[Haskell-beginners] State Monad stack example

[Animesh Saxena]

I am trying to relate the state monad to a stack example and somehow found it easy to get recursively confused!

instance Monad (State s) where
    return x = State $ \s -> (x,s)
    (State h) >>= f = State $ \s -> let (a, newState) = h s
                                                    (State g) = f a
                                                     in g newState

Considering the stack computation

stackManip stack = let 
              ((), newStack1) = push 3 stack
              (a, newStack2) = pop newStack1
               in pop newStack2

in do notation this would become 
do  
   push 3  
   a <- pop  
   pop

If I consider the first computation push 3 >>= pop and try to translate it to the definition there are problems....
Copy paste again, I have 
    (State h) >>= f = State $ \s -> let (a, newState) = h s
                                                    (State g) = f a
                                                     in g newState

f is the push function to which we are shoving the old state. I can't exactly get around to what exactly is the state computation h? Ok assuming it's something which gives me a new state, but then thats push which is function f. 
Then push is applied to a which is assuming 3 in this case. This gives me a new state, which I would say newStack1 from the stockManip above.

Then somehow I apply g to newState?? All the more confusion. Back to the question what exactly is state computation and how is it different from f? It seems to be the same function?


-Animesh




                           
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