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When using multiple Reader/Writer/State transformers in the same monad stack, it becomes necessary to lift the operations in order to affect a specific transformer. Using heterogeneous lists (and all kinds of GHC extensions magic), this package provides transformers that remove that necessity: MultiReaderT/MultiWriterT/MultiStateT can contain a heterogeneous list of values.

The type inferred for the getter/setter determines which value is read/written.


simpleExample :: IO ()
simpleExample = runMultiStateTNil_       -- start with an empty state,
                                         --   i.e. :: MultiStateT '[] IO
              $ withMultiStateA 'H'      -- "adding" a char to the state
              $ withMultiStateA "ello, World!" -- and a string
              $ do                       -- so:
  -- the monad here is MultiStateT '[String, Char] IO
  let combinedPrint = do       -- no type signature necessary
        c  <- mGet             -- type of mGet inferred to be m Char
        cs <- mGet             --              inferred to be m String
        lift $ putStrLn (c:cs)
  mSet 'J'                     -- we modify the Char in the state.
                               -- again, the type is inferred,
                               -- without any manual lifting.

The output is:

Hello, World!
Jello, World!

( you can find both this and a more complex example in an executable in the package. )

Error Messages

If you try to execute an action that requires a specific type in the state, but the current state does not contain that type, the error message is something like

No instance for (Control.Monad.MultiState.ContainsType Foo '[]) x

where Foo is the missing type.

Compatibility with Single-Valued Transformers

It is possible to run single-valued actions inside multi-valued transformers using the inflate functions. A function transforming a multi-valued transformer with exactly one element into a single-valued transformer would be trivial, but it is currently not provided.

Naming Scheme

(Will refer to StateT in this paragraph, but equally valid for Reader/Writer) The mtl monad transformers make use of primarily three methods to “unwrap” a transformed value: runStateT, evalStateT, execStateT. These three all have a type matching the pattern s -> t m a -> m b, they differ in what b is. We will use a different naming scheme, for three reasons:

  1. “run”, “eval” and “exec” are not in any way intuitive, and should be suffixed in any case.

  2. For MultiStateT, it makes sense to transform an existing transformer, adding another state. The signature would be close to that of runStateT, only without the unwrapping part, i.e. s -> t m a -> t' m b, where s is the initial state, and t is t' with another state added.

  3. Sometimes you might want to add/run a single state, or a bunch of them. For example, when running an arbitrary StateT, you would need to provide a HList of initial states, and would receive a HList of final states.

Our naming scheme will instead be:

  1. runStateT.* unwraps a StateT. A suffix controls what exactly is returned by the function. There is a special version for when the list of states is Nil, runStateTNil.

  2. withStateT.* adds one or more states to a subcomputation. A suffix controls the exact return value.

            |     withState                withState .. withState   v
StateT '[s, ..] m --------> StateT '[..] m --------> .. --------> StateT '[] m
            |     <--------                                         |
            |   (withoutState)                                      |
            |                                                       |
            |                                                       |
            |   runStateT                            runStateTNil   |
            \--------------------> m .. <---------------------------/

Specific functions are (constraints omitted):

runMultiStateT = runMultiStateTAS
runMultiStateTA  :: HList s -> MultiStateT s m a -> m a
runMultiStateTAS :: HList s -> MultiStateT s m a -> m (a, s)
runMultiStateTSA :: HList s -> MultiStateT s m a -> m (s, a)
runMultiStateTS  :: HList s -> MultiStateT s m a -> m s
runMultiStateT_  :: HList s -> MultiStateT s m a -> m ()

runMultiStateTNil  :: MultiStateT '[] m a -> m a
runMultiStateTNil_ :: MultiStateT '[] m a -> m ()

