SumProof.sum_ordered: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/contracts/sum_proof.bend as SumProof
Lines 61-78 of bendtorch-core@0.1.0.0/src/tensor/contracts/sum_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/sum_proof.bend&start_line=61&end_line=78

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/storage/LAWS.bend as StorageLaws
import bendtorch-core@0.1.0.0/src/tensor/core.bend as Core
import bendtorch-core@0.1.0.0/src/tensor/lifecycle.bend as Lifecycle
import bendtorch-core@0.1.0.0/src/tensor/reduction.bend as Reduction
import bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend as Replayed
import bendtorch-core@0.1.0.0/src/tensor/contracts/fold.bend as Fold
import bendtorch-core@0.1.0.0/src/tensor/contracts/fold_records.bend as Records
import bendtorch-core@0.1.0.0/src/tensor/contracts/fold_proof.bend as Proof
import bendtorch-core@0.1.0.0/src/tensor/contracts/sum.bend as Sum
import bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend as Laws

def sum_ordered(+shape: Shape.Shape, +fill: F32, +ops: List<&2, StorageLaws.Op>,
  -fits: {Lifecycle.logical_length(Replayed.storage(shape, fill, ops)) == Shape.logical_numel(Shape.dimensions(shape)) : Nat}) ->
  Records.FoldContract<shape, Reduction.sequential_sum(Laws.words(shape, fill, ops, Shape.logical_numel(Shape.dimensions(shape))), 0.0),
    other => Replayed.value(shape, fill, ops, other),
    Sum.sum(Core.Packed{shape, Core.TTensor{Replayed.storage(shape, fill, ops), fits}})>:
  +count = Shape.elements(shape)
  %Shape.elements_exact(shape) :
    Records.FoldContract<shape, Reduction.sequential_sum(Laws.words(shape, fill, ops, _), 0.0),
      other => Replayed.value(shape, fill, ops, other),
      Fold.run(~Unit, ~Sum.add, ~Unit, ~Sum.position, ~Sum.every, Unit{}, Unit{}, count,
        Core.Packed{shape, Core.TTensor{Replayed.storage(shape, fill, ops), fits}})>
  %total_words(shape, fill, ops, count) :
    Records.FoldContract<shape, _,
      other => Replayed.value(shape, fill, ops, other),
      Fold.run(~Unit, ~Sum.add, ~Unit, ~Sum.position, ~Sum.every, Unit{}, Unit{}, count,
        Core.Packed{shape, Core.TTensor{Replayed.storage(shape, fill, ops), fits}})>
  Proof.contract(~Unit, ~Sum.add, ~Unit, ~Sum.position, ~Sum.every, Unit{}, Unit{}, shape, fill, ops, count,
    position_inside(count, Shape.logical_numel(Shape.dimensions(shape)), elements_room(shape)), fits)

Uses (27):
  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=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/shape/core.bend&name=dimensions
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=elements
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=elements_exact
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=logical_numel
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/LAWS.bend&name=Op
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend&name=words
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/fold.bend&name=run
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/fold_proof.bend&name=contract
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/fold_records.bend&name=FoldContract
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend&name=storage
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/sum.bend&name=add
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/sum.bend&name=every
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/sum.bend&name=position
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/sum.bend&name=sum
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/sum_proof.bend&name=elements_room
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/sum_proof.bend&name=position_inside
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/sum_proof.bend&name=total_words
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=Dynamic
  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/lifecycle.bend&name=logical_length
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction.bend&name=sequential_sum