[Haskell-cafe] monad constraint + record update

[Miguel Mitrofanov]

You can use a continuation trick I describe below.

First of all, I would like to work in a more general situation. So,  
instead of working with Set, I'd like to declare two classes:

 > class Returnable m a where ret :: a -> m a

and

 > class Bindable m a b where bind :: m a -> (a -> m b) -> m b

I'm sure you're able to define instances like "instance Ord a =>  
Returnable Set a" by yourself. You'll need MultiParamTypeClasses and  
FlexibleInstances for that to work.

Now, the trick:

 > newtype Restricted r m a = Restricted ((a -> m r) -> m r)
 > instance Monad (Restricted r m) where
 >     return x = Restricted $ \h -> h x
 >     Restricted g >>= f = Restricted $ \h -> g $ \x -> let  
Restricted g' = f x in g' h

Quite simple, and doesn't mention pseudo-monadic structure of "m" at  
all.

Now, the fun part:

 > embed :: Bindable m a r => m a -> Restricted r m a
 > embed mx = Restricted (bind mx)

 > unembed :: Returnable m r => Restricted r m r -> m r
 > unembed (Restricted g) = g ret

You may also want another class

 > class Summable m a where
 >     zero :: m a
 >     plus :: m a -> m a -> m a

and now you can have

 > instance Summable m r => MonadPlus (Restricted r m) where
 >     mzero = Restricted $ const zero
 >     Restricted g1 `mplus` Restricted g2 = Restricted $ \h -> g1 h  
`plus` g2 h

 From now on, you can do something like that:

 > unembed $ do x <- embed $ Set.fromList [6,2,3]
 >              (do y <- return x
 >                  z <- embed $ Set.fromList [1..2]
 >                  guard $ y < 5
 >                  return $ y + z)
 >              `mplus` return 10

and have "fromList [3,4,5,10]", as expected

On 22 Dec 2008, at 20:19, Peter Padawitz wrote:

> I'd like to define a monad Set for types in the class Eq. But how  
> can the arguments of Set be constrained when Set is defined as an  
> instance of Monad? instance Eq a => Monad Set where ... obviously  
> cannot work.
>
> Is there a standard update function for fields in data types,  
> something that OO programmers do with assignments like obj.attr :=  
> value ?
>
> Peter
>
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