//Only four movement commands are understood: north (1), south (2), west (3), and east (4).
type Position = {X:int;Y:int}
let back = function
    | 1L -> 2L
    | 2L -> 1L
    | 3L -> 4L
    | 4L -> 3L
    | _ -> failwith "wrong direction"
let moveTo = function
    | 1L -> fun position -> {position with Y = position.Y + 1}
    | 2L -> fun position -> {position with Y = position.Y - 1}
    | 3L -> fun position -> {position with X = position.X - 1}
    | 4L -> fun position -> {position with X = position.X + 1}
    | _ -> failwith "wrong direction"