We test the hypothesis that the classical and ultra-faint dwarf spheroidal satellites of the our Galaxy have been the building blocks of the Galactic halo by comparing their [O/Fe] and [Ba/Fe] vs. [Fe/H] patterns with the ones observed in Galactic halo stars. The [O/Fe] ratio deviates substantially from the observed abundance ratios in the Galactic halo stars for [Fe/H] > -2 dex, while they overlap for lower metallicities. On the other hand, for the neutron capture elements, the discrepancy is extended at all the metallicities, suggesting that the majority of stars in the halo are likely to have been formed in situ. We present the results for a model considering the effects of an enriched gas stripped from dwarf satellites on the chemical evolution of the Galactic halo. We find that the resulting chemical abundances of the halo stars depend on the adopted infall time-scale, and the presence of a threshold in the gas for star formation.