Types have been introduced to Genetic Programming (GP) by researchers with different motivation. We present the concept of types in GP and introduce a typed GP system, PolyGP, that supports polymorphism through the use of three different kinds of type variable. We demonstrate the usefulness of this kind of polymorphism in GP by evolving two polymorphic programs (nth and map) using the system. Based on the analysis of a series of experimental results, we conclude that this implementation of polymorphism is effective in assisting GP evolutionary search to generate these two programs. PolyGP may enhance the applicability of GP to a new class of problems that are difficult for other polymorphic GP systems to solve.