Compiling with dependent types

Abstract

Dependently typed languages have proven useful for developing large-scale fully verified software, but we do not have any guarantees after compiling that verified software. A verified program written in a dependently typed language, such as Coq, can be type checked to ensure that the program meets its specification. Similarly, type checking prevents us from importing a library and violating the specification declared by its types. Unfortunately, we cannot perform either of these checks after compiling a dependently typed program, since all current implementations erase types before compiling the program. Instead, we must trust the compiler to not introduce errors into the verified code, and, after compilation, trust the programmer to never introduce errors by linking two incompatible program components. As a result, the compiled and linked program is not verified---we have no guarantees about what it will do. In this dissertation, I develop a theory for preserving dependent types through compilation so that we can use type checking after compilation to check that no errors are introduced by the compiler or by linking. Type-preserving compilation is a well-known technique that has been used to design compilers for non-dependently typed languages, such as ML, that statically enforce safety and security guarantees in compiled code. But there are many open challenges in scaling type preservation to dependent types. The key problems are adapting syntactic type systems to interpret low-level representations of code, and breaking the complex mutually recursive structure of dependent type systems to make proving type preservation and compiler correctness feasible. In this dissertation, I explain the concepts required to scale type preservation to dependent types, present a proof architecture and language design that support type preservation, and prove type preservation and compiler correctness for four early-stage compiler translations of a realistic dependently typed calculus. These translations include an A-normal form (ANF), a continuation-passing style (CPS), an abstract closure conversion, and a parametric closure conversion translation.