ReductionPROOF.read_certificate_interpretation: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/reduction_PROOF.bend as ReductionPROOF
Lines 88-115 of bendtorch-core@0.1.0.0/src/tensor/reduction_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction_PROOF.bend&start_line=88&end_line=115

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/reduction.bend as Reduction
import bendtorch-core@0.1.0.0/src/tensor/reduction_LAWS.bend as Laws

def read_certificate_interpretation(+fuel: Nat, -shape: Shape.Shape, -original: Core.Tensor<shape>, +cursor: Nat,
  +accumulator: F32, +head: F32, +values: List<&2, F32>,
  rec: @tensor: Core.Tensor<shape> -> @logical: Laws.LogicalValues(fuel, shape, tensor, 1n+cursor, values) ->
    {Laws.loop_value(shape, Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, F32.add(accumulator, head))) ==
      Some{Reduction.sequential_sum(values, F32.add(accumulator, head))} : Maybe<&2, F32>},
  observed: {Core.checked_observe(shape, original, U32.from_nat(cursor)) == Some{head} : Maybe<&2, F32>},
  remaining: Laws.LogicalValues(fuel, shape, original, 1n+cursor, values), certificate: Core.Read<shape, original, U32.from_nat(cursor)>,
  meaning: {Core.read_value(shape, Core.read_flat(shape, original, U32.from_nat(cursor))) == Core.checked_observe(shape, original, U32.from_nat(cursor)) : Maybe<&2, F32>},
  -kept: @+other: U32 -> {Core.retained_read_observe(shape, Core.read_flat(shape, original, U32.from_nat(cursor)), other) == Core.checked_observe(shape, original, other) : Maybe<&2, F32>}) ->
  {Laws.loop_value(shape, Reduction.read_step(shape,
    tensor => value => Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, value), accumulator, Core.read_flat(shape, original, U32.from_nat(cursor)))) ==
    Some{Reduction.sequential_sum(head <> values, accumulator)} : Maybe<&2, F32>}:
  Core.Read{tensor, +result, +exact} = certificate
  %exact :
    {Laws.loop_value(shape, Reduction.read_step(shape,
      tensor => value => Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, value), accumulator, _)) ==
      Some{Reduction.sequential_sum(head <> values, accumulator)} : Maybe<&2, F32>}
  read_interpretation(fuel, shape, original, cursor, accumulator, head, values, tensor, result, rec, remaining,
    Equal.trans(Maybe<&2, F32>, Core.result_value(result), Core.checked_observe(shape, original, U32.from_nat(cursor)), Some{head},
      Equal.trans(Maybe<&2, F32>, Core.result_value(result), Core.read_value(shape, Core.read_flat(shape, original, U32.from_nat(cursor))),
        Core.checked_observe(shape, original, U32.from_nat(cursor)),
        Equal.cong(Core.Tensor<shape> & Result<&2, &2, Core.Error, F32>, Maybe<&2, F32>, pair => Core.read_value(shape, pair),
          (tensor, result), Core.read_flat(shape, original, U32.from_nat(cursor)), exact),
        meaning), observed),
    other => Equal.trans(Maybe<&2, F32>, Core.checked_observe(shape, tensor, other),
      Core.retained_read_observe(shape, Core.read_flat(shape, original, U32.from_nat(cursor)), other), Core.checked_observe(shape, original, other),
      Equal.cong(Core.Tensor<shape> & Result<&2, &2, Core.Error, F32>, Maybe<&2, F32>, pair => Core.retained_read_observe(shape, pair, other),
        (tensor, result), Core.read_flat(shape, original, U32.from_nat(cursor)), exact), kept(other)))

Uses (27):
  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.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=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=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=Read
  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=read_flat
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=read_value
  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/core.bend&name=retained_read_observe
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction.bend&name=natural_sum_loop
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction.bend&name=read_step
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction.bend&name=sequential_sum
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction_LAWS.bend&name=LogicalValues
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction_LAWS.bend&name=loop_value
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction_PROOF.bend&name=read_interpretation