Is GP Crossover a Local Search Operator ?

In this short paper, backed by probabilistic calculations, a simple model and two experiments, I suggest that standard crossover in GP is a local search operator in the sense that it produces offspring which inherit most of their code from one parent most of the times. This is in strong contrast with the crossover operators used in linear GAs and might cause GP to explore only a small part of the search space and to get easily stuck in local optima.