We have successfully synthesized the fluoride-arsenide compounds Ca$_{1-x}$RE$_x$FeAsF (RE=Nd, Pr; x=0, 0.6). The x-ray powder diffraction confirmed that the main phases of our samples are Ca$_{1-x}$RE$_x$FeAsF with the ZrCuSiAs structure. By measuring resistivity, superconductivity was observed at 57.4 K in Nd-doped and 52.8 K in Pr-doped samples with x=0.6. Bulk superconductivity was also proved by the DC magnetization measurements in both samples. Hall effect measurements revealed hole-like charge carriers in the parent compound CaFeAsF with a clear resistivity anomaly below 118 K, while the Hall coefficient $R_H$ in the normal state is negative for the superconducting samples Ca$_{0.4}$Nd$_{0.6}$FeAsF and Ca$_{0.4}$Pr$_{0.6}$FeAsF. This indicates that the rare earth element doping introduces electrons into CaFeAsF which induces the high temperature superconductivity.
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