def words_cells

bendtorch-core@0.1.0.0 · src/tensor/contracts/binary_proofs.bend:280

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/elementwise.bend as Elementwise
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/pointwise.bend as Pointwise
import bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise_proof.bend as PointwiseProof
import bendtorch-core@0.1.0.0/src/tensor/contracts/broadcast.bend as Broadcast
import bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend as Contracts
import bendtorch-core@0.1.0.0/src/tensor/contracts/binary_LAWS.bend as Laws

280# The words of the family history are `cells`.
281def words_cells(+operation: Elementwise.Operation, +plan: Shape.BroadcastPlan, +left: Shape.Shape, +left_fill: F32, +left_ops: List<&2, StorageLaws.Op>, +right: Shape.Shape, +right_fill: F32, +right_ops: List<&2, StorageLaws.Op>, +count: Nat, +room: {Nat.is_le(count, Shape.logical_numel(Shape.dimensions(Shape.output_shape(plan)))) == True{} : Bool}) ->
282  {Contracts.words(Shape.output_shape(plan), 0.0, Pointwise.writes(~Elementwise.Operation, ~Elementwise.scalar, ~Shape.BroadcastPlan, ~Broadcast.left_map, ~Broadcast.right_map, Shape.logical_numel(Shape.dimensions(Shape.output_shape(plan))), operation, plan, left, left_fill, left_ops, right, right_fill, right_ops), count) == Laws.cells(operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, count) : List<&2, F32>}:
283  match count:
284    case 0n:
285      {==}
286    case 1n+previous:
287      +output = Shape.output_shape(plan)
288      +total = Shape.logical_numel(Shape.dimensions(Shape.output_shape(plan)))
289      +below = Conversion.le_successor_lt(previous, total, room)
290      +position = U32.from_nat(previous)
291      cells_snoc(operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, previous, Contracts.words(output, 0.0, Pointwise.writes(~Elementwise.Operation, ~Elementwise.scalar, ~Shape.BroadcastPlan, ~Broadcast.left_map, ~Broadcast.right_map, Shape.logical_numel(Shape.dimensions(Shape.output_shape(plan))), operation, plan, left, left_fill, left_ops, right, right_fill, right_ops), previous), Replayed.value(output, 0.0, Pointwise.writes(~Elementwise.Operation, ~Elementwise.scalar, ~Shape.BroadcastPlan, ~Broadcast.left_map, ~Broadcast.right_map, Shape.logical_numel(Shape.dimensions(Shape.output_shape(plan))), operation, plan, left, left_fill, left_ops, right, right_fill, right_ops), position),
292        cell(operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, previous), words_cells(operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, previous, Conversion.le_predecessor(previous, total, room)),
293        Equal.trans(F32, Replayed.value(output, 0.0, Pointwise.writes(~Elementwise.Operation, ~Elementwise.scalar, ~Shape.BroadcastPlan, ~Broadcast.left_map, ~Broadcast.right_map, Shape.logical_numel(Shape.dimensions(Shape.output_shape(plan))), operation, plan, left, left_fill, left_ops, right, right_fill, right_ops), position), cell(operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, U32.to_nat(position)), cell(operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, previous),
294          PointwiseProof.writes_value(~Elementwise.Operation, ~Elementwise.scalar, ~Shape.BroadcastPlan, ~Broadcast.left_map, ~Broadcast.right_map, total, operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, output, position,
295            PointwiseProof.word_inside(previous, output, below), Conversion.le_reflexive(total)),
296          Equal.cong(Nat, F32, number => cell(operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, number), U32.to_nat(position), previous, PointwiseProof.word_exact(previous, output, below))))