Implementing Memoization for Partial Evaluation

Memoization is a key ingredient in every partial evaluator. It enables folding by caching previously specialized functions. It is essential to make polyvariant specialization terminate. Its implementation is reasonably straightforward in a standard specializer that represents functions by closures. With the advent of handwritten program-generator generators (PGGs), implementing memoization gets harder, because PGGs use eecient standard representations of data at specialization time. We present several implementations of memoization for PGGs that are able to deal with all features of current partial evaluators, speciically partially static data and functions. The rst implementation is based on message passing. It is simple, portable, and eecient, but only suitable for untyped higher-order languages such as Scheme. The second implementation is geared towards typed language such as SML. Whereas the rst two implementations are completely portable, our third implementation exploits introspective features that may not be available in all implementations. Finally, we demonstrate that PGGs can solve the termination problem for partial evaluation. Our new incremental memoization algorithm performs incremental specialization and guarantees that specialization terminates whenever standard evaluation does. Partial evaluation is a powerful program-specialization technique based on constant propagation. Given the static (known) parameters of a source program, partial evaluation constructs a residual program|a specialized version of the program, which on application to the remaining dynamic parameters produces the same result as the original program applied to all parameters. OOine partial evaluation 10,18] consists of two phases, binding-time analysis (BTA) and static reduction. BTA transforms a program and the binding times (static/dynamic) of the parameters into an annotated program. Subsequently, the specializer applies the program to the static input, reducing static expressions and rebuilding dynamic ones.