Is it possible to create a Monad that count the number of instructions?

Question

Thinking about monad, it came to me the idea of a monad as the way to break with the Von Neumann architecture. The Von Neumann architecture uses a set of instructions (called program) to change the data in memory and the execution of each instruction of the program updates a program counter to know whom instruction is the next to execute.

If we think about the Von Neumann architecture as a monad, the bind operator (>>=) update the program counter. We can make a Monad that break Von Neumann architecture to do more in the bind. As an example, we can have a Monad that count the number of instructions executed in our programs.

But, when I tried to implement that Monad in haskell as:

data Counter a = Counter Integer a
             deriving( Show )

instance Monad Counter where
  (Counter n1 a) >>= f = let Counter _ b = f a
                     in (Counter (n1+1) b)
  return a = Counter 1 a

I notice it'll break de Monads laws, e.g:

return x >>= f            /=   f x

do
   a <- return 3
   return a

do 
   return 3

The two blocks are the same because the monad laws, but they'll return something different because they have different number of instructions (sentences)

Do I made something wrong? or Is it not possible to have such Monad?

Answer 1

Strictly speaking, any such "monad" breaks the monad laws and is thus... not a monad. See this previous question for details. In other words - your guess is correct, it is not possible to have such a monad.