def cells_at

bendtorch-core@0.1.0.0 · src/autograd/broadcast_pointwise_PROOF.bend:80

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/arith.bend as Arith
import bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend as Replayed
import bendtorch-core@0.1.0.0/src/tensor/contracts/broadcast.bend as PointwiseBroadcast
import bendtorch-core@0.1.0.0/src/autograd/reduce_LAWS.bend as ReduceLaws
import bendtorch-core@0.1.0.0/src/autograd/broadcast_pointwise_LAWS.bend as Laws

80def cells_at(+plan: Shape.BroadcastPlan, +shape: Shape.Shape, +fill: F32, +ops: List<&2, StorageLaws.Op>, +count: Nat, +position: Nat,
81  below: {Nat.is_lt(position, count) == True{} : Bool}) ->
82  {ReduceLaws.word_at(Laws.cells(plan, shape, fill, ops, count), position) ==
83    Some{Replayed.value(shape, fill, ops, U32.from_nat(PointwiseBroadcast.left_map(plan, position)))} : Maybe<&2, F32>}:
84  match count:
85    case 0n:
86      Empty.absurd({ReduceLaws.word_at(Nil{}, position) ==
87        Some{Replayed.value(shape, fill, ops, U32.from_nat(PointwiseBroadcast.left_map(plan, position)))} : Maybe<&2, F32>},
88        Arith.lt_zero(position, below))
89    case 1n+previous:
90      cells_step(plan, shape, fill, ops, previous, position, below, Shape.bool_case(Nat.is_eq(position, previous)),
91        inside => cells_at(plan, shape, fill, ops, previous, position, inside))