Control/Monad/Trans/Class.hs

    {-# LANGUAGE CPP #-}
    #if __GLASGOW_HASKELL__ >= 702
    {-# LANGUAGE Safe #-}
    #endif
    #if __GLASGOW_HASKELL__ >= 710
    {-# LANGUAGE AutoDeriveTypeable #-}
    #endif
    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Control.Monad.Trans.Class
    -- 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
    --
    -- 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 'Data.Functor.Identity.Identity', @[]@ or 'IO', and
    -- applies a sequence of monad transformers.
    -----------------------------------------------------------------------------

    module Control.Monad.Trans.Class (
        -- * Transformer class
        MonadTrans(..)

        -- * Conventions
        -- $conventions

        -- * Strict monads
        -- $strict

        -- * Examples
        -- ** Parsing
        -- $example1

        -- ** Parsing and counting
        -- $example2

        -- ** Interpreter monad
        -- $example3
      ) where

    -- | The class of monad transformers.  Instances should satisfy the
    -- following laws, which state that 'lift' is a monad transformation:
    --
    -- * @'lift' . 'return' = 'return'@
    --
    -- * @'lift' (m >>= f) = 'lift' m >>= ('lift' . f)@

    class MonadTrans t where
        -- | Lift a computation from the argument monad to the constructed monad.
        lift :: (Monad m) => m a -> t m a

    {- $conventions
    Most monad transformer modules include the special case of applying
    the transformer to 'Data.Functor.Identity.Identity'.  For example,
    @'Control.Monad.Trans.State.Lazy.State' s@ is an abbreviation for
    @'Control.Monad.Trans.State.Lazy.StateT' s 'Data.Functor.Identity.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 'Control.Monad.Trans.Cont.ContT'
    and 'Control.Monad.Trans.Cont.SelectT' 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
    'Control.Monad.Trans.State.Lazy.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@,

    * @map@/XXX/@T t . 'lift' = 'lift' . t@

    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

    A monad is said to be /strict/ if its '>>=' operation is strict in its first
    argument.  The base monads 'Maybe', @[]@ and 'IO' are strict:

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

    However the monad 'Data.Functor.Identity.Identity' is not:

    >>> runIdentity (undefined >> return 2)
    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.
    -}

    {- $example1

    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 'Control.Monad.Trans.State.Lazy.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.
    -}

    {- $example2

    We can define a parser that also counts by adding a
    'Control.Monad.Trans.Writer.Lazy.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
    'Control.Monad.Trans.State.Lazy.StateT' operations through the
    'Control.Monad.Trans.Writer.Lazy.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.
    -}

    {- $example3

    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 'Control.Monad.Trans.State.Lazy.StateT',
    it already has the state operations @get@ and @set@.

    The first of the 'Control.Monad.Trans.Reader.ReaderT' operations,
    'Control.Monad.Trans.Reader.ask', is a simple action, so we can lift it
    through 'Control.Monad.Trans.State.Lazy.StateT' to @InterpM@ using 'lift':

    > ask :: InterpM Env
    > ask = lift R.ask

    The other 'Control.Monad.Trans.Reader.ReaderT' operation,
    'Control.Monad.Trans.Reader.local', has a suitable type for lifting
    using 'Control.Monad.Trans.State.Lazy.mapStateT':

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

    We also wish to lift the operations of 'Control.Monad.Trans.Except.ExceptT'
    through both 'Control.Monad.Trans.Reader.ReaderT' and
    'Control.Monad.Trans.State.Lazy.StateT'.  For the operation
    'Control.Monad.Trans.Except.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 'Control.Monad.Trans.Except.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 'Control.Monad.Trans.Reader.ReaderT' version followed by the
    'Control.Monad.Trans.State.Lazy.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 'Control.Monad.IO.Class.MonadIO',
    so we can use 'Control.Monad.IO.Class.liftIO' instead:

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

    -}