## 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

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

. If you don't use them, then

behaves like the identity monad. A computation of type

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

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

The

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

. First of all,

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

monad. You can also use the more generic

function, which promotes a base monad computation to

.
Each

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)

The

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

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

The

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

.

### 2.5 Accumulating results

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

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

computation:

listA :: (Alternative f) => [a] -> f a

Using this you can simplify

to:

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)