Portability | portable |
---|---|

Stability | experimental |

Maintainer | ross@soi.city.ac.uk |

Safe Haskell | Safe-Inferred |

Classes for monad transformers.

A monad transformer makes a new monad out of an existing monad, such
that computations of the old monad may be embedded in the new one.
To construct a monad with a desired set of features, one typically
starts with a base monad, such as `Identity`

, `[]`

or `IO`

, and
applies a sequence of monad transformers.

Most monad transformer modules include the special case of applying the
transformer to `Identity`

. For example, `State s`

is an abbreviation
for `StateT s Identity`

.

Each monad transformer also comes with an operation `run`

*XXX* to
unwrap the transformer, exposing a computation of the inner monad.

- class MonadTrans t where
- lift :: Monad m => m a -> t m a

# Transformer class

class MonadTrans t whereSource

The class of monad transformers. Instances should satisfy the
following laws, which state that `lift`

is a transformer of monads:

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

Lift a computation from the argument monad to the constructed monad.

MonadTrans IdentityT | |

MonadTrans ListT | |

MonadTrans MaybeT | |

MonadTrans (ContT r) | |

Error e => MonadTrans (ErrorT e) | |

MonadTrans (ReaderT r) | |

MonadTrans (StateT s) | |

MonadTrans (StateT s) | |

Monoid w => MonadTrans (WriterT w) | |

Monoid w => MonadTrans (WriterT w) | |

Monoid w => MonadTrans (RWST r w s) | |

Monoid w => MonadTrans (RWST r w s) |

# Examples

## Parsing

One might define a parsing monad by adding a state (the `String`

remaining
to be parsed) to the `[]`

monad, which provides non-determinism:

import Control.Monad.Trans.State type Parser = StateT String []

Then `Parser`

is an instance of `MonadPlus`

: monadic sequencing implements
concatenation of parsers, while `mplus`

provides choice.
To use parsers, we need a primitive to run a constructed parser on an
input string:

runParser :: Parser a -> String -> [a] runParser p s = [x | (x, "") <- runStateT p s]

Finally, we need a primitive parser that matches a single character, from which arbitrarily complex parsers may be constructed:

item :: Parser Char item = do c:cs <- get put cs return c

In this example we use the operations `get`

and `put`

from
Control.Monad.Trans.State, which are defined only for monads that are
applications of `StateT`

. Alternatively one could use monad classes
from the `mtl`

package or similar, which contain methods `get`

and `put`

with types generalized over all suitable monads.

## Parsing and counting

We can define a parser that also counts by adding a `WriterT`

transformer:

import Control.Monad.Trans.Class import Control.Monad.Trans.State import Control.Monad.Trans.Writer import Data.Monoid type Parser = WriterT (Sum Int) (StateT String [])

The function that applies a parser must now unwrap each of the monad transformers in turn:

runParser :: Parser a -> String -> [(a, Int)] runParser p s = [(x, n) | ((x, Sum n), "") <- runStateT (runWriterT p) s]

To define `item`

parser, we need to lift the `StateT`

operations through
the `WriterT`

transformers.

item :: Parser Char item = do c:cs <- lift get lift (put cs) return c

In this case, we were able to do this with `lift`

, but operations with
more complex types require special lifting functions, which are provided
by monad transformers for which they can be implemented. If you use the
monad classes of the `mtl`

package or similar, this lifting is handled
automatically by the instances of the classes, and you need only use
the generalized methods `get`

and `put`

.

We can also define a primitive using the Writer:

tick :: Parser () tick = tell (Sum 1)

Then the parser will keep track of how many `tick`

s it executes.