Control.Monad.Trans.Cont

transformers-0.4.2.0: Concrete functor and monad transformers

Copyright | (c) The University of Glasgow 2001
License | BSD-style (see the file LICENSE)
Maintainer | ross@soi.city.ac.uk
Stability | experimental
Portability | portable
Safe Haskell | Safe
Language | Haskell98

Control.Monad.Trans.Cont

Contents

- The Cont monad
  - Delimited continuations
- The ContT monad transformer
  - Delimited continuations
- Lifting other operations

Description

Continuation monads.

Delimited continuation operators are taken from Kenichi Asai and Oleg Kiselyov's tutorial at CW 2011, "Introduction to programming with shift and reset" (http://okmij.org/ftp/continuations/#tutorial).

Synopsis

- type Cont r = ContT r Identity
- cont :: ((a -> r) -> r) -> Cont r a
- runCont :: Cont r a -> (a -> r) -> r
- evalCont :: Cont r r -> r
- mapCont :: (r -> r) -> Cont r a -> Cont r a
- withCont :: ((b -> r) -> a -> r) -> Cont r a -> Cont r b
- reset :: Cont r r -> Cont r' r
- shift :: ((a -> r) -> Cont r r) -> Cont r a
- newtype ContT r m a = ContT {
  - runContT :: (a -> m r) -> m r
  }
- evalContT :: Monad m => ContT r m r -> m r
- mapContT :: (m r -> m r) -> ContT r m a -> ContT r m a
- withContT :: ((b -> m r) -> a -> m r) -> ContT r m a -> ContT r m b
- callCC :: ((a -> ContT r m b) -> ContT r m a) -> ContT r m a
- resetT :: Monad m => ContT r m r -> ContT r' m r
- shiftT :: Monad m => ((a -> m r) -> ContT r m r) -> ContT r m a
- liftLocal :: Monad m => m r' -> ((r' -> r') -> m r -> m r) -> (r' -> r') -> ContT r m a -> ContT r m a

# The Cont monad

type Cont r = ContT r Identity

Continuation monad. `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.

cont :: ((a -> r) -> r) -> Cont r a

Construct a continuation-passing computation from a function. (The inverse of `runCont`)

runCont

Arguments

:: Cont r a | continuation computation (`Cont`).
-> (a -> r) | the final continuation, which produces the final result (often `id`).
-> r |

The result of running a CPS computation with a given final continuation. (The inverse of `cont`)

evalCont :: Cont r r -> r

The result of running a CPS computation with the identity as the final continuation.

-     evalCont (return x) = x

mapCont :: (r -> r) -> Cont r a -> Cont r a

Apply a function to transform the result of a continuation-passing computation.

-     runCont (mapCont f m) = f . runCont m

withCont :: ((b -> r) -> a -> r) -> Cont r a -> Cont r b

Apply a function to transform the continuation passed to a CPS computation.

-     runCont (withCont f m) = runCont m . f

## Delimited continuations

reset :: Cont r r -> Cont r' r

``reset` m` delimits the continuation of any `shift` inside `m`.

-     reset (return m) = return m

shift :: ((a -> r) -> Cont r r) -> Cont r a

``shift` f` captures the continuation up to the nearest enclosing `reset` and passes it to `f`:

-     reset (shift f >>= k) = reset (f (evalCont . k))

# The ContT monad transformer

newtype ContT r m a

The continuation monad transformer. Can be used to add continuation handling to other monads.

Constructors

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

Instances

MonadTrans (ContT r) |
Monad (ContT r m) |
Functor (ContT r m) |
Applicative (ContT r m) |
MonadIO m => MonadIO (ContT r m) |

evalContT :: Monad m => ContT r m r -> m r

The result of running a CPS computation with `return` as the final continuation.

-     evalContT (lift m) = m

mapContT :: (m r -> m r) -> ContT r m a -> ContT r m a

Apply a function to transform the result of a continuation-passing computation.

-     runContT (mapContT f m) = f . runContT m

withContT :: ((b -> m r) -> a -> m r) -> ContT r m a -> ContT r m b

Apply a function to transform the continuation passed to a CPS computation.

-     runContT (withContT f m) = runContT m . f

callCC :: ((a -> ContT r m b) -> ContT r m a) -> ContT r m a

`callCC` (call-with-current-continuation) calls its argument function, passing it the current continuation. It provides an escape continuation mechanism for use with continuation monads. Escape continuations one allow to abort the current computation and return a value immediately. They achieve a similar effect to `throwE` and `catchE` within an `ExceptT` monad. The advantage of this function over calling `return` is that it makes the continuation explicit, allowing more flexibility and better control.

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.

## Delimited continuations

resetT :: Monad m => ContT r m r -> ContT r' m r

``resetT` m` delimits the continuation of any `shiftT` inside `m`.

-     resetT (lift m) = lift m

shiftT :: Monad m => ((a -> m r) -> ContT r m r) -> ContT r m a

``shiftT` f` captures the continuation up to the nearest enclosing `resetT` and passes it to `f`:

-     resetT (shiftT f >>= k) = resetT (f (evalContT . k))

# Lifting other operations

liftLocal :: Monad m => m r' -> ((r' -> r') -> m r -> m r) -> (r' -> r') -> ContT r m a -> ContT r m a

``liftLocal` ask local` yields a `local` function for ``ContT` r m`.