ReductionPROOF.read_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 66-86 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=66&end_line=86

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_interpretation(+fuel: Nat, -shape: Shape.Shape, -original: Core.Tensor<shape>, +cursor: Nat, +accumulator: F32,
  +head: F32, +values: List<&2, F32>, tensor: Core.Tensor<shape>, result: Result<&2, &2, Core.Error, 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>},
  remaining: Laws.LogicalValues(fuel, shape, original, 1n+cursor, values),
  meaning: {Core.result_value(result) == Some{head} : Maybe<&2, F32>},
  -kept: @+other: U32 -> {Core.checked_observe(shape, tensor, 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, (tensor, result))) ==
    Some{Reduction.sequential_sum(head <> values, accumulator)} : Maybe<&2, F32>}:
  match result:
    case Fail{error}:
      Empty.absurd({None{} == Some{Reduction.sequential_sum(head <> values, accumulator)} : Maybe<&2, F32>}, no_value(head, meaning))
    case Done{+value}:
      %Equal.sym(F32, value, head, some_injective(value, head, meaning)) :
        {Laws.loop_value(shape, Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, F32.add(accumulator, _))) ==
          Some{Reduction.sequential_sum(values, F32.add(accumulator, head))} : Maybe<&2, F32>}
      %rec(tensor, logical_keeps(fuel, shape, original, tensor, 1n+cursor, values, remaining, kept)) :
        {Laws.loop_value(shape, Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, F32.add(accumulator, head))) == _ : Maybe<&2, F32>}
      {==}

Uses (23):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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=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=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=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/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=logical_keeps
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction_PROOF.bend&name=no_value
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction_PROOF.bend&name=some_injective