In this paper we first review the main results obtained in the theory of schemata in Genetic Programming (GP) emphasising their strengths and weakneses. Then we propose a new, simpler definition of the concept of schema for GP which is quite close to the original concept of schema in genetic algorithms (GAs). Along with a new form of crossover, one-point crossover, and point mutation this concept of schema has been used to derive an imporved schema theorem for GP which describes the propagation of schemata from one generation to the next. In the paper we discuss this result and show that our schemea theorem is the natural counterpart for GP of the schema theorem for GAs, to which it asymptotically converges.
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