BroadcastPointwiseLAWS.broadcast_to_replayed: law of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/broadcast_pointwise_LAWS.bend as BroadcastPointwiseLAWS
Lines 94-112 of bendtorch-core@0.1.0.0/src/autograd/broadcast_pointwise_LAWS.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/broadcast_pointwise_LAWS.bend&start_line=94&end_line=112

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/autograd/broadcast.bend as Broadcast

# The broadcast_to result is replayed: for every P, if P holds for every
# result that hands back the input with its words and gives an output of the
# plan's shape whose words are `cells`, then P holds for broadcast_to. The
# output word at k is the input word at left_map(plan, k), whatever split of
# the output into parallel halves the build takes, and the output is a
# replayed tensor, so a later law about a replayed contribution, such as
# reduce_to_fiber, applies to it.
law broadcast_to_replayed:
  for +shape: Shape.Shape
  for +target: Shape.Shape
  for +plan: Shape.BroadcastPlan
  for planned: {Shape.broadcast_checked(shape, target) == Done{plan} : Result<&2, &2, Shape.Error, Shape.BroadcastPlan>}
  for same: {Shape.dimensions(Shape.output_shape(plan)) == Shape.dimensions(target) : 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}
  for -P: Core.Dynamic & Result<&2, &1, Broadcast.Error, Core.Dynamic> -> Type
  for h: BroadcastWith(plan, shape, fill, ops, P)
  P(Broadcast.broadcast_to(Core.Packed{shape, Core.TTensor{Replayed.storage(shape, fill, ops), fits}}, target))

Uses (22):
  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=Pair
  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/broadcast.bend&name=Error
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/broadcast.bend&name=broadcast_to
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/broadcast_pointwise_LAWS.bend&name=BroadcastWith
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/broadcast_pointwise_PROOF.bend&name=run_lift
  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/replayed.bend&name=storage
  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