Copyright | (c) Andy Gill 2001 (c) Oregon Graduate Institute of Science and Technology 2001 |
---|---|

License | BSD-style (see the file LICENSE) |

Maintainer | R.Paterson@city.ac.uk |

Stability | experimental |

Portability | portable |

Safe Haskell | Safe |

Language | Haskell98 |

The class of 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.

- class MonadTrans t where

# Transformer class

class MonadTrans t where #

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

is a monad transformation:

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

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

MonadTrans ListT # | |

MonadTrans MaybeT # | |

MonadTrans (ErrorT e) # | |

MonadTrans (ExceptT e) # | |

MonadTrans (IdentityT *) # | |

MonadTrans (StateT s) # | |

MonadTrans (StateT s) # | |

Monoid w => MonadTrans (WriterT w) # | |

Monoid w => MonadTrans (WriterT w) # | |

MonadTrans (ContT * r) # | |

MonadTrans (ReaderT * r) # | |

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

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

# Conventions

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

. For example,

is an abbreviation for
`State`

s

.`StateT`

s `Identity`

Each monad transformer also comes with an operation `run`

*XXX*`T`

to
unwrap the transformer, exposing a computation of the inner monad.
(Currently these functions are defined as field labels, but in the next
major release they will be separate functions.)

All of the monad transformers except `ContT`

are functors on the category of monads: in addition to defining a
mapping of monads, they also define a mapping from transformations
between base monads to transformations between transformed monads,
called `map`

*XXX*`T`

. Thus given a monad transformation `t :: M a -> N a`

,
the combinator `mapStateT`

constructs
a monad transformation

mapStateT t :: StateT s M a -> StateT s N a

For these monad transformers, `lift`

is a natural transformation in the
category of monads, i.e. for any monad transformation `t :: M a -> N a`

,

Each of the monad transformers introduces relevant operations.
In a sequence of monad transformers, most of these operations.can be
lifted through other transformers using `lift`

or the `map`

*XXX*`T`

combinator, but a few with more complex type signatures require
specialized lifting combinators, called `lift`

*Op*
(see Control.Monad.Signatures).

# Strict monads

A monad is said to be *strict* if its `>>=`

operation is strict in its first
argument. The base monads `Maybe`

, `[]`

and `IO`

are strict:

`>>>`

*** Exception: Prelude.undefined`undefined >> return 2 :: Maybe Integer`

However the monad `Identity`

is not:

`>>>`

2`runIdentity (undefined >> return 2)`

In a strict monad you know when each action is executed, but the monad
is not necessarily strict in the return value, or in other components
of the monad, such as a state. However you can use `seq`

to create
an action that is strict in the component you want evaluated.

# 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 the `item`

parser, we need to lift the
`StateT`

operations through the
`WriterT`

transformer.

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.

## Interpreter monad

This example is a cut-down version of the one in
"Monad Transformers and Modular Interpreters",
by Sheng Liang, Paul Hudak and Mark Jones in *POPL'95*
(http://web.cecs.pdx.edu/~mpj/pubs/modinterp.html).

Suppose we want to define an interpreter that can do I/O and has exceptions, an environment and a modifiable store. We can define a monad that supports all these things as a stack of monad transformers:

import Control.Monad.Trans.Class import Control.Monad.Trans.State import qualified Control.Monad.Trans.Reader as R import qualified Control.Monad.Trans.Except as E import Control.Monad.IO.Class type InterpM = StateT Store (R.ReaderT Env (E.ExceptT Err IO))

for suitable types `Store`

, `Env`

and `Err`

.

Now we would like to be able to use the operations associated with each
of those monad transformers on `InterpM`

actions. Since the uppermost
monad transformer of `InterpM`

is `StateT`

,
it already has the state operations `get`

and `set`

.

The first of the `ReaderT`

operations,
`ask`

, is a simple action, so we can lift it
through `StateT`

to `InterpM`

using `lift`

:

ask :: InterpM Env ask = lift R.ask

The other `ReaderT`

operation,
`local`

, has a suitable type for lifting
using `mapStateT`

:

local :: (Env -> Env) -> InterpM a -> InterpM a local f = mapStateT (R.local f)

We also wish to lift the operations of `ExceptT`

through both `ReaderT`

and
`StateT`

. For the operation
`throwE`

, we know `throwE e`

is a simple
action, so we can lift it through the two monad transformers to `InterpM`

with two `lift`

s:

throwE :: Err -> InterpM a throwE e = lift (lift (E.throwE e))

The `catchE`

operation has a more
complex type, so we need to use the special-purpose lifting function
`liftCatch`

provided by most monad transformers. Here we use
the `ReaderT`

version followed by the
`StateT`

version:

catchE :: InterpM a -> (Err -> InterpM a) -> InterpM a catchE = liftCatch (R.liftCatch E.catchE)

We could lift `IO`

actions to `InterpM`

using three `lift`

s, but `InterpM`

is automatically an instance of `MonadIO`

,
so we can use `liftIO`

instead:

putStr :: String -> InterpM () putStr s = liftIO (Prelude.putStr s)