Nathanaƫl Courant and Xavier Leroy. Verified code generation for the polyhedral model. Proc. ACM Program. Lang., 5(POPL):40:1--40:24, 2021.

The polyhedral model is a high-level intermediate representation for loop nests that supports elegantly a great many loop optimizations. In a compiler, after polyhedral loop optimizations have been performed, it is necessary and difficult to regenerate sequential or parallel loop nests before continuing compilation. This paper reports on the formalization and proof of semantic preservation of such a code generator that produces sequential code from a polyhedral representation. The formalization and proofs are mechanized using the Coq proof assistant.

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