In a previous post, I demonstrated how to use the lazy state monad to turn Geraint Jones and Jeremy Gibbon’s breadth-first labeling algorithm into a reusable abstraction, and mentioned that I did not know how to combine the result with continuations. In this post, I will do exactly that.

A hat tip goes to Twan van Laarhoven for suggesting that I split my `fresh`

operator into two, which I adopt in this post. In the comments, `down`

is defined as:

type Fresh n a = State [n] a down :: Fresh n a -> Fresh n a down m = do (n:ns) <- get put ns a <- m ns' <- get put (n:ns') return a

Now, if we naïvely apply the continuation transformer in the Monad Transformer Library, the `get`

and `put`

operators are lifted as follows:

type FreshCC r n a = ContT r (State [n]) a lift :: Monad m => m a -> ContT r m a lift m = ContT (m >>=) down :: FreshCC r n a -> FreshCC r n a down m = do (n:ns) <- lift get lift (put ns) a <- m ns' <- lift get lift (put (n:ns')) return a

The problem is that this replaces the `>>=`

of the lazy state monad with the `>>=`

of the continuation transformer, and these two operators have different strictness properties. This, in turn, leads to non-termination. The trick is not to lift `get`

and `put`

, but rather conjugate `down`

:

lower :: Monad m => ContT a m a -> m a lower m = runContT m return down :: FreshCC a n a -> FreshCC r n a down m = lift $ do (n:ns) <- get put ns a <- lower m ns' <- get put (n:ns') return a -- *or* down = lift . original_down . lower

Now, the conjugation preserves the use of the lazy state monad’s `>>=`

in the definition of `down`

, however it changes the type of the argument from `FreshCC `

to **r** n a`FreshCC `

! The other definitions contained in the previous post stay much the same.**a** n a

Feel free to download freshcc.hs, a full working demonstration of this post. One can even use `callCC`

, `fresh`

, and `down`

in the same computation *and* terminate! Sadly, I don’t have any demonstrations of this combination, nor do I have any applications in mind. My intuition about `callCC`

is currently quite limited in this context.

I have implemented Dan Friedman’s angel-devil-milestone control operators in conjunction with fresh and down, and have used it to duplicate labels and change the shape of a spirited tree; but I’m definitely cheating at this point, as all I have done is observe that the definitions compute *something*. I have no control over what’s going on, nor do I know what the definitions are supposed to compute. (yet)

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