We present an algorithm that canonicalizes the algebraic representations of the topological semantics of machine knitting programs. Machine knitting is a staple technology of modern textile production where hundreds of mechanical needles are manipulated to form yarn into interlocking loop structures. Our semantics are defined using a variant of a monoidal category, and they closely correspond to string diagrams. We formulate our canonicalization as an Abstract Rewriting System (ARS) over words in our category, and prove that our algorithm is correct and runs in polynomial time.

@article{paperbot3049,
  title = {Polynomial-Time Program Equivalence for Machine Knitting},
  author = {Nathan Hurtig and Jenny Han Lin and Thomas S. Price and Adriana Schulz and James McCann and Gilbert Louis Bernstein},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {9},
  number = {ICFP},
  year = {2025},
  doi = {10.1145/3747517}
}