def Final

bendtorch-core@0.1.0.0 · src/autograd/reduce_replayed_proof.bend:1014

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

1014# The parallel reduce over a replayed contribution, in transport form: P
1015# holds for the result if it holds for the contribution replayed with any
1016# history that keeps its words, next to the target replayed with any history
1017# whose cells hold the cell words.
1018def Final(+plan: Shape.BroadcastPlan, +target: Shape.Shape, +shape: Shape.Shape, +fill: F32, +ops: List<&2, StorageLaws.Op>, +map: PlanMap(plan),
1019  -s: Storage.Storage, -P: Core.Dynamic & Result<&2, &1, Reduce.Error, Core.Dynamic> -> Type) -> Type:
1020  @+kept: List<&2, StorageLaws.Op> ->
1021  @values: (@+other: U32 -> {Replayed.value(shape, fill, kept, other) == Replayed.value(shape, fill, ops, other) : F32}) ->
1022  @words: {Laws.words(shape, fill, kept, Shape.logical_numel(Shape.dimensions(shape))) ==
1023    Laws.words(shape, fill, ops, Shape.logical_numel(Shape.dimensions(shape))) : List<&2, F32>} ->
1024  @-kept_fits: {Lifecycle.logical_length(Replayed.storage(shape, fill, kept)) == Shape.logical_numel(Shape.dimensions(shape)) : Nat} ->
1025  @+out: List<&2, StorageLaws.Op> ->
1026  @cells: (@+index: U32 -> @inside: {Nat.is_lt(U32.to_nat(index), Shape.logical_numel(Shape.dimensions(target))) == True{} : Bool} ->
1027    {Replayed.value(target, 0.0, out, index) == cell_word(plan, map, shape, fill, ops, U32.to_nat(index)) : F32}) ->
1028  @-out_fits: {Lifecycle.logical_length(StorageLaws.replay(out, s)) == Shape.logical_numel(Shape.dimensions(target)) : Nat} ->
1029    P((Core.Packed{shape, Core.TTensor{Replayed.storage(shape, fill, kept), kept_fits}},
1030      Done{Core.Packed{target, Core.TTensor{StorageLaws.replay(out, s), out_fits}}}))