In this paper we show that the tensor product technique for constructing variable bindings and for representing symbolic structure - used by Dolan and Dyer (1987) in parts of a connectionist story understanding model, and analyzed in general terms in Smolensky (1987) - can be effectively used to build a simplified version of Touretzky & Hinton's (1988) Distributed Connectionist Production System. The new system is called the Tensor Product Product System (TPPS).