MonadLib

This library provides a collection of monad transformers that can be combined to produce various monads.

Types

The following types define the representations of the computation types supported by the library. Each type adds support for a different effect.

data Id a

Computations with no effects.

Instances

Monad Id

Functor Id

MonadFix Id

Applicative Id

BaseM Id Id

RunM Id a a

data Lift a

Computation with no effects (strict).

Instances

Monad Lift

Functor Lift

MonadFix Lift

Applicative Lift

BaseM Lift Lift

RunM Lift a a

data IdT m a

Adds no new features. Useful as a placeholder.

Instances

MonadT IdT

MonadPlus m => Alternative (IdT m)

Monad m => Monad (IdT m)

Monad m => Functor (IdT m)

MonadFix m => MonadFix (IdT m)

MonadPlus m => MonadPlus (IdT m)

Monad m => Applicative (IdT m)

ContM m => ContM (IdT m)

AbortM m i => AbortM (IdT m) i

RunExceptionM m i => RunExceptionM (IdT m) i

RunWriterM m j => RunWriterM (IdT m) j

RunReaderM m j => RunReaderM (IdT m) j

ExceptionM m j => ExceptionM (IdT m) j

StateM m j => StateM (IdT m) j

WriterM m j => WriterM (IdT m) j

ReaderM m j => ReaderM (IdT m) j

BaseM m n => BaseM (IdT m) n

RunM m a r => RunM (IdT m) a r

data ReaderT i m a

Add support for propagating a context of type i.

Instances

MonadT (ReaderT i)

MonadPlus m => Alternative (ReaderT i m)

Monad m => Monad (ReaderT i m)

Monad m => Functor (ReaderT i m)

MonadFix m => MonadFix (ReaderT i m)

MonadPlus m => MonadPlus (ReaderT i m)

Monad m => Applicative (ReaderT i m)

ContM m => ContM (ReaderT i m)

AbortM m i => AbortM (ReaderT j m) i

RunExceptionM m i => RunExceptionM (ReaderT j m) i

RunWriterM m j => RunWriterM (ReaderT i m) j

Monad m => RunReaderM (ReaderT i m) i

ExceptionM m j => ExceptionM (ReaderT i m) j

StateM m j => StateM (ReaderT i m) j

WriterM m j => WriterM (ReaderT i m) j

Monad m => ReaderM (ReaderT i m) i

BaseM m n => BaseM (ReaderT i m) n

RunM m a r => RunM (ReaderT i m) a (i -> r)

data WriterT i m a

Add support for collecting values of type i. The type i should be a monoid, whose unit is used to represent a lack of a value, and whose binary operation is used to combine multiple values. This transformer is strict in its output component.

Instances

Monoid i => MonadT (WriterT i)

(MonadPlus m, Monoid i) => Alternative (WriterT i m)

(Monad m, Monoid i) => Monad (WriterT i m)

(Monad m, Monoid i) => Functor (WriterT i m)

(MonadFix m, Monoid i) => MonadFix (WriterT i m)

(MonadPlus m, Monoid i) => MonadPlus (WriterT i m)

(Monad m, Monoid i) => Applicative (WriterT i m)

(ContM m, Monoid i) => ContM (WriterT i m)

(AbortM m i, Monoid j) => AbortM (WriterT j m) i

(RunExceptionM m i, Monoid j) => RunExceptionM (WriterT j m) i

(Monad m, Monoid i) => RunWriterM (WriterT i m) i

(RunReaderM m j, Monoid i) => RunReaderM (WriterT i m) j

(ExceptionM m j, Monoid i) => ExceptionM (WriterT i m) j

(StateM m j, Monoid i) => StateM (WriterT i m) j

(Monad m, Monoid i) => WriterM (WriterT i m) i

(ReaderM m j, Monoid i) => ReaderM (WriterT i m) j

(BaseM m n, Monoid i) => BaseM (WriterT i m) n

(Monoid i, RunM m (a, i) r) => RunM (WriterT i m) a r

data StateT i m a

Add support for threading state of type i.

