הבנת CHAD: פיתוח חדש לחישוב תלת-ממדי

תקציר מקורי באנגליתarXiv:2505.15002v3 Announce Type: replace-cross Abstract: Combinatory Homomorphic Automatic Differentiation (CHAD) was originally formulated as a semantics-driven source-to-source transformation for reverse-mode automatic differentiation of total functional programs. We extend CHAD to programs with partial operations, data-dependent conditionals, and while-loops, preserving its defining principle of structure-preserving semantics. Our main contribution is the introduction of iteration-extensive indexed categories, which integrate iteration into dependently typed programming languages. Iteration in the base category lifts to parameterized initial algebras in the indexed category, yielding fibred iteration on the op-Grothendieck construction. Its total category is the category of containers