  The simplest interpretation of the microlensing events observed towards the
Large Magellanic Clouds is that approximately half of the mass of the Milky Way
halo is in the form of MAssive Compact Halo Objects with $M \sim 0.5
M_{\odot}$. It is not possible, due to limits from star counts and chemical
abundance arguments, for faint stars or white dwarves to comprise such a large
fraction of the halo mass. This leads to the consideration of more exotic lens
candidates, such as primordial black holes, or alternative lens locations. If
the lenses are located in the halo of the Milky Way, then constraining their
mass function will shed light on their nature. Using the current microlensing
data we find, for four halo models, the best fit parameters for delta-function,
primordial black hole and various power law mass functions. The best fit
primordial black hole mass functions, despite having significant finite width,
have likelihoods which are similar to, and for one particular halo model
greater than, those of the best fit delta functions . We then use Monte Carlo
simulations to investigate the number of microlensing events necessary to
determine whether the MACHO mass function has significant finite width. If the
correct halo model is known, then $\sim$ 500 microlensing events will be
sufficient, and will also allow determination of the mass function parameters
to $\sim 5%$.
