[Haskell-cafe] Re: A question about mfix

[Wei Hu]

So that's also why the fix function from Data.Function is defined as 

> fix f = let x = f x in x

instead of

> fix f = f $ fix f

right?

But, I think my mfix definition and your mfixLazy definition are still 
semantically equivalent because they expand to the same thing. See the 
following example:

> import Control.Monad.Identity

> -- Strict Identity monad
> data IdentityS a = IdentityS { runIdentityS :: a } deriving Show
> instance Monad IdentityS where
>     return = IdentityS
>     (IdentityS m) >>= k  = k m

> mfix' f = mfix' f >>= f
> mfixLazy f = let x = x >>= f in x

> facFM f = return (\i ->
>   if i == 0
>     then 1
>     else i * f (i - 1)
>   )

> -- correctly outputs 3! = 6    
> test = runIdentity (mfix facFM) 3 

> -- stack overflows
> test2 = runIdentityS (mfix' facFM) 3

> -- hangs
> test3 = runIdentityS (mfixLazy facFM) 3

Thanks for pointing out the sharing part. My original question is still 
unanswered: for lazy monads, can we give such a general mfix definition?