  We exploit the recent observations of extremely metal-poor (EMP) stars in the
Galactic halo and investigate the constraints on the IMF of the stellar
population that left these low-mass survivors of [Fe/H]<-2.5 and the chemical
evolution that they took part in. A high-mass IMF with the typical mass~10Msun
and the overwhelming contribution of low-mass members of binaries to the EMP
survivors are derived from the statistics of carbon-enriched EMP stars with and
without the enhancement of s-process elements (Komiya et al. 2007). We first
examine the analysis to confirm their results for various assumptions on the
mass-ratio distribution function. As compared with the uniform distribution,
the increase or decrease function of the mass ratio gives a higher- or
lower-mass IMF, and a lower-mass IMF results for the independent distribution
with the both members in the same IMF, but the derived ranges of typical mass
differ less than by a factor of two and overlap for the extreme cases.
Furthermore, we prove that the same constraints are placed on the IMF from the
surface density of EMP stars estimated from the surveys and the chemical
evolution consistent with the metal yields of theoretical supernova models. We
then apply the derived high-mass IMF with the binary contribution to show that
the observed MDF of EMP stars can be reproduced not only for the shape but also
for the number of EMP stars. In particular, the scarcity of stars below
[Fe/H]<-4 is naturally explained in terms of the hierarchical structure
formation, and there is no indication of significant changes in the IMF for the
EMP Population. The present study indicates that 3 HMP stars of [Fe/H]<-4 are
the primordial stars that were born as the low-mass members of binaries before
the host clouds were polluted by their own supernovae.