Instances

MonadT (StateT i)

MonadPlus m => Alternative (StateT i m)

Monad m => Monad (StateT i m)

Monad m => Functor (StateT i m)

MonadFix m => MonadFix (StateT i m)

MonadPlus m => MonadPlus (StateT i m)

Monad m => Applicative (StateT i m)

ContM m => ContM (StateT i m)

AbortM m i => AbortM (StateT j m) i

RunExceptionM m i => RunExceptionM (StateT j m) i

RunWriterM m j => RunWriterM (StateT i m) j

RunReaderM m j => RunReaderM (StateT i m) j

ExceptionM m j => ExceptionM (StateT i m) j

Monad m => StateM (StateT i m) i

WriterM m j => WriterM (StateT i m) j

ReaderM m j => ReaderM (StateT i m) j

BaseM m n => BaseM (StateT i m) n

RunM m (a, i) r => RunM (StateT i m) a (i -> r)

data ExceptionT i m a

Add support for exceptions of type i.

Instances

MonadT (ExceptionT i)

MonadPlus m => Alternative (ExceptionT i m)

Monad m => Monad (ExceptionT i m)

Monad m => Functor (ExceptionT i m)

MonadFix m => MonadFix (ExceptionT i m)

MonadPlus m => MonadPlus (ExceptionT i m)

Monad m => Applicative (ExceptionT i m)

ContM m => ContM (ExceptionT i m)

AbortM m i => AbortM (ExceptionT j m) i

Monad m => RunExceptionM (ExceptionT i m) i

RunWriterM m j => RunWriterM (ExceptionT i m) j

RunReaderM m j => RunReaderM (ExceptionT i m) j

Monad m => ExceptionM (ExceptionT i m) i

StateM m j => StateM (ExceptionT i m) j

WriterM m j => WriterM (ExceptionT i m) j

ReaderM m j => ReaderM (ExceptionT i m) j

BaseM m n => BaseM (ExceptionT i m) n

RunM m (Either i a) r => RunM (ExceptionT i m) a r

About the WriterM instance: If an exception is risen while we are collecting output, then the output is lost. If the output is important, then use try to ensure that no exception may occur. Example:

do (r,w) <- collect (try m)
   case r of
     Left err -> ...do something...
     Right a  -> ...do something...

data ChoiceT m a

Add support for multiple answers.

Instances

MonadT ChoiceT

Monad m => Alternative (ChoiceT m)

Monad m => Monad (ChoiceT m)

Monad m => Functor (ChoiceT m)

Monad m => MonadPlus (ChoiceT m)

Monad m => Applicative (ChoiceT m)

ContM m => ContM (ChoiceT m)

AbortM m i => AbortM (ChoiceT m) i

ExceptionM m j => ExceptionM (ChoiceT m) j

StateM m j => StateM (ChoiceT m) j

WriterM m j => WriterM (ChoiceT m) j

ReaderM m j => ReaderM (ChoiceT m) j

BaseM m n => BaseM (ChoiceT m) n

RunM m (Maybe (a, ChoiceT m a)) r => RunM (ChoiceT m) a r

data ContT i m a

Add support for continuations within a prompt of type i.

Instances

MonadT (ContT i)

MonadPlus m => Alternative (ContT i m)

Monad m => Monad (ContT i m)

Monad m => Functor (ContT i m)

MonadPlus m => MonadPlus (ContT i m)

Monad m => Applicative (ContT i m)

Monad m => ContM (ContT i m)

Monad m => AbortM (ContT i m) i

(RunWriterM m j, MonadFix m) => RunWriterM (ContT i m) j

RunReaderM m j => RunReaderM (ContT i m) j

ExceptionM m j => ExceptionM (ContT i m) j

StateM m j => StateM (ContT i m) j

WriterM m j => WriterM (ContT i m) j

ReaderM m j => ReaderM (ContT i m) j

BaseM m n => BaseM (ContT i m) n

RunM m i r => RunM (ContT i m) a ((a -> m i) -> r)

Lifting

The following operations allow us to promote computations in the underlying monad to computations that support an extra effect. Computations defined in this way do not make use of the new effect but can be combined with other operations that utilize the effect.

class MonadT t where

Methods

lift :: Monad m => m a -> t m a

Promote a computation from the underlying monad.

