How to write instance of state Monad

Question

I am very new to monads within haskell and i am trying to develop my knowledge with monads ny creating some instances but I am really quite confused with this one i am getting a few errors and have been at it for a bit as i am still unsure any help and explanations are appreciated this is what i have so far, any ideas where i am going wrong?

newtype ST b = S (Int -> (b, Int))
runState :: ST b  -> Int -> (b, Int)
runState (S b) st = b st 

instance Monad ST where 
return :: b -> ST b
return x = S (\st -> (x, st))       the new state with a b 

(>>=) :: ST b -> (b -> ST c) -> ST c
c >>= c' = S (\st1 ->
                let (b, st2) = runState c st1
                    (c, st3) = runState (c' b) st2
                in  (c, st3))

Answer 1

You might have to give implementations for Applicative and Functor as well:

import Control.Applicative
import Control.Monad (liftM, ap)

newtype ST b = S (Int -> (b, Int))
runState :: ST b  -> Int -> (b, Int)
runState (S b) st = b st 

instance Monad ST where 
  -- return :: b -> ST b
  return x = S (\st -> (x, st))      -- takes in the current state and returns the new state with a b 
  
  -- (>>=) :: ST b -> (b -> ST c) -> ST c
  c >>= c' = S (\st1 ->
                let (b, st2) = runState c st1
                    (c'', st3) = runState (c' b) st2
                in  (c'', st3))


instance Applicative ST where
  pure = return
  (<*>) = ap


instance Functor ST where
  fmap = liftM

I found that here.