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The chemodynamical evolution of a galaxy is a function of several processes including stellar evolution, chemical enrichment, disk heating, radial migration, and extragalactic interactions. The particular combination of processes is embedded in the phase-space and abundance distributions of the stars, and therefore these distributions serve as fossils of a galaxy's formation history.

I describe a further generalization of the extended action-based distribution functions (EDFs) for the Milky Way presented in Sanders et al. 2015 (arXiv:1501.02227) and Das et al. 2016 (arXiv:1603.09332 and arXiv:1608.07297) to incorporate alpha abundances and chemical-kinematic correlations in the thick disk. The functions are thus able to reconstruct separate thick disk, thin disk, and stellar halo populations, and stellar population gradients within them. Using alpha abundance as a proxy for age, observations such as the flaring of the thin disk with age can be reproduced. The functions are fit to eight-dimensional data (phase-space coordinates, metallicity, alpha-abundance) for stars in the TGAS-APOGEE catalogue, thus exploiting some of the best proper motions and abundances available. The complex selection function of the cross-match is conveniently modelled within a Bayesian framework illustrating the power of EDFs for creating state-of-the-art models of Galaxy formation and evolution.