Zaynah Dargaye and Xavier Leroy. Mechanized verification of CPS transformations. In Logic for Programming, Artificial Intelligence and Reasoning, 14th Int. Conf. LPAR 2007, volume 4790 of Lecture Notes in Artificial Intelligence, pages 211-225. Springer, 2007.

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.

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