MatmulProof.parallel_lift: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_proof.bend as MatmulProof
Lines 204-262 of bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_proof.bend&start_line=204&end_line=262

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/matmul.bend as Matrix
import bendtorch-core@0.1.0.0/src/tensor/word_conversion.bend as Conversion
import bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend as Replayed
import bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_parallel_proof.bend as Par
import bendtorch-core@0.1.0.0/src/storage/api.bend as Api
import bendtorch-core@0.1.0.0/src/storage/array.bend as ArrayCore
import bendtorch-core@0.1.0.0/src/tensor/contracts/binary_storage_proof.bend as Owned
import bendtorch-core@0.1.0.0/src/tensor/elementwise.bend as Elementwise

def parallel_lift(+left: Shape.Shape, +right: Shape.Shape, +output: Shape.Shape, +rows: U32, +inner: U32, +right_inner: U32, +columns: U32,
  -le: {Shape.dimensions(left) == [rows, inner] : List<&2, U32>},
  -re: {Shape.dimensions(right) == [right_inner, columns] : List<&2, U32>},
  -oe: {Shape.dimensions(output) == [rows, columns] : List<&2, U32>},
  -compatible: {U32.to_nat(inner) == U32.to_nat(right_inner) : Nat},
  +planned: {Matrix.plan(left, right) == Done{Matrix.Plan{output, rows, inner, right_inner, columns, le, re, oe, compatible}} :
    Result<&2, &2, Matrix.Error, Matrix.Plan<left, right>>},
  +left_fill: F32, +left_ops: List<&2, StorageLaws.Op>,
  -left_fits: {Lifecycle.logical_length(Replayed.storage(left, left_fill, left_ops)) == Shape.logical_numel(Shape.dimensions(left)) : Nat},
  +right_fill: F32, +right_ops: List<&2, StorageLaws.Op>,
  -right_fits: {Lifecycle.logical_length(Replayed.storage(right, right_fill, right_ops)) == Shape.logical_numel(Shape.dimensions(right)) : Nat},
  -P: Result<&2, &1, Matrix.Error, Core.Dynamic & Core.Dynamic & Core.Dynamic> -> Type,
  h: ParallelFinal(left, right, output, inner, columns, left_fill, left_ops, right_fill, right_ops, StorageLaws.created(Shape.count(output), 0.0), P)) ->
  P(Matrix.matmul(Core.Packed{left, Core.TTensor{Replayed.storage(left, left_fill, left_ops), left_fits}}, Core.Packed{right, Core.TTensor{Replayed.storage(right, right_fill, right_ops), right_fits}})):
  +plan : Matrix.Plan<left, right> = Matrix.Plan{output, rows, inner, right_inner, columns, le, re, oe, compatible}
  +facts : MatrixFacts<left, right, output, rows, inner, right_inner, columns> = plan_facts(left, right, plan, planned)
  +le_live = left_dimensions(left, right, output, rows, inner, right_inner, columns, facts)
  +re_live = right_dimensions(left, right, output, rows, inner, right_inner, columns, facts)
  +oe_live = output_dimensions(left, right, output, rows, inner, right_inner, columns, facts)
  +compatible_live = inner_compatible(left, right, output, rows, inner, right_inner, columns, facts)
  +left_extents = Equal.cong(List<&2, U32>, List<&2, Nat>, dims => Shape.naturals(dims), Shape.dimensions(left), [rows, inner], le_live)
  +right_extents = Equal.trans(List<&2, Nat>, Shape.extents(right), [U32.to_nat(right_inner), U32.to_nat(columns)], [U32.to_nat(inner), U32.to_nat(columns)],
    Equal.cong(List<&2, U32>, List<&2, Nat>, dims => Shape.naturals(dims), Shape.dimensions(right), [right_inner, columns], re_live),
    Equal.cong(Nat, List<&2, Nat>, n => [n, U32.to_nat(columns)], U32.to_nat(right_inner), U32.to_nat(inner),
      Equal.sym(Nat, U32.to_nat(inner), U32.to_nat(right_inner), compatible_live)))
  +output_extents = Equal.cong(List<&2, U32>, List<&2, Nat>, dims => Shape.naturals(dims), Shape.dimensions(output), [rows, columns], oe_live)
  %Equal.sym(Result<&2, &2, Matrix.Error, Matrix.Plan<left, right>>, Matrix.plan(left, right), Done{plan}, planned) :
    P(Matrix.parallel_planned(left, right, Core.TTensor{Replayed.storage(left, left_fill, left_ops), left_fits}, Core.TTensor{Replayed.storage(right, right_fill, right_ops), right_fits}, _))
  Replayed.new_lift(output, 0.0,
    result => P(Matrix.parallel_allocated(left, right, output, U32.to_nat(inner), U32.to_nat(columns), Core.TTensor{Replayed.storage(left, left_fill, left_ops), left_fits}, Core.TTensor{Replayed.storage(right, right_fill, right_ops), right_fits}, result)),
    fo => Owned.created_lift(Shape.count(output), 0.0, Conversion.shape_count_within(output),
