BackwardLAWS.reached_exactly: law of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/backward_LAWS.bend as BackwardLAWS
Lines 261-267 of bendtorch-core@0.1.0.0/src/autograd/backward_LAWS.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_LAWS.bend&start_line=261&end_line=267

import Base
import bendtorch-core@0.1.0.0/src/autograd/backward.bend as Backward

# Only the reachable graph: a node has a gradient exactly when the selected
# output reaches it. Every other node, newer or unused, reads None.
law reached_exactly:
  for +graph: List<&2, Backward.Node>
  for +output: Nat
  {somes(Backward.pass(graph, List.length(&2, Backward.Node, graph), output)) ==
    reached(graph, List.length(&2, Backward.Node, graph), output) : List<&2, Bool>}

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.length
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward.bend&name=Node
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward.bend&name=pass
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_LAWS.bend&name=reached
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_LAWS.bend&name=somes
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend&name=pass_reached