SgdLAWS.sgd_step_values: law of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/sgd_LAWS.bend as SgdLAWS
Lines 61-85 of bendtorch-core@0.1.0.0/src/autograd/sgd_LAWS.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/sgd_LAWS.bend&start_line=61&end_line=85

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/gradient.bend as Gradient
import bendtorch-core@0.1.0.0/src/autograd/tensor_backward.bend as Backward
import bendtorch-core@0.1.0.0/src/autograd/sgd.bend as Sgd

# A parameter whose slot holds g gets p - lr * g on the parallel elementwise
# build, in transport form: for a replayed value p and a replayed gradient g
# whose shapes broadcast, for every P, if P holds for every result that keeps
# the node, the shape, the saved values and g with its words, and holds a
# value of the plan's shape whose word k is scalar(Descend{lr},
# p[left_map(plan, k)], g[right_map(plan, k)]) (sgd_descend_scalar: p - lr *
# g), next to Done, then P holds for the step of that parameter.
law sgd_step_values:
  for +lr: F32
  for node: Backward.Node
  for +shape: Shape.Shape
  for saved: Backward.Saved
  for +g_shape: Shape.Shape
  for +plan: Shape.BroadcastPlan
  for planned: {Shape.broadcast_checked(shape, g_shape) == Done{plan} : Result<&2, &2, Shape.Error, Shape.BroadcastPlan>}
  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 +g_fill: F32
  for +g_ops: List<&2, StorageLaws.Op>
  for -g_fits: {Lifecycle.logical_length(Replayed.storage(g_shape, g_fill, g_ops)) == Shape.logical_numel(Shape.dimensions(g_shape)) : Nat}
  for -P: Backward.Entry & Result<&2, &2, Sgd.Error, Unit> -> Type
  for h: DescendWith(lr, node, shape, saved, plan, fill, ops, g_shape, g_fill, g_ops, P)
  P(Sgd.descend(lr, Backward.Entry{node, shape, Core.Packed{shape, Core.TTensor{Replayed.storage(shape, fill, ops), fits}}, saved,
    Gradient.Held{Core.Packed{g_shape, Core.TTensor{Replayed.storage(g_shape, g_fill, g_ops), g_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=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Result
  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/autograd/gradient.bend&name=Slot
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/sgd.bend&name=Error
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/sgd.bend&name=descend
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/sgd.bend&name=descended
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/sgd_LAWS.bend&name=DescendWith
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward.bend&name=Entry
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward.bend&name=Node
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward.bend&name=Saved
  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_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=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/lifecycle.bend&name=logical_length