# Contstuff

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The [http://hackage.haskell.org/package/contstuff 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''. | The [http://hackage.haskell.org/package/contstuff 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''. | ||

− | == ContT == | + | == Basics == |

+ | === ContT === | ||

The <hask>ContT</hask> 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: | The <hask>ContT</hask> 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: | ||

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* etc. | * etc. | ||

− | All these features are effects of <hask>ContT</hask>. If you don't use them, then <hask>ContT</hask> behaves like the identity monad. A computation of type <hask>ContT r m a</hask> is a CPS computation with an intermediate result of type <hask>a</hask> and a final result of type <hask>r</hask>. The <hask>r</hask> type can be polymorphic most of the time. You only need to specify it, if you use some of the CPS effects like <hask>abort</hask>. Let's have a look at a small example: | + | All these features are effects of <hask>ContT</hask>. If you don't use them, then <hask>ContT</hask> behaves like the identity monad. A computation of type <hask>ContT r m a</hask> is a CPS computation with an intermediate result of type <hask>a</hask> and a final result of type <hask>r</hask>. The <hask>r</hask> type can be polymorphic most of the time. You only need to specify it, if you use some of the CPS effects like <hask>abort</hask>. |

+ | |||

+ | To run a <hask>ContT</hask> computation you can use <hask>runContT</hask> or the convenience function <hask>evalContT</hask>: | ||

+ | |||

+ | <haskell> | ||

+ | runContT :: (a -> m r) -> ContT r m a -> m r | ||

+ | evalContT :: Applicative m => ContT r m r -> m r | ||

+ | </haskell> | ||

+ | |||

+ | The <hask>runContT</hask> function takes a final continuation transforming the last intermediate result into a final result. The <hask>evalContT</hask> function simply passes <hask>pure</hask> as the final continuation. | ||

+ | |||

+ | === Abortion === | ||

+ | |||

+ | Let's have a look at a small example: | ||

<haskell> | <haskell> | ||

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Each <hask>ContT</hask> 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 <hask>abort</hask> function does that. | Each <hask>ContT</hask> 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 <hask>abort</hask> function does that. | ||

− | + | === Resumption and branches === | |

+ | |||

+ | You can capture the current continuation using the common <hask>callCC</hask> function. If you just need branches, there are two handy functions for this: | ||

<haskell> | <haskell> | ||

− | + | labelCC :: a -> ContT r m (a, Label (ContT r m) a) | |

− | + | goto :: Label (ContT r m) a -> a -> ContT r m b | |

</haskell> | </haskell> | ||

− | The <hask> | + | These slightly complicated looking functions are actually very simple to use: |

+ | |||

+ | <haskell> | ||

+ | 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) | ||

+ | </haskell> | ||

+ | |||

+ | The <hask>labelCC</hask> function establishes a label to jump to by capturing its own continuation. It returns both its argument and a label. The <hask>goto</hask> function takes a label and a new argument. The effect is jumping to the corresponding label, but returning the new argument. So when <hask>labelCC</hask> is reached the <hask>i</hask> variable becomes 0. Later <hask>goto</hask> jumps back to the same point, but gives <hask>i</hask> a new value 1, as if <hask>labelCC</hask> 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 <hask>ContT</hask> computation. | ||

+ | |||

+ | === Lifting === | ||

+ | |||

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

+ | |||

+ | <haskell> | ||

+ | 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 | ||

+ | </haskell> | ||

+ | |||

+ | The <hask>lift</hask> function promotes a computation of the underlying monad. The <hask>base</hask> function promotes a computation of the base monad. It is a generalization of <hask>liftIO</hask> from other monad transformer libraries. Finally there is <hask>io</hask>, which is simply an alias for <hask>base</hask>, but restricted to <hask>IO</hask>. | ||

+ | |||

+ | === Accumulating results === | ||

+ | |||

+ | <hask>ContT</hask> does not require the underlying functor to be a monad. Whenever the underlying functor is an <hask>Alternative</hask> functor, there is support for accumulating results using the <hask>(<|>)</hask> combinator. In other words, if <hask>m</hask> is an <hask>Alternative</hask>, then <hask>ContT r m</hask> is, too. Here is an example: | ||

+ | |||

+ | <haskell> | ||

+ | testComp3 :: Num a => ContT r [] (a, a) | ||

+ | testComp3 = do | ||

+ | x <- pure 10 <|> pure 20 | ||

+ | y <- pure (x+1) <|> pure (x-1) | ||

+ | return (x, y) | ||

+ | </haskell> | ||

+ | |||

+ | The ''contstuff'' library implements a convenience function <hask>listA</hask>, which turns a list into an <hask>Alternative</hask> computation: | ||

+ | |||

+ | <haskell> | ||

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

+ | </haskell> | ||

+ | |||

+ | Using this you can simplify <hask>testComp3</hask> to: | ||

+ | |||

+ | <haskell> | ||

+ | testComp3' :: Num a => ContT r [] (a, a) | ||

+ | testComp3' = do | ||

+ | x <- listA [10, 20] | ||

+ | y <- listA [x+1, x-1] | ||

+ | return (x, y) | ||

+ | </haskell> | ||

+ | |||

+ | You can collapse branches using <hask>abort</hask>: | ||

+ | |||

+ | <haskell> | ||

+ | 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) | ||

+ | </haskell> |

## Revision as of 23:49, 20 September 2010

## Contents |

## 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

TheContT

- abortion (premature termination),
- resumption (start a computation at a certain spot),
- branches (aka
*goto*), - result accumulation,
- etc.

ContT

ContT

ContT r m a

a

r

r

abort

ContT

runContT

evalContT

runContT :: (a -> m r) -> ContT r m a -> m r evalContT :: Applicative m => ContT r m r -> m r

runContT

evalContT

pure

### 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 ()

ContT

ContT

io

liftIO

inBase

IO

base

ContT

ContT

abort

### 2.3 Resumption and branches

You can capture the current continuation using the commoncallCC

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)

labelCC

goto

labelCC

i

goto

i

labelCC

ContT

### 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

lift

base

liftIO

io

base

IO

### 2.5 Accumulating results

ContT

Alternative

(<|>)

m

Alternative

ContT r m

testComp3 :: Num a => ContT r [] (a, a) testComp3 = do x <- pure 10 <|> pure 20 y <- pure (x+1) <|> pure (x-1) return (x, y)

*contstuff*library implements a convenience function

listA

Alternative

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

testComp3

testComp3' :: Num a => ContT r [] (a, a) testComp3' = do x <- listA [10, 20] y <- listA [x+1, x-1] return (x, y)

abort

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)