  Magnetic reconnection provides the primary source for explosive energy
release, plasma heating and particle acceleration in many astrophysical
environments. The last years witnessed a revival of interest in the MHD tearing
instability as a driver for efficient reconnection. It has been established
that, provided the current sheet aspect ratio becomes small enough ($a/L \sim
S^{-1/3}$ for a given Lundquist number $S\gg 1$), reconnection occurs on ideal
Alfv\'en timescales and becomes independent on $S$. Here we investigate, by
means of two-dimensional simulations, the \emph{ideal} tearing instability in
the Hall-MHD regime, which is appropriate when the width of the resistive layer
$\delta$ becomes comparable to the ion inertial length $d_i$. Moreover, we
study in detail the spontaneous development and reconnection of secondary
current sheets, which for high $S$ naturally adjust to the ideal aspect ratio
and hence their evolution proceeds very rapidly. For moderate low $S$, the
aspect ratio tends to the Sweet-Parker scaling ($a/L \sim S^{-1/2}$), in order
to fulfill the condition $\delta \ll a$ necessary for the onset of a tearing
instability. When the Hall term is included, the reconnection rate of this
secondary nonlinear phase is enhanced and, depending on the ratio $d_i/\delta$,
can be twice with respect to the pure MHD case, and up to ten times larger than
the linear phase. Therefore, the evolution of the tearing instability in thin
current sheets in the Hall-MHD regime naturally leads to an explosive
disruption of the reconnecting site and to energy release on super-Alfv\'enic
timescales, as required to explain astrophysical observations.