Instances

MonadT ChoiceT

MonadT IdT

MonadT (ContT i)

MonadT (ExceptionT i)

MonadT (StateT i)

Monoid i => MonadT (WriterT i)

MonadT (ReaderT i)

class (Monad m, Monad n) => BaseM m n | m -> n where

Methods

inBase :: n a -> m a

Promote a computation from the base monad.

Instances

BaseM [] []

BaseM IO IO

BaseM Maybe Maybe

BaseM Lift Lift

BaseM Id Id

BaseM m n => BaseM (ChoiceT m) n

BaseM m n => BaseM (IdT m) n

BaseM (ST s) (ST s)

BaseM (Cont i) (Cont i)

BaseM (Exception i) (Exception i)

BaseM (State i) (State i)

Monoid i => BaseM (Writer i) (Writer i)

BaseM (Reader i) (Reader i)

BaseM m n => BaseM (ContT i m) n

BaseM m n => BaseM (ExceptionT i m) n

BaseM m n => BaseM (StateT i m) n

(BaseM m n, Monoid i) => BaseM (WriterT i m) n

BaseM m n => BaseM (ReaderT i m) n

Effect Classes

The following classes define overloaded operations that can be used to define effectful computations.

class Monad m => ReaderM m i | m -> i where

Classifies monads that provide access to a context of type i.

Methods

ask :: m i

Get the context.

Instances

ReaderM m j => ReaderM (ChoiceT m) j

ReaderM m j => ReaderM (IdT m) j

ReaderM (Reader i) i

ReaderM m j => ReaderM (ContT i m) j

ReaderM m j => ReaderM (ExceptionT i m) j

ReaderM m j => ReaderM (StateT i m) j

(ReaderM m j, Monoid i) => ReaderM (WriterT i m) j

Monad m => ReaderM (ReaderT i m) i

class Monad m => WriterM m i | m -> i where

Classifies monads that can collect values of type i.

Methods

put :: i -> m ()

Add a value to the collection.

Instances

WriterM m j => WriterM (ChoiceT m) j

WriterM m j => WriterM (IdT m) j

Monoid i => WriterM (Writer i) i

WriterM m j => WriterM (ContT i m) j

WriterM m j => WriterM (ExceptionT i m) j

WriterM m j => WriterM (StateT i m) j

(Monad m, Monoid i) => WriterM (WriterT i m) i

WriterM m j => WriterM (ReaderT i m) j

class Monad m => StateM m i | m -> i where

Classifies monads that propagate a state component of type i.

Methods

get :: m i

Get the state.

set :: i -> m ()

Set the state.

Instances

StateM m j => StateM (ChoiceT m) j

StateM m j => StateM (IdT m) j

StateM (State i) i

StateM m j => StateM (ContT i m) j

StateM m j => StateM (ExceptionT i m) j

Monad m => StateM (StateT i m) i

(StateM m j, Monoid i) => StateM (WriterT i m) j

StateM m j => StateM (ReaderT i m) j

class Monad m => ExceptionM m i | m -> i where

Classifies monads that support raising exceptions of type i.

Methods

raise :: i -> m a

Raise an exception.

