[whitten]

As I recall, memorization usually involves associating the results of calling a pure function with the particular input values so the computation of the function is reduced to a lookup operation.

The calculation of the pure function is still used for any other combination of input values.

Supercompilation looks at the unevaluated symbolic recursive code and replaces the code in some cases with simpler, specialized code tuned to the actual input values, so does a memoizing not only of the result, but the code used to calculate the function to begin with.