  We report the Hall resistivity, $\rho_{xy}$ of polycrystalline
SmFeAsO$_{1-x}$F$_{x}$ for four different fluorine concentrations from the
onset of superconductivity through the collapse of the structural phase
transition. For the two more highly-doped samples, $\rho_{xy}$ is linear in
magnetic field up to 50 T with only weak temperature dependence, reminiscent of
a simple Fermi liquid. For the lightly-doped samples with $x<0.15$, we find a
low temperature regime characterized $\rho_{xy}(H)$ being both non-linear in
magnetic field and strongly temperature dependent even though the Hall angle is
small. The onset temperature for this non-linear regime is in the vicinity of
the structural phase (SPT)/spin density wave (SDW) transitions. The temperature
dependence of the Hall resistivity is consistent with a thermal activation of
carriers across an energy gap. The evolution of the energy gap with doping is
reported.
