Abstract. This paper presents the formal verification of a compiler front-end that translates a subset of the C language into the Cminor intermediate language. The semantics of the source and target languages as well as the translation between them have been written in the specification language of the Coq proof assistant. The proof of observational semantic equivalence between the source and generated code has been machine-checked using Coq. An executable compiler was obtained by automatic extraction of executable Caml code from the Coq specification of the translator, combined with a certified compiler back-end generating PowerPC assembly code from Cminor, described in previous work.
Abstract. Transformation to continuation-passing style (CPS) is often performed by optimizing compilers for functional programming languages. As part of the development and proof of correctness of a compiler for the mini-ML functional language, we have mechanically verified the correctness of two CPS transformations for a call-by-value λ-calculus with n-ary functions, recursive functions, data types and pattern-matching. The transformations generalize Plotkin's original call-by-value transformation and Danvy and Nielsen's optimized transformation, respectively. We used the Coq proof assistant to formalize the transformations and conduct and check the proofs. Originalities of this work include the use of big-step operational semantics to avoid difficulties with administrative redexes, and of two-sorted de Bruijn indices to avoid difficulties with α-conversion.
Function uncurrying is an important optimization for the efficient execution of functional programming languages. This optimization replaces curried functions by uncurried, multiple-argument functions, while preserving the ability to evaluate partial applications. First-order uncurrying (where curried functions are optimized only in the static scopes of their definitions) is well understood and implemented by many compilers, but its extension to higher-order functions (where uncurrying can also be performed on parameters and results of higher-order functions) is challenging. This article develops a generic framework that expresses higher-order uncurrying optimizations as type-directed insertion of coercions, and prove its correctness. The proof uses step-indexed logical relations and was entirely mechanized using the Coq proof assistant.
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