A Linear First-Order Functional Intermediate Language for Verified Compilers

We present the linear first-order intermediate language IL for verified compilers. IL is a functional language with calls to a nondeterministic environment. We give IL terms a second, imperative semantic interpretation and obtain a register transfer language. For the imperative interpretation we establish a notion of live variables. Based on live variables, we formulate a decidable property called coherence ensuring that the functional and the imperative interpretation of a term coincide. We formulate a register assignment algorithm for IL and prove its correctness. The algorithm translates a functional IL program into an equivalent imperative IL program. Correctness follows from the fact that the algorithm reaches a coherent program after consistently renaming local variables. We prove that the maximal number of live variables in the initial program bounds the number of different variables in the final coherent program. The entire development is formalized in Coq.Comment: Addressed comments from reviewers (ITP 2015): (1) Added discussion of a paper in related work (2) Added definition of renamed-apart in appendix (3) Formulation changes in a coupe of place

Formal Verification of Coalescing Graph-Coloring Register Allocation

International audienceIterated Register Coalescing (IRC) is a widely used heuristic for performing register allocation via graph coloring. Many implementations in existing compilers follow (more or less faithfully) the imperative algorithm published in 1996. Several mistakes have been found in some of these implementations. In this paper, we present a formal verification (in Coq) of the whole IRC algorithm. We detail a specification that can be used as a reference for IRC. We also define the theory of register-interference graphs; we implement a purely functional version of the IRC algorithm, and we prove the total correctness of our implementation. The automatic extraction of our IRC algorithm into Caml yields a program with competitive performance. This work has been integrated into the CompCert verified compiler