MatmulPROOF.dot_extend: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend as MatmulPROOF
Lines 126-147 of bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&start_line=126&end_line=147

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/tensor/core.bend as Core
import bendtorch-core@0.1.0.0/src/tensor/matmul.bend as Matrix
import bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/tensor/dot_fold.bend as DotFold

def dot_extend(+fuel: Nat, +left: Shape.Shape, +right: Shape.Shape, -a: Core.Tensor<left>, -b: Core.Tensor<right>,
  -ra: Core.Tensor<left>, -rb: Core.Tensor<right>, +row: U32, +column: U32, +cursor: Nat, +accumulator: F32, +lv: F32, +rv: F32,
  result: Result<&2, &1, Matrix.Error, Core.Tensor<left> & Core.Tensor<right> & F32>,
  next: Laws.DotResultMeaning(fuel, left, right, ra, rb, row, column, 1n+cursor, F32.add(accumulator, F32.mul(lv, rv)), result),
  -exact: {U32.to_nat(U32.from_nat(cursor)) == cursor : Nat},
  -lo: {Laws.coordinate_observe(left, a, [row, U32.from_nat(cursor)]) == Some{lv} : Maybe<&2, F32>},
  -ro: {Laws.coordinate_observe(right, b, [U32.from_nat(cursor), column]) == Some{rv} : Maybe<&2, F32>},
  -left_kept: @+other: U32 -> {Core.checked_observe(left, ra, other) == Core.checked_observe(left, a, other) : Maybe<&2, F32>},
  -right_kept: @+other: U32 -> {Core.checked_observe(right, rb, other) == Core.checked_observe(right, b, other) : Maybe<&2, F32>}) ->
  Laws.DotResultMeaning(1n+fuel, left, right, a, b, row, column, cursor, accumulator, result):
  match result:
    case Fail{error}:
      Unit{}
    case Done{pair}:
      (final_a, final_b, value) = pair
      Laws.DotMeaning{values, logical, fold, lk, rk} = next
      Laws.DotMeaning{DotFold.Factors{lv, rv} <> values,
        Laws.DotStep{exact, lo, ro, logical_dot_original(fuel, left, right, a, b, ra, rb, row, column, 1n+cursor, values, logical, left_kept, right_kept)}, fold,
        other => Equal.trans(Maybe<&2, F32>, Core.checked_observe(left, final_a, other),
          Core.checked_observe(left, ra, other), Core.checked_observe(left, a, other), lk(other), left_kept(other)),
        other => Equal.trans(Maybe<&2, F32>, Core.checked_observe(right, final_b, other),
          Core.checked_observe(right, rb, other), Core.checked_observe(right, b, other), rk(other), right_kept(other))}

Uses (24):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32.mul
  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=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Result
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  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=Base/base.bend&name=Unit
  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/tensor/core.bend&name=Tensor
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=checked_observe
  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=Error
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend&name=DotMeaning
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend&name=DotResultMeaning
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend&name=DotStep
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend&name=coordinate_observe
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&name=logical_dot_original