Recently I had to navigatate trough data structures chained with mutable referenes in th STM monad. The problem is that their values are enveloped in  Either or Maybe results.<div><br><div>functional compositions in the Either of Maybe , or list  monads are not possible when the values are  embedded inside effect monads (i.e. STM or IO) . I tried  to find some trick to handle it.</div>

<div><br></div><div>to summarize, given:</div><div><br></div><div> foo, :  a -&gt; m (Maybe b)</div><div><div> bar :   b -&gt; m (Maybe c)</div></div><div><div> baz :  c -&gt; m (Maybe d)</div></div><div><br></div><div>how to compose foo bar and baz? Or, at least,  Are something out there to handle it in the less painful way?.</div>

<div><br></div><div><br></div><div>I solved the generalized problem  (chaining  any double monadic combination) with a sort of monadic connector that acts as a &quot; double monadic&quot; operator   &gt;&gt;&gt;&gt;==  so that</div>

<div><br></div><div>return. return (x :: a) &gt;&gt;&gt;&gt;== foo &gt;&gt;&gt;== bar &gt;&gt;&gt;== baz  </div><div><br></div><div>can be possible. Although I don&#39;t know if  it is the best solution. I wonder why nobody has written about it before:</div>

<div><div><br></div><div>class (Monad m, Monad n) =&gt; Bimonad m n where</div><div> (&gt;&gt;&gt;=)   ::  n a -&gt; (a -&gt; m(n b)) -&gt; m(n b)</div><div><br></div><div><div>(&gt;&gt;&gt;&gt;==) :: (Bimonad m n) =&gt; m (n a) -&gt; (a -&gt; m(n b)) -&gt; m (n b)</div>

<div>(&gt;&gt;&gt;&gt;==) x  f =  x &gt;&gt;= \y -&gt; y &gt;&gt;&gt;=  f</div><div><br></div><div>x &gt;&gt;&gt;&gt; f = x &gt;&gt;&gt;&gt;== \ _-&gt; f</div></div><div><br></div><div>infixl 1 &gt;&gt;&gt;&gt;==, &gt;&gt;&gt;&gt;</div>

<div><br></div><div>The instance for handling the Maybe monad under any other monad is very similar to the definition of the &quot;normal&quot; monad:</div><div><br></div><div>instance (Monad m) =&gt; Bimonad m Maybe where</div>

<div>   Just x  &gt;&gt;&gt;= f = f x</div><div>   Nothing &gt;&gt;&gt;= _ = return $ Nothing</div><div><br></div><div><br></div></div><div><br></div></div><div><br></div>