  Aims: We study single and binary white dwarfs in the inner halo of the Milky
Way in order to learn more about the conditions under which the population of
halo stars was born, such as the initial mass function (IMF), the star
formation history, or the binary fraction. Methods: We simulate the evolution
of low-metallicity halo stars at distances up to ~ 3 kpc using the binary
population synthesis code SeBa. We use two different white dwarf cooling models
to predict the present-day luminosities of halo white dwarfs. We determine the
white dwarf luminosity functions (WDLFs) for eight different halo models and
compare these with the observed halo WDLF of white dwarfs in the SuperCOSMOS
Sky Survey. Furthermore, we predict the properties of binary white dwarfs in
the halo and determine the number of halo white dwarfs that is expected to be
observed with the Gaia satellite. Results: By comparing the WDLFs, we find that
a standard IMF matches the observations more accurately than a top-heavy one,
but the difference with a bottom-heavy IMF is small. A burst of star formation
13 Gyr ago fits slightly better than a star formation burst 10 Gyr ago and also
slightly better than continuous star formation $10-13$ Gyrs ago. Gaia will be
the first instrument to constrain the bright end of the field halo WDLF, where
contributions from binary WDs are considerable. Many of these will have He
cores, of which a handful have atypical surface gravities ($\log g < 6$) and
reach luminosities $\log(L/L_\odot) > 0$ in our standard model for WD cooling.
These so called pre-WDs, if observed, can help us to constrain white dwarf
cooling models and might teach us something about the fraction of halo stars
that reside in binaries.
