ReductionPROOF.decision_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 117-141 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=117&end_line=141

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 decision_interpretation(+fuel: Nat, -shape: Shape.Shape, tensor: 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>},
  logical: Laws.LogicalStep<fuel, shape, tensor, cursor, head, values>,
  decision: Shape.BoolCase<Nat.is_eq(U32.to_nat(U32.from_nat(cursor)), cursor)>) ->
  Laws.Interpretation<Laws.loop_value(shape, Reduction.sum_decided(shape,
    tensor => value => Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, value), tensor, cursor, U32.from_nat(cursor), accumulator, decision)),
    Some{Reduction.sequential_sum(head <> values, accumulator)}>:
  Laws.LogicalStep{exact, observed, remaining} = logical
  match decision:
    case Shape.BFalse{equal}:
      Laws.Interpretation{unit => Empty.absurd({None{} == Some{Reduction.sequential_sum(head <> values, accumulator)} : Maybe<&2, F32>},
        conversion_clash(U32.to_nat(U32.from_nat(cursor)), cursor, exact, equal))}
    case Shape.BTrue{equal}:
      Laws.Interpretation{unit =>
        prove : @certificates: Core.SourceRead<shape, tensor, U32.from_nat(cursor)> & Core.SourceReadKeeps<shape, tensor, U32.from_nat(cursor)> ->
          {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, tensor, U32.from_nat(cursor)))) ==
            Some{Reduction.sequential_sum(head <> values, accumulator)} : Maybe<&2, F32>} =
          \{Tuple: \{Core.SourceRead: meaning => \{Core.SourceReadKeeps: kept =>
            read_certificate_interpretation(fuel, shape, tensor, cursor, accumulator, head, values, rec, observed, remaining,
              Core.read_certificate(shape, tensor, U32.from_nat(cursor)), meaning, kept)}}}
        prove((Core.source_read_model(shape, tensor, U32.from_nat(cursor)), Core.source_read_keeps(shape, tensor, U32.from_nat(cursor))))}

Uses (30):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  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/shape/core.bend&name=BoolCase
  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=SourceRead
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=SourceReadKeeps
  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=read_certificate
  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=source_read_keeps
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=source_read_model
  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.bend&name=sum_decided
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction_LAWS.bend&name=Interpretation
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction_LAWS.bend&name=LogicalStep
  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=conversion_clash
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction_PROOF.bend&name=read_certificate_interpretation