ReducePROOF.indexed_retains: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/reduce_PROOF.bend as ReducePROOF
Lines 174-186 of bendtorch-core@0.1.0.0/src/autograd/reduce_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_PROOF.bend&start_line=174&end_line=186

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/storage/main.bend as Storage
import bendtorch-core@0.1.0.0/src/tensor/core.bend as Core
import bendtorch-core@0.1.0.0/src/tensor/elementwise_totality.bend as Totality
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 Laws
import bendtorch-core@0.1.0.0/src/tensor/elementwise_parallel_proof.bend as Parallel
import bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend as MatmulProof

def indexed_retains(+shape: Shape.Shape, tensor: Core.Tensor<shape>, +target: Shape.Shape, +plan: Shape.BroadcastPlan, output: Core.Tensor<target>,
  +depth: Nat, +length: Nat, -valid: {Storage.bounds(depth, length) == True{} : Bool},
  -exact: {length == Shape.logical_numel(Shape.dimensions(target)) : Nat},
  map: Shape.Index<Shape.extents(Shape.left_shape(plan)), Shape.extents(Shape.right_shape(plan)), Shape.extents(Shape.output_shape(plan))>) ->
  Laws.Retained<Core.Packed{shape, tensor}, Reduce.parallel_indexed(Core.Packed{shape, tensor}, target, plan, output, depth, length, valid, exact, map)>:
  match map:
    case Shape.Unindexed{zero}:
      Laws.Retained{property => {==}}
    case Shape.Indexed{rows, same}:
      MatmulProof.take_lift(shape, tensor,
        pair => Laws.Retained<Core.Packed{shape, tensor}, Reduce.parallel_rows(plan, target, depth, length, valid, exact, pair, rows)>,
        kept => copy => taken => Laws.Retained{{\{Parallel.Taken: depth => balanced => reads => retained => retained} :
          Parallel.Taken<Core.Packed{shape, tensor}, (Core.Packed{shape, kept}, copy)> -> Totality.SameSource(Core.Packed{shape, tensor}, Core.Packed{shape, kept})}(taken)})

Uses (21):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce.bend&name=parallel_indexed
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce.bend&name=parallel_rows
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_LAWS.bend&name=Retained
  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=Index
  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=dimensions
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=extents
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=left_shape
  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/shape/core.bend&name=right_shape
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/main.bend&name=bounds
  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_parallel_proof.bend&name=Taken
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise_totality.bend&name=SameSource
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&name=take_lift