A Higher-Order Abstract Syntax Approach to Verified Transformations on Functional Programs

We describe an approach to the verified implementation of transformations on functional programs that exploits the higher-order representation of syntax. In this approach, transformations are specified using the logic of hereditary Harrop formulas (HOHH). On the one hand, these specifications serve directly as implementations, being programs in the language λProlog. On the other hand, they can be used as input to the Abella system, which allows us to prove properties about them and thereby about the implementations. We argue that this approach is especially effective in realizing transformations that analyze binding structure. We consider in detail the case of typed closure conversion, a transformation that changes such structure in programs. We present a concise encoding of the transformation in λProlog and show how Abella can be used to prove the correctness of the encoding.