ReduceReplayedProof.pair_eq: 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 808-819 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=808&end_line=819 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/storage/api.bend as Api import bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_parallel_proof.bend as Par import bendtorch-core@0.1.0.0/src/tensor/parallel.bend as Parallel import bendtorch-core@0.1.0.0/src/autograd/reduce.bend as Reduce def pair_eq(+plan: Shape.BroadcastPlan, +rows: List<&2, Shape.Row>, +rows_exact: {rows == Shape.index_table(Shape.extents(Shape.left_shape(plan)), Shape.extents(Shape.right_shape(plan)), Shape.extents(Shape.output_shape(plan))) : List<&2, Shape.Row>}, +shape: Shape.Shape, +fill: F32, +ops: List<&2, StorageLaws.Op>, +h: List<&2, Api.Effect>, +d: Nat, +f: F32, +count: Nat, +source: Par.Source, +facts: Facts, +base: Nat, low: F32 & Array & Unit, leaf_facts: TreeEq(plan, rows, rows_exact, shape, fill, ops, h, d, f, count, 0n, base, Parallel.leaf(~(Array & Unit), low))) -> TreeEq(plan, rows, rows_exact, shape, fill, ops, h, d, f, count, 1n, base, Parallel.pair(~Reduce.Fibers, ~Array, ~Unit, ~Reduce.cell_at, Reduce.fibers(Reduce.Fibers{rows, Shape.extents(Shape.output_shape(plan))}), count, base, low)): (x, state) = low (array, none) = state (ex, ek) = leaf_facts %Equal.sym(Array & Unit, (array, none), (Api.arr(h, d, f), Unit{}), ek) : TreeEq(plan, rows, rows_exact, shape, fill, ops, h, d, f, count, 1n, base, Parallel.pair_join(~(Array & Unit), x, Reduce.cell_at(Reduce.fibers(Reduce.Fibers{rows, Shape.extents(Shape.output_shape(plan))}), Nat.add(1n, base), _, Nat.is_lt(Nat.add(1n, base), count)))) pair_join_eq(plan, rows, rows_exact, shape, fill, ops, h, d, f, count, base, x, Reduce.cell_at(Reduce.fibers(Reduce.Fibers{rows, Shape.extents(Shape.output_shape(plan))}), Nat.add(1n, base), (Api.arr(h, d, f), Unit{}), Nat.is_lt(Nat.add(1n, base), count)), ex, cell_eq(plan, rows, rows_exact, shape, fill, ops, h, d, f, count, source, facts, Nat.add(1n, base), Nat.is_lt(Nat.add(1n, base), count), {==})) Uses (32): 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=Base/base.bend&name=Unit https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce.bend&name=Fibers https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce.bend&name=cell_at https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce.bend&name=fibers https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend&name=Facts https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend&name=TreeEq https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend&name=cell_eq https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend&name=pair_join_eq 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=Row 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=extents https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=index_table https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=left_shape https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=output_shape https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=right_shape 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/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