This paper reports on the development and formal certification (proof of semantic preservation) of a compiler from Cminor (a C-like imperative language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a certified compiler is useful in the context of formal methods applied to the certification of critical software: the certification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well.

Abstract. This paper illustrates the use of coinductive definitions and proofs in big-step operational semantics, enabling the latter to describe diverging evaluations in addition to terminating evaluations. We show applications to proofs of type soundness and to proofs of semantic preservation for compilers. 1

This paper presents a formal description of a small functional language with dependent types. The language contains data types, mutual recursive/inductive definitions and a universe of small types. The syntax, semantics and type system is specified in such a way that the implementation of a parser, interpreter and type checker is straightforward. The main difficulty is to design the conversion algorithm in such a way that it works for open expressions. The paper ends with a complete implementation in Haskell (around 400 lines of code).

Type checkers for dependent types need to evaluate user defined functions during type checking. For this, current implementations typically use an interpreter, which has drawbacks. We show, how at this stage compiled code can be used for a language with lazy evaluation.