In Chapter 16 of "The Seasoned Schemer", the authors define a recursive procedure "depth", which returns 'pizza nested in n lists, e.g (depth 3) is (((pizza))). They then improve it as "depthM", which caches its return values using set! in the lists Ns and Rs, which together form a lookup-table, so you don't have to recurse all the way down if you reach a return value you've seen before. E.g. If I've already computed (depthM 8), when I later compute (depthM 9), I just lookup the return value of (depthM 8) and cons it onto null, instead of recursing all the way down to (depthM 0).

But then they move the Ns and Rs inside the procedure, and initialize them to null with "let". Why doesn't this completely defeat the point of caching the return values? From a bit of experimentation, it appears that the Ns and Rs are being reinitialized on every call to "depthM".

Am I misunderstanding their point?

I guess my question is really this: Is there a way in Scheme to have lexically-scoped variables preserve their values in between calls to a procedure, like you can do in Perl 5.10 with "state" variables?