Personal tools


From HaskellWiki

Revision as of 00:50, 30 September 2010 by Ertes (Talk | contribs)

Jump to: navigation, search


1 Introduction

The contstuff library implements a number of monad transformers and monads, which make heavy use of continuation passing style (CPS). This makes them both fast and flexible. Please note that this is neither a CPS tutorial nor a monad transformer tutorial. You should understand these concepts, before attempting to use contstuff.

2 Basics

2.1 ContT

The ContT monad transformer is the simplest of all CPS-based monads. It essentially gives you access to the current continuation, which means that it lets you label certain points of execution and reuse these points later in interesting ways. With ContT you get an elegant encoding of computations, which support:

  • abortion (premature termination),
  • resumption (start a computation at a certain spot),
  • branches (aka goto),
  • result accumulation,
  • etc.
All these features are effects of ContT. If you don't use them, then ContT behaves like the identity monad. A computation of type
ContT r m a
is a CPS computation with an intermediate result of type
and a final result of type
. The
type can be polymorphic most of the time. You only need to specify it, if you use some of the CPS effects like
. To run a ContT computation you can use
or the convenience function
runContT  :: (a -> m r) -> ContT r m a -> m r
evalContT :: Applicative m => ContT r m r -> m r
function takes a final continuation transforming the last intermediate result into a final result. The
function simply passes
as the final continuation.

2.2 Abortion

Let's have a look at a small example:

testComp1 :: ContT () IO ()
testComp1 =
  forever $ do
    txt <- io getLine
    case txt of
      "info" -> io $ putStrLn "This is a test computation."
      "quit" -> abort ()
      _      -> return ()
This example demonstrates the most basic feature of ContT. First of all, ContT is a monad transformer, so you can for example lift IO actions to a CPS computation. The
function is a handy tool, which corresponds to
from other transformer libraries and to
from monadLib, but is restricted to the IO monad. You can also use the more generic
function, which promotes a base monad computation to ContT. Each ContT subcomputation receives a continuation, which is a function, to which the subcomputation is supposed to pass the result. However, the subcomputation may choose not to call the continuation at all, in which case the entire computation finishes with a final result. The
function does that.

2.3 Resumption and branches

You can capture the current continuation using the common
function. If you just need branches, there are two handy functions for this:
labelCC :: a -> ContT r m (a, Label (ContT r m) a)
goto    :: Label (ContT r m) a -> a -> ContT r m b

These slightly complicated looking functions are actually very simple to use:

testComp2 :: ContT r IO ()
testComp2 = do
  (i, again) <- labelCC 0
  io (print i)
  when (i < 10) $ goto again (i+1)
  io (putStrLn $ "Final result: " ++ show i)
function establishes a label to jump to by capturing its own continuation. It returns both its argument and a label. The
function takes a label and a new argument. The effect is jumping to the corresponding label, but returning the new argument. So when
is reached the
variable becomes 0. Later
jumps back to the same point, but gives
a new value 1, as if
were originally called with 1 as the argument.

Labels are first class values in contstuff. This means you can carry them around. They are only limited in that they can't be carried outside of a ContT computation.

2.4 Lifting

As noted earlier there are three lifting functions, which you can use to access monads in lower layers of the transformer stack:

lift :: (Transformer t, Monad m) => m a -> t m a
base :: (LiftBase m a) => Base m a -> m a
io   :: (Base m a ~ IO a, LiftBase m a) => Base m a -> m a
function promotes a computation of the underlying monad. The
function promotes a computation of the base monad. It is a generalization of
from other monad transformer libraries. Finally there is
, which is simply an alias for
, but restricted to IO.

2.5 Accumulating results

ContT does not require the underlying functor to be a monad. Whenever the underlying functor is an
functor, there is support for accumulating results using the
combinator. In other words, if
is an
, then
ContT r m
is, too. Here is an example:
testComp3 :: Num a => ContT r [] (a, a)
testComp3 = do
  x <- pure 10 <|> pure 20
  y <- pure (x+1) <|> pure (x-1)
  return (x, y)
The contstuff library implements a convenience function
, which turns a list into an
listA :: (Alternative f) => [a] -> f a
Using this you can simplify
testComp3' :: Num a => ContT r [] (a, a)
testComp3' = do
  x <- listA [10, 20]
  y <- listA [x+1, x-1]
  return (x, y)
You can collapse branches using
testComp4 :: Num a => ContT (a, a) [] (a, a)
testComp4 = do
  x <- listA [10, 20]
  when (x == 10) (abort (10, 10))
  y <- listA [x+1, x-1]
  return (x, y)