  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.
