferring the activation and inhibition effects of proteins in a reaction model, and another one for checking or inferring the topology of compartments or locations. We show that the framework of abstract interpretation elegantly applies to the formalization of these abstractions and to the implementation of linear time type checking as well as type inference algorithms. Through some examples, we show that the analysis of biochemical models by type inference provides accurate and useful information. Interestingly, such a mathematical formalization of the abstractions used in systems biology already provides some guidelines for the extensions of biochemical reaction rule languages.