The Continuation monad

• Overview
• Motivation
• Definition
• Example

Abuse of the Continuation monad can produce code that is impossible to understand and maintain.

Before using the Continuation monad, be sure that you have a firm understanding of continuation-passing style (CPS) and that continuations represent the best solution to your particular design problem. Many algorithms which require continuations in other languages do not require them in Haskell, due to Haskell's lazy semantics.

Continuations represent the future of a computation, as a function from an intermediate result to the final result. In continuation-passing style, computations are built up from sequences of nested continuations, terminated by a final continuation (often id) which produces the final result. Since continuations are functions which represent the future of a computation, manipulation of the continuation functions can achieve complex manipulations of the future of the computation, such as interrupting a computation in the middle, aborting a portion of a computation, restarting a computation and interleaving execution of computations. The Continuation monad adapts CPS to the structure of a monad.

newtype Cont r a = Cont { runCont :: ((a -> r) -> r) } -- r is the final result type of the whole computation 
  
instance Monad (Cont r) where 
    return a       = Cont $ \k -> k a                       -- i.e. return a = \k -> k a 
    (Cont c) >>= f = Cont $ \k -> c (\a -> runCont (f a) k) -- i.e. c >>= f = \k -> c (\a -> f a k) 

The Continuation monad represents computations in continuation-passing style. Cont r a is a CPS computation that produces an intermediate result of type a within a CPS computation whose final result type is r.

The return function simply creates a continuation which passes the value on. The >>= operator adds the bound function into the continuation chain.

class (Monad m) => MonadCont m where 
    callCC :: ((a -> m b) -> m a) -> m a 
 
instance MonadCont (Cont r) where 
    callCC f = Cont $ \k -> runCont (f (\a -> Cont $ \_ -> k a)) k

The MonadCont class provides the callCC function, which provides an escape continuation mechanism for use with Continuation monads. Escape continuations allow you to abort the current computation and return a value immediately. They achieve a similar effect to throwError and catchError within an Error monad.

callCC calls a function with the current continuation as its argument (hence the name). The standard idiom used with callCC is to provide a lambda-expression to name the continuation. Then calling the named continuation anywhere within its scope will escape from the computation, even if it is many layers deep within nested computations.

In addition to the escape mechanism provided by callCC, the Continuation monad can be used to implement other, more powerful continuation manipulations. These other mechanisms have fairly specialized uses, however — and abuse of them can easily create fiendishly obfuscated code — so they will not be covered here.

This example gives a taste of how escape continuations work. The example function uses escape continuations to perform a complicated transformation on an integer.

{- We use the continuation monad to perform "escapes" from code blocks.
   This function implements a complicated control structure to process
   numbers:

   Input (n)       Output                       List Shown
   =========       ======                       ==========
   0-9             n                            none
   10-199          number of digits in (n/2)    digits of (n/2)
   200-19999       n                            digits of (n/2)
   20000-1999999   (n/2) backwards              none
   >= 2000000      sum of digits of (n/2)       digits of (n/2)
-}  
fun :: Int -> String
fun n = (`runCont` id) $ do
        str <- callCC $ \exit1 -> do                        -- define "exit1"
          when (n < 10) (exit1 (show n))
          let ns = map digitToInt (show (n `div` 2))
          n' <- callCC $ \exit2 -> do                       -- define "exit2"
            when ((length ns) < 3) (exit2 (length ns))
            when ((length ns) < 5) (exit2 n)
            when ((length ns) < 7) $ do let ns' = map intToDigit (reverse ns)
                                        exit1 (dropWhile (=='0') ns')  --escape 2 levels
            return $ sum ns
          return $ "(ns = " ++ (show ns) ++ ") " ++ (show n')
        return $ "Answer: " ++ str