Verified tensor-program optimization via high-level scheduling rewrites

We present a lightweight Coq framework for optimizing tensor kernels written in pure, functional array language. Optimizations rely on user scheduling using series of verified, semantics-preserving rewrites. Unusually compilation targeting imperative code with arrays and nested loops, all rewrites are source-to-source within purely Our language comprises set core constructs expressing high-level computation detail what we call reshape operators, which can be derived from but trigger low-level decisions about storage patterns ordering. demonstrate that not only is this system capable deriving the optimizations existing state-of-the-art languages like Halide generating comparably performant code, it also able to schedule family useful program transformations beyond reachable Halide.