We explore a novel approach to higher-order program analysis which brings ideas of on-demand lookup from first-order CFL-reachability program analyses to higher-order programs. The analysis needs to produce only a control-flow graph; it can derive all other information including values of variables directly from the graph. Several challenges had to be overcome, including how to build the control-flow graph on-the-fly and how to deal with nonlocal variables in functions. The resulting analysis is flow- and context-sensitive with a provable polynomial-time bound. The analysis is formalized and proved correct and terminating, and an initial implementation is described.
