ReduceFoldLAWS.reduce_to_fiber: law of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/reduce_fold_LAWS.bend as ReduceFoldLAWS
Lines 75-94 of bendtorch-core@0.1.0.0/src/autograd/reduce_fold_LAWS.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_fold_LAWS.bend&start_line=75&end_line=94

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/contracts/replayed.bend as Replayed
import bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend as Contracts
import bendtorch-core@0.1.0.0/src/autograd/reduce.bend as Reduce
import bendtorch-core@0.1.0.0/src/autograd/reduce_LAWS.bend as ReduceLaws
import bendtorch-core@0.1.0.0/src/autograd/reduce_fold.bend as ReduceFold

# reduce_to through the ordered-fold family: when the target broadcasts to
# exactly the contribution's dimensions, reducing a replayed contribution
# succeeds with the target's dimensions, every target cell holds
# `ReduceLaws.fiber` over the contribution's words in index order, the value
# `reduce_fold_fiber` states for `ReduceFold.cell`, and the returned
# contribution keeps every word.
law reduce_to_fiber:
  for +target: Shape.Shape
  for +shape: Shape.Shape
  for +plan: Shape.BroadcastPlan
  for planned: {Shape.broadcast_checked(target, shape) == Done{plan} : Result<&2, &2, Shape.Error, Shape.BroadcastPlan>}
  for same: {Shape.dimensions(Shape.output_shape(plan)) == Shape.dimensions(shape) : List<&2, U32>}
  for +fill: F32
  for +ops: List<&2, StorageLaws.Op>
  for -fits: {Lifecycle.logical_length(Replayed.storage(shape, fill, ops)) == Shape.logical_numel(Shape.dimensions(shape)) : Nat}
  ReduceToContract<target, shape,
    index => ReduceLaws.fiber(plan, Contracts.words(shape, fill, ops, Shape.logical_numel(Shape.dimensions(shape))),
      index, Shape.logical_numel(Shape.dimensions(shape))),
    other => Replayed.value(shape, fill, ops, other),
    Reduce.reduce_to(Core.Packed{shape, Core.TTensor{Replayed.storage(shape, fill, ops), fits}}, target)>

Uses (23):
  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=Result
  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/autograd/reduce.bend&name=reduce_to
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_LAWS.bend&name=fiber
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_fold_LAWS.bend&name=ReduceToContract
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_to_fold_PROOF.bend&name=reduce_to_fiber
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=BroadcastPlan
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Error
  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=broadcast_checked
  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=logical_numel
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=output_shape
  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/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/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