Programming type-safe transformations using higher-order abstract syntax

When verifying that compiler phases preserve some property of the compiled program, a major difficulty resides in how to represent and manipulate variable bindings, often imposing extra complexity both on the compiler writer and the verification effort. In this paper, we show how Beluga's dependent contextual types let us use higher-order abstract syntax (HOAS) to implement a type-preserving compiler for the simply-typed lambda-calculus, including transformations such as closure conversion and hoisting. Unlike previous implementations, which have to abandon HOAS locally in favor of a first-order binder representation, we are able to take advantage of HOAS throughout the compiler pipeline, so that the compiler code stays clean and we do not need extra lemmas about binder manipulation. Our work demonstrates that HOAS encodings offer substantial benefits to certified programming. Scope and type safety of the code transformations are statically guaranteed, and our implementation nicely mirrors the paper proof of type preservation, and can hence be seen as an encoding of the proof which happens to be executable as well.