def above

bendtorch-core@0.1.0.0 · src/tensor/permute_build_proof.bend:581

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/storage/arith.bend as Arith
import bendtorch-core@0.1.0.0/src/storage/model.bend as Model
import bendtorch-core@0.1.0.0/src/tensor/contracts/build_facts.bend as Facts
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

581# A subtree whose positions all lie above k is the same for k and 1 + k.
582def above(+input: Shape.Shape, +axes: List<&2, U32>, +fill: F32, +ops: List<&2, StorageLaws.Op>, +k: Nat, +depth: Nat, +b: Nat, +h: {Nat.is_lt(k, b) == True{} : Bool}) ->
583  {spec(input, axes, fill, ops, k, depth, b) == spec(input, axes, fill, ops, 1n+k, depth, b) : Array<F32>}:
584  match depth:
585    case 0n:
586      %Equal.sym(Bool, Nat.is_lt(b, k), False{}, Facts.lt_asym(k, b, h)) :
587        {ALeaf{leaf(input, axes, fill, ops, b, _)} == ALeaf{leaf(input, axes, fill, ops, b, Nat.is_lt(b, 1n+k))} : Array<F32>}
588      %Equal.sym(Bool, Nat.is_lt(b, 1n+k), False{}, Facts.above_false(k, b, h)) :
589        {ALeaf{0.0} == ALeaf{leaf(input, axes, fill, ops, b, _)} : Array<F32>}
590      {==}
591    case 1n+inner:
592      +high = Nat.add(Model.capacity(inner), b)
593      %Equal.sym(Array<F32>, spec(input, axes, fill, ops, k, inner, b), spec(input, axes, fill, ops, 1n+k, inner, b), above(input, axes, fill, ops, k, inner, b, h)) :
594        {ANode{_, spec(input, axes, fill, ops, k, inner, high)} == spec(input, axes, fill, ops, 1n+k, 1n+inner, b) : Array<F32>}
595      %Equal.sym(Array<F32>, spec(input, axes, fill, ops, k, inner, high), spec(input, axes, fill, ops, 1n+k, inner, high),
596        above(input, axes, fill, ops, k, inner, high, Arith.lt_le_trans(k, b, high, h, Api.le_add_left(Model.capacity(inner), b)))) :
597        {ANode{spec(input, axes, fill, ops, 1n+k, inner, b), _} == spec(input, axes, fill, ops, 1n+k, 1n+inner, b) : Array<F32>}
598      {==}