An Internalist Approach to Correct-by-Construction Compilers

In this paper we present a methodology to organize the construction of a correct compiler, taking advantage of the power of full dependently type systems. The basic idea consists in decorating the abstract syntax of languages with their semantics, allowing to express the correctness of the compiler at type level. We show our methodology in a first small example and then explore how it can be promoted to more realistic languages, realizing that our internalistic approach is feasible for defining a correct-by-construction compiler from an imperative language with conditional iteration to a stack based intermediate language. We also show how this methodology can be combined with the externalist approach, compiling from the intermediate language to an assembly-like low level code and separately proving its correctness.