Effective Reduction and Conversion Strategies for Combinators

We imagine that we are computing with combinators or lambda terms and that successive terms are related by one-step reduction or expansion. We have a term on our screen and we want to click on a redex to be reduced (or expanded) to obtain the next screenful. The choice of redex is determined by a strategy for achieving our ends. Such a strategy must be effective in the sense of being computable. Memory is a serious constraint, since only one term fits on our screen at a time.