LAWS.matmul_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 148-170 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=148&end_line=170

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/dot.bend as Dot
import bendtorch-core@0.1.0.0/src/tensor/contracts/fold_records.bend as FoldRecords

# Ordered-fold family, matmul: for every plan of a product of two replayed
# matrices, matmul succeeds with a rows x columns output whose cell
# (row, column) holds `DotFold.dot_fold` of the cell's factor pairs in
# increasing k, starting at +0.0, the value `dot_ordered` states for
# `Dot.dot`, and both returned inputs keep every word.
law matmul_ordered:
  for +left: Shape.Shape
  for +right: Shape.Shape
  for +plan: Matrix.Plan<left, right>
  for planned: {Matrix.plan(left, right) == Done{plan} : Result<&2, &2, Matrix.Error, Matrix.Plan<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, matrix_rows(left, right, plan), matrix_columns(left, right, plan),
    row => column => DotFold.dot_fold(factors(row, column, matrix_inner(left, right, plan), matrix_columns(left, right, plan),
      left, left_fill, left_ops, right, right_fill, right_ops, matrix_inner(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(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 (24):
  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=factors
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend&name=matrix_columns
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend&name=matrix_inner
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend&name=matrix_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/matmul_proof.bend&name=matmul_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=Plan
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=matmul
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=plan