BinaryLAWS.binary_replayed: law of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/contracts/binary_LAWS.bend as BinaryLAWS
Lines 51-74 of bendtorch-core@0.1.0.0/src/tensor/contracts/binary_LAWS.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/binary_LAWS.bend&start_line=51&end_line=74

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/elementwise.bend as Elementwise
import bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend as Replayed

# The parallel elementwise build exports its replayed result. For two
# replayed inputs whose shapes broadcast, for every P, if P holds for every
# result that hands back both inputs with their words and gives an output of
# the plan's shape whose words are `cells`, then P holds for
# `Elementwise.binary`. The output word at k is the value the pointwise family
# writes at k, whatever split of the output into parallel halves the build
# takes, and the output is a replayed tensor, so a law about replayed tensors
# applies to it.
law binary_replayed:
  for +operation: Elementwise.Operation
  for +left: Shape.Shape
  for +right: Shape.Shape
  for +plan: Shape.BroadcastPlan
  for planned: {Shape.broadcast_checked(left, right) == Done{plan} : Result<&2, &2, Shape.Error, Shape.BroadcastPlan>}
  for +left_fill: F32
  for +left_ops: List<&2, StorageLaws.Op>
  for -left_fits: {Lifecycle.logical_length(Replayed.storage(left, left_fill, left_ops)) == Shape.logical_numel(Shape.dimensions(left)) : Nat}
  for +right_fill: F32
  for +right_ops: List<&2, StorageLaws.Op>
  for -right_fits: {Lifecycle.logical_length(Replayed.storage(right, right_fill, right_ops)) == Shape.logical_numel(Shape.dimensions(right)) : Nat}
  for -P: (Core.Dynamic & Core.Dynamic) & Result<&2, &1, Core.Error, Core.Dynamic> -> Type
  for h: BinaryWith(operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, P)
  P(Elementwise.binary(operation, Core.Packed{left, Core.TTensor{Replayed.storage(left, left_fill, left_ops), left_fits}},
    Core.Packed{right, Core.TTensor{Replayed.storage(right, right_fill, right_ops), right_fits}}))

Uses (21):
  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=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/storage/LAWS.bend&name=Op
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/binary_LAWS.bend&name=BinaryWith
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/binary_proofs.bend&name=binary_replayed
  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=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/elementwise.bend&name=Operation
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise.bend&name=binary
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/lifecycle.bend&name=logical_length