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

@article{paperbot1544,
  title = {Verified tensor-program optimization via high-level scheduling rewrites},
  author = {Amanda Liu and Gilbert Louis Bernstein and Adam Chlipala and Jonathan Ragan-Kelley},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {6},
  number = {POPL},
  year = {2022},
  doi = {10.1145/3498717}
}