  The chemical evolution of fluorine is investigated in a sample of Milky Way
red giantstars that span a significant range in metallicity from [Fe/H] $\sim$
-1.3 to 0.0 dex. Fluorine abundances are derived from vibration-rotation lines
of HF in high-resolution infraredspectra near $\lambda$ 2.335 $\mu$m. The red
giants are members of the thin and thick disk / halo,with two stars being
likely members of the outer disk Monoceros overdensity. At lowermetallicities,
with [Fe/H]<-0.4 to -0.5, the abundance of F varies as a primary element with
respect to the Fe abundance, with a constant subsolar value of [F/Fe] $\sim$
-0.3 to -0.4 dex. At larger metallicities, however, [F/Fe] increases rapidly
with [Fe/H] anddisplays a near-secondary behavior with respect to Fe.
Comparisons with various models of chemical evolution suggest that in the
low-metallicity regime (dominated hereby thick disk stars), a primary evolution
of $^{19}$F with Fe, with a subsolar [F/Fe] valuethat roughly matches the
observed plateau can be reproduced by a model incorporatingneutrino
nucleosynthesis in the aftermath of the core collapse in supernovae of type II
(SN II). A primary behavior for [F/Fe] at low metallicity is also observed for
a model including rapid rotating low-metallicity massive stars but this
overproduces [F/Fe] atlow metallicity. The thick disk red giants in our sample
span a large range of galactocentric distance (Rg $\sim$ 6--13.7 kpc), yet
display a $\sim$constant value of [F/Fe], indicating a very flat gradient (with
a slope of 0.02 $\pm$ 0.03 dex/kpc) of this elemental ratio over asignificant
portion of the Galaxy having|Z|>300 pc away from the Galaxy mid-plane.