      st => (ParallelFinal(left, right, output, inner, columns, left_fill, left_ops, right_fill, right_ops, st, P) ->
        @-fo: {Lifecycle.logical_length(st) == Shape.logical_numel(Shape.dimensions(output)) : Nat} ->
        P(Matrix.parallel_allocated(left, right, output, U32.to_nat(inner), U32.to_nat(columns), Core.TTensor{Replayed.storage(left, left_fill, left_ops), left_fits}, Core.TTensor{Replayed.storage(right, right_fill, right_ops), right_fits}, Done{Core.TTensor{st, fo}}))),
      zero => final => fo =>
        Par.storage_shift(output, StorageLaws.replay(Par.writes(U32.to_nat(inner), U32.to_nat(columns), left, left_fill, left_ops, right, right_fill, right_ops, U32.to_nat(Shape.count(output))), Storage.Empty{}), Storage.Empty{}, Owned.replay_empty(Par.writes(U32.to_nat(inner), U32.to_nat(columns), left, left_fill, left_ops, right, right_fill, right_ops, U32.to_nat(Shape.count(output)))),
          st => k => P(Done{(Core.Packed{left, Core.TTensor{Replayed.storage(left, left_fill, left_ops), left_fits}}, Core.Packed{right, Core.TTensor{Replayed.storage(right, right_fill, right_ops), right_fits}}, Core.Packed{output, Core.TTensor{st, k}})}),
          final(left_ops)(other => {==})({==})(left_fits)(right_ops)(other => {==})({==})(right_fits))(fo),
      d => fits => f => final => fo =>
        Par.input_take(left, left_fill, left_ops,
          taken => P(Matrix.parallel_output(output, U32.to_nat(inner), U32.to_nat(columns), d, U32.to_nat(Shape.count(output)), f, fo,
            taken, Elementwise.take(Core.pack(right, Core.TTensor{Replayed.storage(right, right_fill, right_ops), right_fits})))),
          left_kept => left_values => left_words => ha => dl => fa => lsrc => left_kept_fits =>
            Par.input_take(right, right_fill, right_ops,
              taken => P(Matrix.parallel_output(output, U32.to_nat(inner), U32.to_nat(columns), d, U32.to_nat(Shape.count(output)), f, fo,
                (Core.Packed{left, Core.TTensor{Replayed.storage(left, left_fill, left_kept), left_kept_fits}}, Api.arr(ha, dl, fa)), taken)),
              right_kept => right_values => right_words => hb => dr => fb => rsrc => right_kept_fits =>
                Par.storage_shift(output,
                  StorageLaws.replay(Par.writes(U32.to_nat(inner), U32.to_nat(columns), left, left_fill, left_ops, right, right_fill, right_ops, U32.to_nat(Shape.count(output))), Storage.Owned{d, U32.to_nat(Shape.count(output)), Array.new(F32, d, 0.0), ArrayCore.new_balanced(F32, d, 0.0), f}),
                  Storage.Owned{d, U32.to_nat(Shape.count(output)),
                    Matrix.build(d, Matrix.product_splits(d, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), U32.to_nat(Shape.count(output)), 0n, Api.arr(ha, dl, fa), Api.arr(hb, dr, fb)),
                    Matrix.build_balanced(d, Matrix.product_splits(d, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), U32.to_nat(Shape.count(output)), 0n, Api.arr(ha, dl, fa), Api.arr(hb, dr, fb)),
                    f},
                  Par.output_eq(U32.to_nat(inner), U32.to_nat(columns), left, left_fill, left_ops, ha, dl, fa, right, right_fill, right_ops, hb, dr, fb,
                    lsrc, rsrc, output, U32.to_nat(rows), left_extents, right_extents, output_extents, d, fits, f),
                  st => k => P(Done{(Core.Packed{left, Core.TTensor{Replayed.storage(left, left_fill, left_kept), left_kept_fits}},
                    Core.Packed{right, Core.TTensor{Replayed.storage(right, right_fill, right_kept), right_kept_fits}},
                    Core.Packed{output, Core.TTensor{st, k}})}),
                  final(left_kept)(left_values)(left_words)(left_kept_fits)(right_kept)(right_values)(right_words)(right_kept_fits))(fo))(right_fits))(left_fits))(h)(fo))

Uses (55):
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  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  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
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  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
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  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=extents
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  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=Error
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  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=parallel_output
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