Instances

ExceptionM IO SomeException

ExceptionM m j => ExceptionM (ChoiceT m) j

ExceptionM m j => ExceptionM (IdT m) j

ExceptionM (Exception i) i

ExceptionM m j => ExceptionM (ContT i m) j

Monad m => ExceptionM (ExceptionT i m) i

ExceptionM m j => ExceptionM (StateT i m) j

(ExceptionM m j, Monoid i) => ExceptionM (WriterT i m) j

ExceptionM m j => ExceptionM (ReaderT i m) j

class Monad m => ContM m where

Classifies monads that provide access to a computation's continuation.

Methods

callWithCC :: ((a -> Label m) -> m a) -> m a

Capture the current continuation.

Instances

ContM m => ContM (ChoiceT m)

ContM m => ContM (IdT m)

ContM (Cont i)

Monad m => ContM (ContT i m)

ContM m => ContM (ExceptionT i m)

ContM m => ContM (StateT i m)

(ContM m, Monoid i) => ContM (WriterT i m)

ContM m => ContM (ReaderT i m)

class Monad m => AbortM m i where

Classifies monads that support aborting the program and returning a given final result of type i.

Methods

abort :: i -> m a

Abort the program with the given value as final result.

Instances

AbortM IO ExitCode

AbortM m i => AbortM (ChoiceT m) i

AbortM m i => AbortM (IdT m) i

Monad m => AbortM (ContT i m) i

AbortM m i => AbortM (ExceptionT j m) i

AbortM m i => AbortM (StateT j m) i

(AbortM m i, Monoid j) => AbortM (WriterT j m) i

AbortM m i => AbortM (ReaderT j m) i

data Label m

An explicit representation for monadic continuations.

labelCC :: ContM m => a -> m (a, a -> Label m)

Capture the current continuation. This function is like return, except that it also captures the current continuation. Later, we can use jump to repeat the computation from this point onwards but with a possibly different value.

labelCC_ :: forall m. ContM m => m (Label m)

Capture the current continuation. Later we can use jump to restart the program from this point.

jump :: Label m -> m a

Restart a previously captured computation.

labelC :: (forall b. m b) -> Label m

Label a given continuation.

callCC :: ContM m => ((a -> m b) -> m a) -> m a

A version of callWithCC that avoids the need for an explicit use of the jump function.

Execution

Eliminating Effects

The following functions eliminate the outermost effect of a computation by translating a computation into an equivalent computation in the underlying monad. (The exceptions are Id and Lift which are not transformers but ordinary monads and so, their run operations simply eliminate the monad.)

runId :: Id a -> a

Get the result of a pure computation.

runLift :: Lift a -> a

Get the result of a pure strict computation.

runIdT :: IdT m a -> m a

Remove an identity layer.

runReaderT :: i -> ReaderT i m a -> m a

Execute a reader computation in the given context.

runWriterT :: Monad m => WriterT i m a -> m (a, i)

Execute a writer computation. Returns the result and the collected output.

runStateT :: i -> StateT i m a -> m (a, i)

Execute a stateful computation in the given initial state. The second component of the result is the final state.

runExceptionT :: ExceptionT i m a -> m (Either i a)

Execute a computation with exceptions. Successful results are tagged with Right, exceptional results are tagged with Left.

runContT :: (a -> m i) -> ContT i m a -> m i

Execute a computation with the given continuation.

runChoiceT :: Monad m => ChoiceT m a -> m (Maybe (a, ChoiceT m a))

Execute a computation that may return multiple answers. The resulting computation returns Nothing if no answers were found, or Just (answer,new_comp), where answer is an answer, and new_comp is a computation that may produce more answers. The search is depth-first and left-biased with respect to the mplus operation.

findOne :: Monad m => ChoiceT m a -> m (Maybe a)

Execute a computation that may return multiple answers, returning at most one answer.

findAll :: Monad m => ChoiceT m a -> m [a]

Execute a computation that may return multiple answers, collecting all possible answers.

class Monad m => RunM m a r | m a -> r where

Generalized running.

