Formalizing Machine Knitting: Towards Optimizing Compilers via Category Theory

This blog post explores the surprising connection between machine knitting and theoretical computer science. The author tackles the problem of defining rigorous semantics for machine knitting programs, highlighting the challenge of strand crossings and their impact on program commutativity. By leveraging algebraic topology and the theory of braided monoidal categories, a polynomial-time algorithm for program canonicalization is developed. This enables compiler optimization and opens doors for more sophisticated analysis and design of machine knitting languages. The work bridges programming languages, topology, category theory, and even hints at connections to quantum computing.