def above

bendtorch-core@0.1.0.0 · src/autograd/reduce_replayed_proof.bend:291

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/storage/model.bend as Model
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/storage/api.bend as Api

291# A subtree whose positions all lie above k is the same for k and 1 + k.
292def above(+plan: Shape.BroadcastPlan, +map: PlanMap(plan), +shape: Shape.Shape, +fill: F32, +ops: List<&2, StorageLaws.Op>, +k: Nat, +depth: Nat, +b: Nat, +h: {Nat.is_lt(k, b) == True{} : Bool}) ->
293  {out_spec(plan, map, shape, fill, ops, k, depth, b) == out_spec(plan, map, shape, fill, ops, 1n+k, depth, b) : Array<F32>}:
294  match depth:
295    case 0n:
296      %Equal.sym(Bool, Nat.is_lt(b, k), False{}, lt_asym(k, b, h)) :
297        {ALeaf{out_leaf(plan, map, shape, fill, ops, b, _)} == ALeaf{out_leaf(plan, map, shape, fill, ops, b, Nat.is_lt(b, 1n+k))} : Array<F32>}
298      %Equal.sym(Bool, Nat.is_lt(b, 1n+k), False{}, above_false(k, b, h)) :
299        {ALeaf{0.0} == ALeaf{out_leaf(plan, map, shape, fill, ops, b, _)} : Array<F32>}
300      {==}
301    case 1n+inner:
302      +high = Nat.add(Model.capacity(inner), b)
303      %Equal.sym(Array<F32>, out_spec(plan, map, shape, fill, ops, k, inner, b), out_spec(plan, map, shape, fill, ops, 1n+k, inner, b), above(plan, map, shape, fill, ops, k, inner, b, h)) :
304        {ANode{_, out_spec(plan, map, shape, fill, ops, k, inner, high)} == out_spec(plan, map, shape, fill, ops, 1n+k, 1n+inner, b) : Array<F32>}
305      %Equal.sym(Array<F32>, out_spec(plan, map, shape, fill, ops, k, inner, high), out_spec(plan, map, shape, fill, ops, 1n+k, inner, high),
306        above(plan, map, shape, fill, ops, k, inner, high, Arith.lt_le_trans(k, b, high, h, Api.le_add_left(Model.capacity(inner), b)))) :
307        {ANode{out_spec(plan, map, shape, fill, ops, 1n+k, inner, b), _} == out_spec(plan, map, shape, fill, ops, 1n+k, 1n+inner, b) : Array<F32>}
308      {==}