At first, I tried to solve mutual recursive module problem. However, my effort to solve this problem makes the code worse.

Original problem

I have two module like

module W where

import T

data W = W  { wName  :: String
            , queue  :: [T W]}`

and

module T where

import W

data T = T { tName  :: String
            , tUpdate :: W -> IO W}

class Manage a where
    update :: a -> W -> IO W

instance Manage T where
    update = tUpdate

These modules are not able to work, because of mutual recursive modules problem.

So I changed module T, according to this link

New solution with data variable

module T where

data T w = T { tName  :: String
            , tUpdate :: w -> IO w}

class Manage a where
    update :: a -> w -> IO w

instance Manage (T w) where
    update = tUpdate

However, this code makes error like:

Couldn't match type ‘w’ with ‘w1’
  ‘w’ is a rigid type variable bound by
      the instance declaration at TestModule2.hs:12:10
  ‘w1’ is a rigid type variable bound by
       the type signature for update :: T w -> w1 -> IO w1
       at TestModule2.hs:13:5
Expected type: T w -> w1 -> IO w1
  Actual type: T w -> w -> IO w
Relevant bindings include
  update :: T w -> w1 -> IO w1 (bound at TestModule2.hs:13:5)
In the expression: tUpdate
In an equation for ‘update’: update = tUpdate

So, I tried many things to solve this problem like

Introduce new class like State w to represent data W

To solve rigid type variable ..., I introduced new class.

{-# LANGUAGE InstanceSigs, Rank2Types #-}
module T where

.....

data T w = T  { tName  :: String
              , tUpdate :: (State w) => w -> IO w}

class Manage a where
    update :: (State w) => a -> (w -> IO w)

instance (State w) => Manage (T w) where
    update :: T w -> w -> IO w
    update = tUpdate

But this code also makes error like:

Method signature does not match class; it should be
  update :: forall w1. State w1 => T w -> w1 -> IO w1
In the instance declaration for ‘Manage (T w)’

I followed this suggestion, but this doesn't work. Moreover, w1 and w should be same type.

Do I need to define class or class method other way?

So, What do I need to study and how could I solve this problem?

I tried more things, but I couldn't solve this. What do I need to study to solve this problem? And how could I solve this problem?

Important points:

1. I need to separate this two module.
2. As possible as I can, I do not want to use hs-boot, but more elegant way