docs: def add_functions(spec_dict: Mapping[str, Any]) -> Mapping[str, Any]:
      """Add function keys to spec_dict
  
      Args:
          spec_dict (Mapping[str, Any]): bel specification dictionary
  
      Returns:
          Mapping[str, Any]: bel specification dictionary with added function keys
      """
  
      # Class 'Mapping' does not define '__setitem__', so the '[]' operator cannot be used on its instances
      spec_dict["functions"]["list"] = []
      spec_dict["functions"]["list_long"] = []
      spec_dict["functions"]["list_short"] = []
  
      spec_dict["functions"]["primary"] = {}
      spec_dict["functions"]["primary"]["list_long"] = []
      spec_dict["functions"]["primary"]["list_short"] = []
  
      spec_dict["functions"]["modifier"] = {}
      spec_dict["functions"]["modifier"]["list_long"] = []
      spec_dict["functions"]["modifier"]["list_short"] = []
  
      spec_dict["functions"]["to_short"] = {}
      spec_dict["functions"]["to_long"] = {}
  
      for func_name in spec_dict["functions"]["info"]:
  
          abbreviated_name = spec_dict["functions"]["info"][func_name]["abbreviation"]
  
          spec_dict["functions"]["list"].extend((func_name, abbreviated_name))
  
          spec_dict["functions"]["list_long"].append(func_name)
          spec_dict["functions"]["list_short"].append(abbreviated_name)
  
          if spec_dict["functions"]["info"][func_name]["type"] == "primary":
              spec_dict["functions"]["primary"]["list_long"].append(func_name)
              spec_dict["functions"]["primary"]["list_short"].append(abbreviated_name)
          else:
              spec_dict["functions"]["modifier"]["list_long"].append(func_name)
              spec_dict["functions"]["modifier"]["list_short"].append(abbreviated_name)
  
          spec_dict["functions"]["to_short"][abbreviated_name] = abbreviated_name
          spec_dict["functions"]["to_short"][func_name] = abbreviated_name
  
          spec_dict["functions"]["to_long"][abbreviated_name] = func_name
          spec_dict["functions"]["to_long"][func_name] = func_name
  
      return spec_dict