  Treating inflation as an effective theory, we expect the effective Lagrangian
to contain higher-dimensional kinetic operators suppressed by the scale of UV
physics. When these operators are powers of the inflaton kinetic energy, the
scalar field can support a period of noncanonical inflation which is smoothly
connected to the usual slow-roll inflation. We show how to construct
noncanonical inflationary solutions to the equations of motion for the first
time, and demonstrate that noncanonical inflation is an attractor in phase
space for all small- and large-field models. We identify some sufficient
conditions on the functional form of the Lagrangian that lead to successful
noncanonical inflation since not every Lagrangian with higher-dimensional
kinetic operators can support noncanonical inflation. This extends the class of
known viable Lagrangians and excludes many Lagrangians which do not work.
