The ordering of reductions

Evaluation Order and Infinite Lists - slide 14 : 27

Given a complex expression, there are many different orderings of the applicable reductions

Using normal-order reduction, the first reduction to perform is the one at the outer level of the expression (the leftmost reduction first).

Using applicative-order reduction, the first reduction to perform is the inner leftmost reduction.

Normal-order reduction represents evaluation by need
Applicative-order reduction evaluates all constituent expressions, some of which are unnecessary or perhaps even harmful.
- As such, there is often a need to control the evaluation process with special forms that use non-standard evaluation strategies