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def complete_align

bendtorch-core@0.1.0.0 · src/shape/plan_proofs.bend:163

import bendtorch-core@0.1.0.0/src/shape/plan_proofs.bend as PlanProofs
import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend as Nats
import bendtorch-core@0.1.0.0/src/shape/construct_proofs.bend as Construct
import bendtorch-core@0.1.0.0/src/shape/LAWS.bend as Laws

163def complete_align(+left: Shape.Shape, +right: Shape.Shape, +left_padding: Nat, +right_padding: Nat, -minimal: Shape.PadMinimal<left_padding, right_padding>, +alignment: Shape.Alignment<Shape.pad_words(left_padding, Shape.dimensions(left)), Shape.pad_words(right_padding, Shape.dimensions(right))>, -target: List<&2, Nat>, seen: {Some{target} == aligned_output(Shape.pad_words(left_padding, Shape.dimensions(left)), Shape.pad_words(right_padding, Shape.dimensions(right)), alignment) : Maybe<&2, List<&2, Nat>>}, +rank_bound: Shape.LE(List.length(&2, Nat, target), 4n), +capacity_bound: Shape.LE(Shape.numel(target), 1048576n)) -> {Laws.broadcast_built(Shape.broadcast_checked.align(left, right, left_padding, right_padding, minimal, alignment)) == True{} : Bool}:
164  match alignment:
165    case Shape.Misaligned{}:
166      Empty.absurd({False{} == True{} : Bool}, some_none(List<&2, Nat>, target, seen))
167    case Shape.Aligns{+output, aligned}:
168      +same = some_injective(List<&2, Nat>, target, Shape.naturals(output), seen)
169      +rank_fits = Nats.le_rewrite(Shape.rank_dimensions(output), List.length(&2, Nat, target), 4n, Equal.trans(Nat, List.length(&2, Nat, target), List.length(&2, Nat, Shape.naturals(output)), Shape.rank_dimensions(output), Equal.cong(List<&2, Nat>, Nat, values => List.length(&2, Nat, values), target, Shape.naturals(output), same), Equal.sym(Nat, Shape.rank_dimensions(output), List.length(&2, Nat, Shape.naturals(output)), Shape.rank_naturals(output))), rank_bound)
170      +capacity_fits = Nats.le_rewrite(Shape.numel(Shape.naturals(output)), Shape.numel(target), 1048576n, Equal.cong(List<&2, Nat>, Nat, values => Shape.numel(values), target, Shape.naturals(output), same), capacity_bound)
171      complete_construct(left, right, left_padding, right_padding, minimal, output, Shape.broadcast_checked.repad(left_padding, right_padding, Shape.dimensions(left), Shape.dimensions(right), output, aligned), Shape.construct(output), Construct.construction_complete(output, Shape.bool_case(Nat.is_le(Shape.rank_dimensions(output), 4n)), Nats.le_true(Shape.rank_dimensions(output), 4n, rank_fits), capacity_fits))

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