  The suggestion that roughly half the mass of the galactic halo might be in
the form of white dwarfs, together with the limits on the infrared background
light and on the initial metallicity of the galactic disk, would set strong
constraints on the initial mass function (IMF) of the halo. Particular IMFs
have been proposed to cut off both the numbers of low-mass stars contributing
to the infrared background and of high-mass stars which contribute to the
growth of metallicity when they promptly explode as gravitational-collapse
(Type II and Type Ib/c) supernovae. Here we examine the further contribution to
metallicity from the Type Ia (thermonuclear) supernovae which would later be
produced from the halo white dwarf population. We find that, for most of the
evolutionary scenarios for the Type Ia supernova progenitor systems proposed so
far, the constraints on the white dwarf mass fraction in the halo from the
predicted production of iron would be extremely severe. When the predicted iron
excess is not so large, then the exceedingly high Type Ia supernova rate
predicted for the present time would also exclude a major contribution of white
dwarfs to the halo mass. The white dwarf contribution, in all cases, should be
below 5-10%. Besides, for the IMFs considered, the duration of the halo burst
should be shorter than 1 Gyr in order to avoid too large a spread in the iron
abundances of Population II halo dwarfs, and the predicted halo $[O/Fe]$ ratio
would be at odds with observations.
