# Jones-Optimal Partial Evaluation by Specialization-Safe Normalization

• Matt Brown
• Jens Palsberg

We present partial evaluation by specialization-safe normalization, a novel partial evaluation technique that is Jones-optimal, that can be self-applied to achieve the Futamura projections and that can be type-checked to ensure it always generates code with the correct type. Jones-optimality is the gold-standard for nontrivial partial evaluation and guarantees that a specializer can remove an entire layer of interpretation. We achieve Jones-optimality by using a novel affine-variable static analysis that directs specialization-safe normalization to always decrease a program’s runtime.

We demonstrate the robustness of our approach by showing Jones-optimality in a variety of settings. We have formally proved that our partial evaluator is Jones-optimal for call-by-value reduction, and we have experimentally shown that it is Jones-optimal for call-by-value, normal-order, and memoized normal-order. Each of our experiments tests Jones-optimality with three different self-interpreters.

We implemented our partial evaluator in F$_\omega^{\mu i}$, a recent language for typed self-applicable meta-programming. It is the first Jones-optimal and self-applicable partial evaluator whose type guarantees that it always generates type-correct code.