TensorVjpPROOF.nt_word: 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 937-960 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=937&end_line=960

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/contracts/replayed.bend as Replayed
import bendtorch-core@0.1.0.0/src/autograd/tensor_vjp_LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/tensor/observation.bend as Values
import bendtorch-core@0.1.0.0/src/tensor/transpose_PROOF.bend as TransposeProof
import bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend as MatrixIndex

# Factor k of cell (row, column) of a `Kept` right operand of dimensions
# [columns, inner] is the word right^T holds at k * columns + column.
def nt_word(+right: Shape.Shape, +fill: F32, +ops: List<&2, StorageLaws.Op>, +columns: U32, +inner: U32,
  +matrix: {Shape.dimensions(right) == [columns, inner] : List<&2, U32>},
  +column: Nat, +column_below: {Nat.is_lt(column, U32.to_nat(columns)) == True{} : Bool},
  +k: Nat, +below: {Nat.is_lt(k, U32.to_nat(inner)) == True{} : Bool}) ->
  {Replayed.value(right, fill, ops, U32.from_nat(Nat.add(Nat.mul(column, U32.to_nat(inner)), k))) ==
    Replayed.value(right, fill, ops, U32.from_nat(Values.permute_source_index(right, Laws.swapped(right),
      Nat.add(Nat.mul(k, U32.to_nat(columns)), column)))) : F32}:
  +across = U32.to_nat(columns)
  +span = U32.to_nat(inner)
  +source = Nat.add(Nat.mul(column, span), k)
  +extents = Equal.cong(List<&2, U32>, List<&2, Nat>, dims => Shape.naturals(dims), Shape.dimensions(right), [columns, inner], matrix)
  %Equal.sym(List<&2, U32>, Laws.swapped(right), [1, 0], swapped_matrix(right, columns, inner, matrix)) :
    {Replayed.value(right, fill, ops, U32.from_nat(source)) ==
      Replayed.value(right, fill, ops, U32.from_nat(Values.permute_source_index(right, _, Nat.add(Nat.mul(k, across), column)))) : F32}
  %Equal.sym(Maybe<&2, U32>, Values.permute_source(right, [1, 0], U32.from_nat(Nat.add(Nat.mul(k, across), column))), Some{U32.from_nat(source)},
    TransposeProof.permute_source_transposed(right, columns, inner, matrix, k, below, column, column_below)) :
    {Replayed.value(right, fill, ops, U32.from_nat(source)) ==
      Replayed.value(right, fill, ops, U32.from_nat(U32.to_nat(Maybe.default(&2, U32, _, 0)))) : F32}
  %Equal.sym(Nat, U32.to_nat(U32.from_nat(source)), source,
    MatrixIndex.word_exact(source, right, MatrixIndex.left_below(across, span, column, column_below, right, extents, k, below))) :
    {Replayed.value(right, fill, ops, U32.from_nat(source)) == Replayed.value(right, fill, ops, U32.from_nat(_)) : F32}
  {==}

Uses (26):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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=Maybe
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe.default
  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_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=swapped
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_vjp_PROOF.bend&name=swapped_matrix
  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=naturals
  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/replayed.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend&name=left_below
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend&name=word_exact
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/observation.bend&name=permute_source
  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/transpose_PROOF.bend&name=permute_source_transposed