LAWS.matmul_nt_ordered: law of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend as LAWS
Lines 336-360 of bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend&start_line=336&end_line=360

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/core.bend as Core
import bendtorch-core@0.1.0.0/src/tensor/lifecycle.bend as Lifecycle
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/contracts/replayed.bend as Replayed
import bendtorch-core@0.1.0.0/src/tensor/contracts/fold_records.bend as FoldRecords

# `matmul_nt(x, W)` is the product of two `Kept` operands, x @ W^T: cell
# (row, column) folds x[row, k] * W[column, k], the words of x at
# row * inner + k and of W at column * inner + k, in increasing k from +0.0.
law matmul_nt_ordered:
  for +left: Shape.Shape
  for +right: Shape.Shape
  for +plan: Matrix.Product<Matrix.Kept{}, Matrix.Kept{}, left, right>
  for planned: {Matrix.product_plan(Matrix.Kept{}, Matrix.Kept{}, left, right) == Done{plan} :
    Result<&2, &2, Matrix.Error, Matrix.Product<Matrix.Kept{}, Matrix.Kept{}, left, right>>}
  for +left_fill: F32
  for +left_ops: List<&2, StorageLaws.Op>
  for -left_fits: {Lifecycle.logical_length(Replayed.storage(left, left_fill, left_ops)) == Shape.logical_numel(Shape.dimensions(left)) : Nat}
  for +right_fill: F32
  for +right_ops: List<&2, StorageLaws.Op>
  for -right_fits: {Lifecycle.logical_length(Replayed.storage(right, right_fill, right_ops)) == Shape.logical_numel(Shape.dimensions(right)) : Nat}
  FoldRecords.MatmulContract<left, right, product_rows(Matrix.Kept{}, Matrix.Kept{}, left, right, plan),
    product_columns(Matrix.Kept{}, Matrix.Kept{}, left, right, plan),
    row => column => DotFold.dot_fold(product_factors(row, column, Matrix.Kept{}, Matrix.Kept{},
      product_inner(Matrix.Kept{}, Matrix.Kept{}, left, right, plan), product_rows(Matrix.Kept{}, Matrix.Kept{}, left, right, plan),
      product_columns(Matrix.Kept{}, Matrix.Kept{}, left, right, plan),
      left, left_fill, left_ops, right, right_fill, right_ops, product_inner(Matrix.Kept{}, Matrix.Kept{}, left, right, plan)), 0.0),
    other => Replayed.value(left, left_fill, left_ops, other),
    other => Replayed.value(right, right_fill, right_ops, other),
    Matrix.matmul_nt(Core.Packed{left, Core.TTensor{Replayed.storage(left, left_fill, left_ops), left_fits}},
      Core.Packed{right, Core.TTensor{Replayed.storage(right, right_fill, right_ops), right_fits}})>

Uses (25):
  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=Result
  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/shape/core.bend&name=logical_numel
  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_columns
  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/LAWS.bend&name=product_inner
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend&name=product_rows
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/fold_records.bend&name=MatmulContract
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/product_proof.bend&name=product_ordered
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend&name=storage
  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/core.bend&name=Dynamic
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=Tensor
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/dot_fold.bend&name=dot_fold
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/lifecycle.bend&name=logical_length
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=Error
  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/matmul.bend&name=Product
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=matmul_nt
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=product_plan