LAWS.dot_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 106-134 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=106&end_line=134

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/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, dot instance: for every in-bounds output cell of a
# product of a rows x inner and an inner x columns replayed matrix, the dot
# product succeeds with `DotFold.dot_fold` of the cell's factor pairs in
# increasing k, starting at +0.0, and both returned inputs keep every word.
law dot_ordered:
  for +rows: Nat
  for +inner: Nat
  for +columns: Nat
  for +row: Nat
  for row_below: {Nat.is_lt(row, rows) == True{} : Bool}
  for +column: Nat
  for column_below: {Nat.is_lt(column, columns) == True{} : Bool}
  for +left: Shape.Shape
  for left_extents: {Shape.extents(left) == [rows, inner] : List<&2, Nat>}
  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: Shape.Shape
  for right_extents: {Shape.extents(right) == [inner, columns] : List<&2, 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.PairFoldContract<left, right,
    DotFold.dot_fold(factors(row, column, inner, columns, left, left_fill, left_ops, right, right_fill, right_ops, inner), 0.0),
    other => Replayed.value(left, left_fill, left_ops, other),
    other => Replayed.value(right, right_fill, right_ops, other),
    Dot.dot(Dot.Cell{row, column, inner, columns},
      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 (21):
  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.is_lt
  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=extents
  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/dot.bend&name=Cell
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/dot.bend&name=dot
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/dot_proof.bend&name=dot_ordered
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/fold_records.bend&name=PairFoldContract
  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