ReduceReplayedProof.Final: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend as ReduceReplayedProof
Lines 1014-1030 of bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend&start_line=1014&end_line=1030

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/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/tensor/contracts/LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/autograd/reduce.bend as Reduce

# The parallel reduce over a replayed contribution, in transport form: P
# holds for the result if it holds for the contribution replayed with any
# history that keeps its words, next to the target replayed with any history
# whose cells hold the cell words.
def Final(+plan: Shape.BroadcastPlan, +target: Shape.Shape, +shape: Shape.Shape, +fill: F32, +ops: List<&2, StorageLaws.Op>, +map: PlanMap(plan),
  -s: Storage.Storage, -P: Core.Dynamic & Result<&2, &1, Reduce.Error, Core.Dynamic> -> Type) -> Type:
  @+kept: List<&2, StorageLaws.Op> ->
  @values: (@+other: U32 -> {Replayed.value(shape, fill, kept, other) == Replayed.value(shape, fill, ops, other) : F32}) ->
  @words: {Laws.words(shape, fill, kept, Shape.logical_numel(Shape.dimensions(shape))) ==
    Laws.words(shape, fill, ops, Shape.logical_numel(Shape.dimensions(shape))) : List<&2, F32>} ->
  @-kept_fits: {Lifecycle.logical_length(Replayed.storage(shape, fill, kept)) == Shape.logical_numel(Shape.dimensions(shape)) : Nat} ->
  @+out: List<&2, StorageLaws.Op> ->
  @cells: (@+index: U32 -> @inside: {Nat.is_lt(U32.to_nat(index), Shape.logical_numel(Shape.dimensions(target))) == True{} : Bool} ->
    {Replayed.value(target, 0.0, out, index) == cell_word(plan, map, shape, fill, ops, U32.to_nat(index)) : F32}) ->
  @-out_fits: {Lifecycle.logical_length(StorageLaws.replay(out, s)) == Shape.logical_numel(Shape.dimensions(target)) : Nat} ->
    P((Core.Packed{shape, Core.TTensor{Replayed.storage(shape, fill, kept), kept_fits}},
      Done{Core.Packed{target, Core.TTensor{StorageLaws.replay(out, s), out_fits}}}))

Uses (26):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=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=bendtorch-core@0.1.0.0/src/autograd/reduce.bend&name=Error
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend&name=PlanMap
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend&name=cell_word
  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=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=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/storage/LAWS.bend&name=replay
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/main.bend&name=Storage
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend&name=words
  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/contracts/replayed.bend&name=value
  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/lifecycle.bend&name=logical_length