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

BaseM Id Id

data Lift a

Computation with no effects (strict).

Instances

Monad Lift

Functor Lift

MonadFix Lift

BaseM Lift Lift

data IdT m a

Add nothing. Useful as a placeholder.

Instances

MonadT IdT

Monad m => Monad (IdT m)

Monad m => Functor (IdT m)

MonadFix m => MonadFix (IdT m)

MonadPlus m => MonadPlus (IdT m)

ContM m => ContM (IdT m)

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

data ReaderT i m a

Add support for propagating a context.

Instances

MonadT (ReaderT i)

Monad m => Monad (ReaderT i m)

Monad m => Functor (ReaderT i m)

MonadFix m => MonadFix (ReaderT i m)

MonadPlus m => MonadPlus (ReaderT i m)

ContM m => ContM (ReaderT i m)

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

data WriterT i m a

Add support for collecting values.

Instances

Monoid i => MonadT (WriterT i)

(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)

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

(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

data StateT i m a

Add support for threading state.

Instances

MonadT (StateT i)

Monad m => Monad (StateT i m)

Monad m => Functor (StateT i m)

MonadFix m => MonadFix (StateT i m)

MonadPlus m => MonadPlus (StateT i m)

ContM m => ContM (StateT i m)

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

data ExceptionT i m a

Add support for exceptions.

Instances

MonadT (ExceptionT i)

Monad m => Monad (ExceptionT i m)

Monad m => Functor (ExceptionT i m)

MonadFix m => MonadFix (ExceptionT i m)

MonadPlus m => MonadPlus (ExceptionT i m)

ContM m => ContM (ExceptionT i m)

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

data ContT i m a

Add support for jumps.

Instances

MonadT (ContT i)

Monad m => Monad (ContT i m)

Monad m => Functor (ContT i m)

Monad m => ContM (ContT i m)

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

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 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 (IdT m) n

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 (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 (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 (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 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

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

Capture the current continuation.

Instances

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)

data Label m a

An explicit representation for continuations that store a value.

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

Capture the current continuation This function is like return, except that it also captures the current continuation. Later we can use jump to go back to the continuation with a possibly different value.

jump :: ContM m => a -> Label m a -> m b

Change the value passed to a previously captured continuation.

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 monas 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 :: 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.

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 computation.

Instances

RunReaderM m j => RunReaderM (IdT m) j

RunReaderM (Reader i) i

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 computation.

Instances

RunWriterM m j => RunWriterM (IdT m) j

Monoid i => RunWriterM (Writer i) i

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)

Exceptions are explicit in the result.

Instances

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

Deriving functions

data Iso m n

A isomorphism between (usually) monads. Typically the constructor and selector of a newtype delcaration.

Constructors

Iso

Fields

close :: forall a. m a -> n a

open :: forall a. n a -> m a

derive_fmap :: Functor m => Iso m n -> (a -> b) -> n a -> n b

Derive the implementation of fmap from Functor.

derive_return :: Monad m => Iso m n -> a -> n a

Derive the implementation of return from Monad.

derive_bind :: Monad m => Iso m n -> n a -> (a -> n b) -> n b

Derive the implementation of >>= from Monad.

derive_fail :: Monad m => Iso m n -> String -> n a

derive_mfix :: MonadFix m => Iso m n -> (a -> n a) -> n a

Derive the implementation of mfix from MonadFix.

derive_ask :: ReaderM m i => Iso m n -> n i

Derive the implementation of ask from ReaderM.

derive_put :: WriterM m i => Iso m n -> i -> n ()

Derive the implementation of put from WriterM.

derive_get :: StateM m i => Iso m n -> n i

Derive the implementation of get from StateM.

derive_set :: StateM m i => Iso m n -> i -> n ()

Derive the implementation of set from StateM.

derive_raise :: ExceptionM m i => Iso m n -> i -> n a

Derive the implementation of raise from ExceptionM.

derive_callCC :: ContM m => Iso m n -> ((a -> n b) -> n a) -> n a

Derive the implementation of callCC from ContM.

derive_local :: RunReaderM m i => Iso m n -> i -> n a -> n a

Derive the implementation of local from RunReaderM.

derive_collect :: RunWriterM m i => Iso m n -> n a -> n (a, i)

Derive the implementation of collect from RunWriterM.

derive_try :: RunExceptionM m i => Iso m n -> n a -> n (Either i a)

Derive the implementation of try from RunExceptionM.

derive_lift :: (MonadT t, Monad m) => Iso (t m) n -> m a -> n a

derive_inBase :: BaseM m x => Iso m n -> x a -> n a

Miscellaneous

version :: (Int, Int, Int)

The current version of the library.

module Control.Monad