MatmulPROOF.output_source: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend as MatmulPROOF
Lines 1527-1578 of bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&start_line=1527&end_line=1578

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/matmul.bend as Matrix
import bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/storage/main.bend as Storage
import bendtorch-core@0.1.0.0/src/tensor/elementwise_parallel_proof.bend as Parallel

def output_source(+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},
  +depth: Nat, +length: Nat, -valid: {Storage.bounds(depth, length) == True{} : Bool},
  -exact: {length == Shape.logical_numel(Shape.dimensions(output)) : Nat},
  -a: Core.Tensor<left>, -b: Core.Tensor<right>,
  -kept_left: Core.Tensor<left>, -copy_left: Array<F32>, -taken_left: Parallel.Taken<Core.Packed{left, a}, (Core.Packed{left, kept_left}, copy_left)>,
  -kept_right: Core.Tensor<right>, -copy_right: Array<F32>, -taken_right: Parallel.Taken<Core.Packed{right, b}, (Core.Packed{right, kept_right}, copy_right)>) ->
  Laws.SourceMatmul<Core.Packed{left, a}, Core.Packed{right, b}, Matrix.parallel_output(output, U32.to_nat(inner), U32.to_nat(columns), depth, length,
    valid, exact, (Core.Packed{left, kept_left}, copy_left), (Core.Packed{right, kept_right}, copy_right))>:
  Laws.SourceMatmul{unit => Laws.MatmulSuccess{left, right, Matrix.Plan{output, rows, inner, right_inner, columns, le, re, oe, compatible},
    a, b, kept_left, kept_right,
    Core.TTensor{Storage.Owned{depth, length,
      Matrix.build(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
      Matrix.build_balanced(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
      valid}, exact},
    {==}, {==}, {==}, {==}, {==},
    Laws.ProductPrefix{
      other => {\{Parallel.Fact: p => p} : Parallel.Fact<{Core.checked_observe(left, kept_left, other) == Core.checked_observe(left, a, other) : Maybe<&2, F32>}> ->
        {Core.checked_observe(left, kept_left, other) == Core.checked_observe(left, a, other) : Maybe<&2, F32>}}(
        taken_keeps(left, a, kept_left, copy_left, taken_left, other)),
      other => {\{Parallel.Fact: p => p} : Parallel.Fact<{Core.checked_observe(right, kept_right, other) == Core.checked_observe(right, b, other) : Maybe<&2, F32>}> ->
        {Core.checked_observe(right, kept_right, other) == Core.checked_observe(right, b, other) : Maybe<&2, F32>}}(
        taken_keeps(right, b, kept_right, copy_right, taken_right, other)),
      position => earlier =>
        {\{Parallel.Taken: dl => bl => left_reads => left_same =>
          {\{Parallel.Taken: dr => br => right_reads => right_same =>
            {\{Parallel.Fact: p => p} :
              Parallel.Fact<Laws.ProductCell<inner, left, right, a, b, output,
                Core.TTensor{Storage.Owned{depth, length,
                  Matrix.build(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
                  Matrix.build_balanced(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
                  valid}, exact}, position>> ->
              Laws.ProductCell<inner, left, right, a, b, output,
                Core.TTensor{Storage.Owned{depth, length,
                  Matrix.build(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
                  Matrix.build_balanced(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
                  valid}, exact}, position>}(
              product_cell(left, right, output, rows, inner, right_inner, columns, le, re, oe, compatible, depth, length, valid, exact,
                a, b, dl, dr, copy_left, copy_right, bl, br, left_reads, right_reads, position, earlier))} :
            Parallel.Taken<Core.Packed{right, b}, (Core.Packed{right, kept_right}, copy_right)> ->
            Laws.ProductCell<inner, left, right, a, b, output,
              Core.TTensor{Storage.Owned{depth, length,
                Matrix.build(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
                Matrix.build_balanced(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
                valid}, exact}, position>}(taken_right)} :
          Parallel.Taken<Core.Packed{left, a}, (Core.Packed{left, kept_left}, copy_left)> ->
          Laws.ProductCell<inner, left, right, a, b, output,
            Core.TTensor{Storage.Owned{depth, length,
              Matrix.build(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
              Matrix.build_balanced(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
              valid}, exact}, position>}(taken_left)}}}

Uses (30):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array
  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=Maybe
  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=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/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/main.bend&name=Storage
  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/core.bend&name=checked_observe
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise_parallel_proof.bend&name=Fact
  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/matmul.bend&name=Plan
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=build
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=build_balanced
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=parallel_output
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=product_splits
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend&name=MatmulSuccess
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend&name=ProductCell
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend&name=ProductPrefix
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend&name=SourceMatmul
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&name=product_cell
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&name=taken_keeps