Instrumented State monad

Question

I am trying to give Monad and MonadState instances for State' that counts the number of (>>=), return, get and put operations.

data Counts = Counts { binds   :: Int
                 , returns :: Int
                 , gets    :: Int
                 , puts    :: Int
                 }

newtype State' s a = State' { runState' :: (s, Counts) -> (a, s, Counts) }

That's what I have already done, and as far as I understand what is going on, this code should work:

instance Monad State' where
  return     = State' ( \(s, counts) -> (x, s, counts mappend oneReturn))
  (>>=) st f = State' ( \(s, counts) -> let (x, s', counts') = runState' (s, counts) in runState' ((f x), (s', counts' mappend oneBind)) )

instance Monad m => MonadState m State' where
   get    = State' ( \(s, counts) -> (s, s, counts mappend oneGet) )
   put st = State' ( \(s, counts) -> ((), st, counts mappend onePut) )

But I get this error message:

Expecting one more argument to ‘State'’
Expected kind ‘* -> *’, but ‘State'’ has kind ‘* -> * -> *’

Why?

Answer 1

The point is in the sentence

Expected kind ‘* -> *’, but ‘State'’ has kind ‘* -> * -> *’

If you check the kind of State' with GHCi using :k command you will see that State' has kind * -> * -> * which simply speaking means that it requires to be parametrized by two types of kind * to produce finalized * type. Monads are as you see restricted to * -> *. For instance Maybe is a Monad, while Maybe Int is not.

To fix your case you will need to apply the state type to State' and then you will be able to declare it as a Monad:

instance Monad (State' s) where

---

The error in the second part is a bit conceptual – what is m in your declaration? MonadState is a subclass of Monad, so every instance of MonadState is also instance of Monad. With this in mind the correct notation should make some sense:

instance MonadState s (State' s) where

You don't want to mention this Monad – it is derivable from the class declaration.