MatmulParallelProof.pair_eq: def of bendtorch-core@0.1.0.0 Import: import bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_parallel_proof.bend as MatmulParallelProof Lines 667-684 of bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_parallel_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_parallel_proof.bend&start_line=667&end_line=684 import Base import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape import bendtorch-core@0.1.0.0/src/storage/LAWS.bend as StorageLaws import bendtorch-core@0.1.0.0/src/tensor/matmul.bend as Matrix import bendtorch-core@0.1.0.0/src/tensor/parallel.bend as Parallel import bendtorch-core@0.1.0.0/src/storage/api.bend as Api def pair_eq(+span: Nat, +columns: Nat, +left: Shape.Shape, +left_fill: F32, +left_ops: List<&2, StorageLaws.Op>, +ha: List<&2, Api.Effect>, +dl: Nat, +fa: F32, +right: Shape.Shape, +right_fill: F32, +right_ops: List<&2, StorageLaws.Op>, +hb: List<&2, Api.Effect>, +dr: Nat, +fb: F32, +count: Nat, +lsrc: Source, +rsrc: Source, +output: Shape.Shape, +rows: Nat, +left_extents: {Shape.extents(left) == [rows, span] : List<&2, Nat>}, +right_extents: {Shape.extents(right) == [span, columns] : List<&2, Nat>}, +output_extents: {Shape.extents(output) == [rows, columns] : List<&2, Nat>}, +count_exact: {count == Shape.logical_numel(Shape.dimensions(output)) : Nat}, +base: Nat, low: F32 & Array & Array, leaf_facts: TreeEq(span, columns, left, left_fill, left_ops, ha, dl, fa, right, right_fill, right_ops, hb, dr, fb, count, 0n, base, Parallel.leaf(~(Array & Array), low))) -> TreeEq(span, columns, left, left_fill, left_ops, ha, dl, fa, right, right_fill, right_ops, hb, dr, fb, count, 1n, base, Parallel.pair(~Matrix.Dims, ~Array, ~Array, ~Matrix.cell_at, Matrix.dims(Matrix.Dims{span, columns}), count, base, low)): (x, inputs) = low (la, ra) = inputs (ex, kept) = leaf_facts (el, er) = kept %Equal.sym(Array, la, Api.arr(ha, dl, fa), el) : TreeEq(span, columns, left, left_fill, left_ops, ha, dl, fa, right, right_fill, right_ops, hb, dr, fb, count, 1n, base, Parallel.pair_join(~(Array & Array), x, Matrix.cell_at(Matrix.dims(Matrix.Dims{span, columns}), Nat.add(1n, base), (_, ra), Nat.is_lt(Nat.add(1n, base), count)))) %Equal.sym(Array, ra, Api.arr(hb, dr, fb), er) : TreeEq(span, columns, left, left_fill, left_ops, ha, dl, fa, right, right_fill, right_ops, hb, dr, fb, count, 1n, base, Parallel.pair_join(~(Array & Array), x, Matrix.cell_at(Matrix.dims(Matrix.Dims{span, columns}), Nat.add(1n, base), (Api.arr(ha, dl, fa), _), Nat.is_lt(Nat.add(1n, base), count)))) pair_join_eq(span, columns, left, left_fill, left_ops, ha, dl, fa, right, right_fill, right_ops, hb, dr, fb, count, base, x, Matrix.cell_at(Matrix.dims(Matrix.Dims{span, columns}), Nat.add(1n, base), (Api.arr(ha, dl, fa), Api.arr(hb, dr, fb)), Nat.is_lt(Nat.add(1n, base), count)), ex, cell_eq(span, columns, left, left_fill, left_ops, ha, dl, fa, right, right_fill, right_ops, hb, dr, fb, count, lsrc, rsrc, output, rows, left_extents, right_extents, output_extents, count_exact, Nat.add(1n, base), Nat.is_lt(Nat.add(1n, base), count), {==})) Uses (26): https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym 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.add 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=Sigma 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=extents 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/api.bend&name=Effect https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/api.bend&name=arr https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_parallel_proof.bend&name=Source https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_parallel_proof.bend&name=TreeEq https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_parallel_proof.bend&name=cell_eq https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_parallel_proof.bend&name=pair_join_eq https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=Dims https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=cell_at https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=dims https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/parallel.bend&name=leaf https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/parallel.bend&name=pair https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/parallel.bend&name=pair_join