  The construction of an electron--positron collider "Higgs factory" has been
stalled for a decade, not because of feasibility but because of the cost of
conventional radio-frequency (RF) acceleration. Plasma-wakefield acceleration
promises to alleviate this problem via significant cost reduction based on its
orders-of-magnitude higher accelerating gradients. However, plasma-based
acceleration of positrons is much more difficult than for electrons. We propose
a collider scheme that avoids positron acceleration in plasma, using a mixture
of beam-driven plasma-wakefield acceleration to high energy for the electrons
and conventional RF acceleration to low energy for the positrons. We emphasise
the benefits of asymmetric energies, asymmetric bunch charges and asymmetric
transverse emittances. The implications for luminosity and experimentation at
such an asymmetric facility are explored and found to be comparable to
conventional facilities; the cost is found to be much lower. Some of the areas
in which R\&D is necessary to make HALHF a reality are highlighted,including
estimates for the improvement required in key technologies. These range from a
factor of 10 to a factor of 1000.
