BroadcastPROOF.finish_mapping: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/broadcast_PROOF.bend as BroadcastPROOF
Lines 136-171 of bendtorch-core@0.1.0.0/src/autograd/broadcast_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/broadcast_PROOF.bend&start_line=136&end_line=171

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/tensor/core.bend as Core
import bendtorch-core@0.1.0.0/src/tensor/elementwise.bend as Elementwise
import bendtorch-core@0.1.0.0/src/tensor/elementwise_totality.bend as Totality
import bendtorch-core@0.1.0.0/src/tensor/elementwise_PROOF.bend as ElementwiseProof
import bendtorch-core@0.1.0.0/src/tensor/projection_LAWS.bend as Projection
import bendtorch-core@0.1.0.0/src/autograd/broadcast.bend as Broadcast
import bendtorch-core@0.1.0.0/src/autograd/broadcast_LAWS.bend as Laws

def finish_mapping(-input: Core.Dynamic, +target: Shape.Shape, -zeros: Core.Tensor<target>, +plan: Shape.BroadcastPlan,
  pair: (Core.Dynamic & Core.Dynamic) & Result<&2, &1, Core.Error, Core.Dynamic>,
  -dims: Totality.DimensionsModel<Shape.dimensions(Shape.output_shape(plan)), pair>,
  -mapping: Elementwise.MappingModel<Elementwise.KeepLeft{}, plan, input, Core.Packed{target, zeros}, pair>,
  -same_dims: {Shape.dimensions(Shape.output_shape(plan)) == Shape.dimensions(target) : List<&2, U32>},
  -right_dims: {Shape.dimensions(Shape.right_shape(plan)) == Shape.dimensions(target) : List<&2, U32>}) ->
  WithModel<input, target, Done{plan}, Broadcast.finish(pair)>:
  ((left, right), result) = pair
  match result:
    case Fail{error}:
      WithModel{Unit{}}
    case Done{output}:
      WithModel{(
        Equal.trans(List<&2, U32>, Totality.dimensions(output), Shape.dimensions(Shape.output_shape(plan)), Shape.dimensions(target),
          {\{Totality.DimensionsModel: exact => exact} : Totality.DimensionsModel<Shape.dimensions(Shape.output_shape(plan)), ((left, right), Done{output})> ->
            {Totality.dimensions(output) == Shape.dimensions(Shape.output_shape(plan)) : List<&2, U32>}}(dims),
          same_dims),
        index => inside => Equal.trans(Maybe<&2, F32>, Core.observe_dynamic(output, index),
          Elementwise.expected(Elementwise.KeepLeft{}, plan, input, Core.Packed{target, zeros}, index),
          Laws.source_value(input, Projection.offset_spec(plan, U32.to_nat(index))),
          {\{Elementwise.MappingModel: prefix => prefix} :
            Elementwise.MappingModel<Elementwise.KeepLeft{}, plan, input, Core.Packed{target, zeros}, ((left, right), Done{output})> ->
            Elementwise.PrefixMapping(Elementwise.KeepLeft{}, plan, input, Core.Packed{target, zeros},
              Shape.logical_numel(Shape.dimensions(Shape.output_shape(plan))), output)}(mapping)(index)(
            %Equal.sym(List<&2, U32>, Shape.dimensions(Shape.output_shape(plan)), Shape.dimensions(target), same_dims) :
              Shape.LT(U32.to_nat(index), Shape.logical_numel(_))
            inside),
          {\{Holds: proof => proof} : Holds<{Elementwise.expected(Elementwise.KeepLeft{}, plan, input, Core.Packed{target, zeros}, index) ==
    Laws.source_value(input, Projection.offset_spec(plan, U32.to_nat(index))) : Maybe<&2, F32>}> -> {Elementwise.expected(Elementwise.KeepLeft{}, plan, input, Core.Packed{target, zeros}, index) ==
    Laws.source_value(input, Projection.offset_spec(plan, U32.to_nat(index))) : Maybe<&2, F32>}}(
            mapped_value(plan, index, input, target, zeros, right_dims,
              ElementwiseProof.indices_success(plan, index,
                {\{Holds: proof => proof} : Holds<{Nat.is_lt(U32.to_nat(index), Shape.elements(Shape.output_shape(plan))) == True{} : Bool}> ->
                  {Nat.is_lt(U32.to_nat(index), Shape.elements(Shape.output_shape(plan))) == True{} : Bool}}(
                  output_inside(plan, target, index, same_dims, inside))))))
      )}

Uses (39):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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=Maybe
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  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=Sigma
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  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/broadcast.bend&name=finish
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/broadcast_LAWS.bend&name=source_value
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/broadcast_PROOF.bend&name=Holds
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/broadcast_PROOF.bend&name=WithModel
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/broadcast_PROOF.bend&name=mapped_value
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/broadcast_PROOF.bend&name=output_inside
  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=LT
  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=elements
  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/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/core.bend&name=observe_dynamic
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise.bend&name=MappingModel
  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=PrefixMapping
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise.bend&name=expected
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise_PROOF.bend&name=indices_success
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise_totality.bend&name=DimensionsModel
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise_totality.bend&name=dimensions
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/projection_LAWS.bend&name=offset_spec