TensorVjpPROOF.tn_factors: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/tensor_vjp_PROOF.bend as TensorVjpPROOF
Lines 1018-1047 of bendtorch-core@0.1.0.0/src/autograd/tensor_vjp_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_vjp_PROOF.bend&start_line=1018&end_line=1047

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/storage/LAWS.bend as StorageLaws
import bendtorch-core@0.1.0.0/src/tensor/word_conversion.bend as Conversion
import bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend as Replayed
import bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend as Contracts
import bendtorch-core@0.1.0.0/src/autograd/tensor_vjp_LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/tensor/matmul.bend as Matrix
import bendtorch-core@0.1.0.0/src/tensor/dot_fold.bend as DotFold
import bendtorch-core@0.1.0.0/src/tensor/observation.bend as Values

def tn_factors(+row: Nat, +column: Nat, +columns: Nat, +left: Shape.Shape, +left_fill: F32, +left_ops: List<&2, StorageLaws.Op>,
  +right: Shape.Shape, +right_fill: F32, +right_ops: List<&2, StorageLaws.Op>, +inner: U32, +rows: U32,
  +matrix: {Shape.dimensions(left) == [inner, rows] : List<&2, U32>},
  +row_below: {Nat.is_lt(row, U32.to_nat(rows)) == True{} : Bool},
  +count: Nat, +room: {Nat.is_le(count, U32.to_nat(inner)) == True{} : Bool}) ->
  {Contracts.product_factors(row, column, Matrix.Swapped{}, Matrix.Swapped{}, U32.to_nat(inner), U32.to_nat(rows), columns,
    left, left_fill, left_ops, right, right_fill, right_ops, count) ==
    Laws.left_transposed_factors(row, column, U32.to_nat(inner), columns, left, left_fill, left_ops, Laws.swapped(left),
      right, right_fill, right_ops, count) : List<&2, DotFold.Factors>}:
  match count:
    case 0n:
      {==}
    case 1n+previous:
      +span = U32.to_nat(inner)
      +height = U32.to_nat(rows)
      factors_snoc(
        Contracts.product_factors(row, column, Matrix.Swapped{}, Matrix.Swapped{}, span, height, columns,
          left, left_fill, left_ops, right, right_fill, right_ops, previous),
        Laws.left_transposed_factors(row, column, span, columns, left, left_fill, left_ops, Laws.swapped(left),
          right, right_fill, right_ops, previous),
        Replayed.value(left, left_fill, left_ops, U32.from_nat(Nat.add(Nat.mul(previous, height), row))),
        Replayed.value(right, right_fill, right_ops, U32.from_nat(Nat.add(Nat.mul(previous, columns), column))),
        Replayed.value(left, left_fill, left_ops,
          U32.from_nat(Values.permute_source_index(left, Laws.swapped(left), Nat.add(Nat.mul(row, span), previous)))),
        Replayed.value(right, right_fill, right_ops, U32.from_nat(Nat.add(Nat.mul(previous, columns), column))),
        tn_factors(row, column, columns, left, left_fill, left_ops, right, right_fill, right_ops, inner, rows, matrix,
          row_below, previous, Conversion.le_predecessor(previous, span, room)),
        tn_word(left, left_fill, left_ops, inner, rows, matrix, row, row_below, previous,
          Conversion.le_successor_lt(previous, span, room)),
        {==})

Uses (25):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_vjp_LAWS.bend&name=left_transposed_factors
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_vjp_LAWS.bend&name=swapped
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_vjp_PROOF.bend&name=factors_snoc
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_vjp_PROOF.bend&name=tn_word
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Shape
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=dimensions
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/LAWS.bend&name=Op
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend&name=product_factors
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/dot_fold.bend&name=Factors
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=Order
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/observation.bend&name=permute_source_index
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/word_conversion.bend&name=le_predecessor
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/word_conversion.bend&name=le_successor_lt