Methods

runM :: m a -> r

Instances

RunM Lift a a

RunM Id a a

RunM IO a (IO a)

RunM m (Maybe (a, ChoiceT m a)) r => RunM (ChoiceT m) a r

RunM m a r => RunM (IdT m) a r

RunM m (Either i a) r => RunM (ExceptionT i m) a r

(Monoid i, RunM m (a, i) r) => RunM (WriterT i m) a r

RunM m i r => RunM (ContT i m) a ((a -> m i) -> r)

RunM m (a, i) r => RunM (StateT i m) a (i -> r)

RunM m a r => RunM (ReaderT i m) a (i -> r)

Nested Execution

The following classes define operations that are overloaded versions of the run operations. Unlike the run operations, these functions do not change the type of the computation (i.e., they do not remove a layer). Instead, they perform the effects in a ``separate effect thread''.

class ReaderM m i => RunReaderM m i | m -> i where

Classifies monads that support changing the context for a sub-computation.

Methods

local :: i -> m a -> m a

Change the context for the duration of a sub-computation.

Instances

RunReaderM m j => RunReaderM (IdT m) j

RunReaderM (Reader i) i

RunReaderM m j => RunReaderM (ContT i m) j

RunReaderM m j => RunReaderM (ExceptionT i m) j

RunReaderM m j => RunReaderM (StateT i m) j

(RunReaderM m j, Monoid i) => RunReaderM (WriterT i m) j

Monad m => RunReaderM (ReaderT i m) i

class WriterM m i => RunWriterM m i | m -> i where

Classifies monads that support collecting the output of a sub-computation.

Methods

collect :: m a -> m (a, i)

Collect the output from a sub-computation.

Instances

RunWriterM m j => RunWriterM (IdT m) j

Monoid i => RunWriterM (Writer i) i

(RunWriterM m j, MonadFix m) => RunWriterM (ContT i m) j

RunWriterM m j => RunWriterM (ExceptionT i m) j

RunWriterM m j => RunWriterM (StateT i m) j

(Monad m, Monoid i) => RunWriterM (WriterT i m) i

RunWriterM m j => RunWriterM (ReaderT i m) j

class ExceptionM m i => RunExceptionM m i | m -> i where

Classifies monads that support handling of exceptions.

Methods

try :: m a -> m (Either i a)

Convert computations that may raise an exception into computations that do not raise exception but instead, yield a tagged results. Exceptions are tagged with Left, successful computations are tagged with Right.

Instances

RunExceptionM IO SomeException

RunExceptionM m i => RunExceptionM (IdT m) i

RunExceptionM (Exception i) i

Monad m => RunExceptionM (ExceptionT i m) i

RunExceptionM m i => RunExceptionM (StateT j m) i

(RunExceptionM m i, Monoid j) => RunExceptionM (WriterT j m) i

RunExceptionM m i => RunExceptionM (ReaderT j m) i

Utility functions

asks :: ReaderM m r => (r -> a) -> m a

Apply a function to the environment. Useful for accessing environmnt components.

puts :: WriterM m w => (a, w) -> m a

Add content the output and return a result.

sets :: StateM m s => (s -> (a, s)) -> m a

Update the state and return a result.

sets_ :: StateM m s => (s -> s) -> m ()

Updates the state with the given function.

raises :: ExceptionM m x => Either x a -> m a

Either raise an exception or return a value. Left values signify the we should raise an exception, Right values indicate success.

mapReader :: RunReaderM m r => (r -> r) -> m a -> m a

Modify the environment for the duration of a computation.

mapWriter :: RunWriterM m w => (w -> w) -> m a -> m a

Modify the output of a computation.

mapException :: RunExceptionM m x => (x -> x) -> m a -> m a

Modify the exception that was risen by a computation.

handle :: RunExceptionM m x => m a -> (x -> m a) -> m a

Apply the given exception handler, if a computation raises an exception.

Miscellaneous

version :: (Int, Int, Int)

The current version of the library.

module Control.Monad