def below

bendtorch-core@0.1.0.0 · src/autograd/reduce_replayed_proof.bend:310

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/api.bend as Api
import bendtorch-core@0.1.0.0/src/shape/index_proofs.bend as Index

310# A subtree whose positions all lie below k is the same for k and 1 + k.
311def below(+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_le(Nat.add(Model.capacity(depth), b), k) == True{} : Bool}) ->
312  {out_spec(plan, map, shape, fill, ops, k, depth, b) == out_spec(plan, map, shape, fill, ops, 1n+k, depth, b) : Array<F32>}:
313  match depth:
314    case 0n:
315      +lower = below_true(b, k, h)
316      %Equal.sym(Bool, Nat.is_lt(b, k), True{}, lower) :
317        {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>}
318      %Equal.sym(Bool, Nat.is_lt(b, 1n+k), True{}, lt_succ_right(b, k, lower)) :
319        {ALeaf{cell_word(plan, map, shape, fill, ops, b)} == ALeaf{out_leaf(plan, map, shape, fill, ops, b, _)} : Array<F32>}
320      {==}
321    case 1n+inner:
322      +c = Model.capacity(inner)
323      +high = Nat.add(c, b)
324      +nested = Equal.trans(Bool, Nat.is_le(Nat.add(c, high), k), Nat.is_le(Nat.add(Nat.add(c, c), b), k), True{},
325        Equal.cong(Nat, Bool, x => Nat.is_le(x, k), Nat.add(c, high), Nat.add(Nat.add(c, c), b), Index.add_assoc(c, c, b)), h)
326      +low_h = le_trans(high, Nat.add(c, high), k, le_add_cong(c, b, high, Api.le_add_left(c, b)), nested)
327      %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), below(plan, map, shape, fill, ops, k, inner, b, low_h)) :
328        {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>}
329      %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), below(plan, map, shape, fill, ops, k, inner, high, nested)) :
330        {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>}
331      {==}