type logical_plan =
  | Project of logical_plan option * string list
  | Scan of string (* Table name *)
  | Filter of logical_plan 
  | Join of logical_plan * Ast.join_type * logical_plan 
  | Group of logical_plan * string list

let rec ast_to_logical ast =
  match ast with 
  | Ast.Select(cols, table_exp) -> Project((table_expression_to_logical table_exp), (columns_to_logical cols))
  | _ -> failwith "Query not supported yet"

and table_expression_to_logical table_exp = 
  match table_exp with
  | Ast.TableExpression(Some(tables), None, None) -> tables_to_logical tables
  | _ -> failwith "Table expression not supported yet"

and columns_to_logical columns =
  let rec aux cols acc = 
    match  cols with
    | [] -> acc
    | Ast.Column(col,_)::l ->
      let s = expression_to_logical col in
      aux l (s::acc)
    | _ -> failwith "Not supported"
  in 
  aux columns []

and expression_to_logical exp =
  match exp with
  | Ast.Ref(s) -> s
  | _ -> failwith "Expression not supported yet"

and tables_to_logical tables =
  let rec aux t =
    match t with
    | [] -> None
    | [Ast.Table(table_name)] -> Some(Scan(table_name))
    | _ -> failwith "tables not supported"
  in
  match tables with
  | None -> None
  | Some(t) -> aux t


let rec pp_logical_plan plan =
  match plan with 
  | Project(plan2, name) -> pp_logical_plan plan2 ^ (String.concat ";" name)
  | _ -> "Not supported"