let left (Loc(t, p)) =
    match p with
    | Top -> failwith "left at top"
    | Node(l::left, up, right) -> Loc(l, Node(left, up, t::right))
    | Node([], up, right) -> failwith "left of first"

  let right (Loc(t, p)) =
    match p with
    | Top -> failwith "right at top"
    | Node(left, up, r::right) -> Loc(r, Node(t::left, up, right))
    | _ -> failwith "right of last"

  let up (Loc(t, p)) =
    match p with
    | Top -> failwith "up at top"
    | Node (left, up, right) -> Loc(Section((List.rev left) @ (t::right)), up)

  let down (Loc(t, p)) =
    match t with
    | Item(_) -> failwith "down with item"
    | Section(t1::trees) -> Loc(t1, Node([], p, trees))
    | _ -> failwith "down of empty"