In SICP Chapter 4, the metacircular evaluator is modified by separating the syntax analysis from the execution, making the eval procedure look like:
(define (eval exp env)
((analyze exp) env))
and the book says that this will save work since analyze will be called once on an expression, while the execution procedure may be called many times.
My question is, how does this optimization work? It will work for recursive procedure calls, but how about other cases? The evaluator evaluates expressions one after another, eval will still be called on each expression even if they have identical forms.
You need to see several things: (a) the analyze function walks over each expression exactly once, (b) there is no code outside of analyze that scans the syntax, (c) the function that analyze returns does not call itself therefore running that function never leads to any further scanning of the syntax, (d) this is all unlike the usual evaluation functions where calling a function twice means that its syntax is scanned twice.
BTW, a much better name for analyze is compile -- it really does translate the input language (sexprs) to a target one (a function, acting as the machine code here).