You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: reachability.rb
    path of file: ./repos/rbsyn/lib/rbsyn
    
    the code of the file until where you have to start completion: =begin
path = (type -> method -> type -> ..., tenv)
queue = initial_set of path
while depth < max_depth {
  type = consume item from queue
  find all possible methods in the type
  compute targs of the methods
  check if the targs can be constructed from the tenv
  if yes {
    compute tout for that method
    push the path to the queue
  }
}
take paths in the queue that end with the type that we need
=end

class CallChain
  attr_reader :path, :tenv

  def initialize(path, tenv)
    raise RbSynError, "expect path to be an array" unless path.is_a? Array
    raise RbSy
    
  def paths_to_type(target, depth, variance=COVARIANT)
    curr_depth = 0
    types = types_from_tenv(@initial_tenv)
    queue = types.map { |t| CallChain.new([t], types) }

    until curr_depth == depth do
      new_queue = []
      queue.each { |path|
        trecv = path.last
        mthds = methods_of(trecv)
        mthds.delete(:__getobj__)
        mthds.each { |mthd, info|
          tmeth = info[:type]
          targs = compute_targs(trecv, tmeth)
          next if targs.any? { |t| t.is_a? RDL::Type::BotType }
          tout = compute_tout(trecv, tmeth, targs)
          # convert :self types to actual object
          tout = trecv if tout.is_a?(RDL::Type::VarType) && tout.name == :self
          new_tenv = make_new_tenv(tout, path.tenv)
          new_queue << CallChain.new(path.path + [mthd, tout], new_tenv)
        }
      }
      queue = new_queue
      curr_depth += 1
    end
    chains_with_type(queue, target, variance)
  end