MatmulPROOF.left_pair: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend as MatmulPROOF
Lines 198-214 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=198&end_line=214

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

def left_pair(+fuel: Nat, +left: Shape.Shape, +right: Shape.Shape, -a: Core.Tensor<left>, b: Core.Tensor<right>,
  ra: Core.Tensor<left>, result: Result<&2, &2, Core.Error, F32>,
  +row: U32, +column: U32, +cursor: Nat, +accumulator: F32,
  -rec: @a: Core.Tensor<left> -> @b: Core.Tensor<right> -> @+value: F32 ->
    Laws.SourceDot<fuel, left, right, a, b, row, column, 1n+cursor, value, Matrix.natural_dot(fuel, left, right, a, b, row, column, 1n+cursor, value)>,
  -exact_cursor: {U32.to_nat(U32.from_nat(cursor)) == cursor : Nat},
  -meaning: @unit: Unit -> {Core.result_value(result) == Laws.coordinate_observe(left, a, [row, U32.from_nat(cursor)]) : Maybe<&2, F32>},
  -left_kept: @+other: U32 -> {Core.checked_observe(left, ra, other) == Core.checked_observe(left, a, other) : Maybe<&2, F32>}) ->
  Laws.SourceDot<1n+fuel, left, right, a, b, row, column, cursor, accumulator, Matrix.left_read(left, right,
    a => b => value => Matrix.natural_dot(fuel, left, right, a, b, row, column, 1n+cursor, value), b, [U32.from_nat(cursor), column], accumulator, (ra, result))>:
  match result:
    case Fail{error}:
      Laws.SourceDot{unit => Unit{}}
    case Done{+lv}:
      right_certificate(fuel, left, right, a, b, ra, row, column, cursor, accumulator, lv, rec, exact_cursor,
        Equal.sym(Maybe<&2, F32>, Some{lv}, Laws.coordinate_observe(left, a, [row, U32.from_nat(cursor)]), meaning(Unit{})), left_kept,
        coordinate_certificate(right, b, [U32.from_nat(cursor), column]))

Uses (22):
  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=Nat
  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=Error
  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/core.bend&name=result_value
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=left_read
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=natural_dot
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend&name=SourceDot
  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=coordinate_certificate
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&name=right_certificate