The suggestion that roughly half the mass of the Galactic halo might b
e in the form of white dwarfs, together with the limits on its mass fr
action in faint red stars and on the initial metallicity of the Galact
ic disk, would set strong constraints on the initial mass function (IM
F) 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 that 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 Type Ia (thermonuclear) supernovae that would later be produced f
rom the halo white dwarf population. We find that, for most of the evo
lutionary scenarios for the Type Ia supernova progenitor systems propo
sed so far, constraints on the white dwarf mass fraction in the halo f
rom the predicted production of iron would be extremely severe. When t
he predicted iron excess is not so large, the exceedingly high Type la
supernova rate predicted for the present time would also exclude a ma
jor contribution of white dwarfs to the halo mass. The white dwarf con
tribution, in all cases, should be below 5%-10%. Besides, for the IMFs
considered, the duration of the halo burst should be shorter than 1 G
yr in order to avoid too large a spread in the iron abundances of Popu
lation II halo dwarfs, and the predicted halo [O/Fe] ratio would be at
odds with observations.