def left_walk_bound

bendtorch-core@0.1.0.0 · src/tensor/contracts/broadcast_proof.bend:23

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/shape/flat.bend as Flat
import bendtorch-core@0.1.0.0/src/storage/arith.bend as Arith
import bendtorch-core@0.1.0.0/src/tensor/contracts/broadcast.bend as Broadcast

23def left_walk_bound(+plan: Shape.BroadcastPlan,
24  map: Shape.Index<Shape.extents(Shape.left_shape(plan)), Shape.extents(Shape.right_shape(plan)), Shape.extents(Shape.output_shape(plan))>,
25  +index: Nat, below: {Nat.is_lt(index, Shape.logical_numel(Shape.dimensions(Shape.output_shape(plan)))) == True{} : Bool}) ->
26  {Nat.is_lt(Broadcast.left_walk(Shape.extents(Shape.left_shape(plan)), Shape.extents(Shape.right_shape(plan)), Shape.extents(Shape.output_shape(plan)), map, index),
27    Shape.logical_numel(Shape.dimensions(Shape.left_shape(plan)))) == True{} : Bool}:
28  match map:
29    case Shape.Indexed{rows, exact}:
30      Equal.sym(Bool, True{}, Nat.is_lt(Shape.walk_left(rows, index), Shape.logical_numel(Shape.dimensions(Shape.left_shape(plan)))),
31        %Shape.elements_exact(Shape.left_shape(plan)) : {True{} == Nat.is_lt(Shape.walk_left(rows, index), _) : Bool}
32        Flat.left_bound(plan, rows, exact, index, output_inside(plan, index, below)))
33    case Shape.Unindexed{zero}:
34      Empty.absurd({Nat.is_lt(0n, Shape.logical_numel(Shape.dimensions(Shape.left_shape(plan)))) == True{} : Bool},
35        Arith.lt_zero(index,
36          %Equal.sym(Nat, 0n, Shape.numel(Shape.extents(Shape.output_shape(plan))), zero) : {Nat.is_lt(index, _) == True{} : Bool}
37          below))