Mechanically Verifying the Correctness of an Offline Partial Evaluator

We show that using deductive systems to specify an offline partial evaluator allows one to specify, prototype, and mechanically verify correctness via meta-programming — all within a single framework. For a λ-mix-style partial evaluator, we specify binding-time constraints using a natural-deduction logic, and the associated program specializer using natural (aka “deductive”) semantics. These deductive systems can be directly encoded in the Elf programming language — a logic programming language based on the LF logical framework. The specifications are then executable as logic programs. This provides a prototype implementation of the partial evaluator. Moreover, since deductive system proofs are accessible as objects in Elf, many aspects of the partial evaluator correctness proofs (e.g., the correctness of binding-time analysis) can be coded in Elf and mechanically checked.