withMultiState = withMultiStateAS
withMultiStateA  :: s -> MultiStateT (s ': ss) m a -> MultiStateT ss m a
withMultiStateAS :: s -> MultiStateT (s ': ss) m a -> MultiStateT ss m (a, s)
withMultiStateSA :: s -> MultiStateT (s ': ss) m a -> MultiStateT ss m (s, a)
withMultiStateS  :: s -> MultiStateT (s ': ss) m a -> MultiStateT ss m s
withMultiState_  :: s -> MultiStateT (s ': ss) m a -> MultiStateT ss m ()

withMultiStates = withMultiStatesAS
withMultiStatesAS :: HList s1 -> MultiStateT (Append s1 s2) m a -> MultiStateT s2 m (a, HList s1)
withMultiStatesSA :: HList s1 -> MultiStateT (Append s1 s2) m a -> MultiStateT s2 m (HList s1, a)
withMultiStatesA  :: HList s1 -> MultiStateT (Append s1 s2) m a -> MultiStateT s2 m a
withMultiStatesS  :: HList s1 -> MultiStateT (Append s1 s2) m a -> MultiStateT s2 m (HList s1)
withMultiStates_  :: HList s1 -> MultiStateT (Append s1 s2) m a -> MultiStateT s2 m ()

withoutMultiState :: MultiStateT ss m a -> MultiStateT (s ': ss) m a

Known Deficits

This package currently lacks a complete set of “lifting instances”, i.e. instance definitions for classes such as mtl’s MonadWriter “over” the newly introduced monad transformers, as in

instance (MonadWriter w m) => MonadWriter w (MultiStateT c m) where ..

These “lifting instances” would be necessary to achieve full compatibility with existing transformers. Ping me if you find anything specific missing.




Changelog for multistate package May 2020

  • Adapt for ghc-8.10
  • Add nix-expressions for testing against different ghc versions
  • Drop support for ghc < 8.4 June 2019

  • Adapt for ghc-8.8 (optimistically; QuickCheck does not build so tests are untested) October 2018

  • Adapt for ghc-8.6 (really, this time)
  • Make package -Wcompat-ible April 2018

  • Adapt for ghc-8.4
  • Drop support for ghc<8.0
  • Add class MonadMultiGet that roughly translates to “any read access” (instances for Reader and State)
  • Add data-type MultiGST that has a single taggified HList instead of the three r, w, s lists with MultiRWS August 2017

  • Adapt for ghc-8.2

  • Minor strictness fix for MultiRWS May 2016

  • Adapt for ghc-8 March 2016

  • Add new method withoutMultiFoo, inverse of withMultiFoo February 2016

  • Add instances:

    • MonadIO
    • Alternative
    • MonadPlus
    • MonadBase
    • MonadTransControl
    • MonadBaseControl June 2015

  • Add MonadFix instances June 2015

  • Export classes from transformer modules June 2015

  • Add MultiRWST

  • Add inflate functions (e.g. StateT _ -> MultiStateT _)

  • Improve lazyness

  • Move changelog from to March 2015

  • Breaking changes (!):

    Refactor some parts of the interface, see “naming scheme” in the README; The changes are:

    old new
    withMultiFoo withMultiFooA
    withMultiFoos withMultiFoosA
    mAskRaw mGetRaw
    evalMultiStateT runMultiStateTNil
    evalMultiStateTWithInitial runMultiStateTA
    evalMultiReaderT runMultiReaderTNil
    evalMultiReaderTWithInitial runMultiReaderTA
    execMultiWriterT runMultiWriterTW
  • Start using hspec; Add proper cabal test-suite. March 2015

  • Refactor from Control.Monad.* to Control.Monad.Trans.*

  • Put classes (MonadMulti*) into separate modules

  • Add Strict and Lazy variants

  • Deprecate previous modules January 2015

  • Add MultiWriter

  • Fixity for (:+:)

  • support ghc-7.10 January 2015

  • Start using DataKinds and TypeOperators to make the HList representation more readable. The translation roughly is:

    Null        -> '[]
    Cons a Null -> '[a]
    Cons a b    -> a ': b
    TNull       -> HNil
    TCons a b   -> a :+: b
  • Remove dependency on tfp package. September 2014

  • Add example

  • Clean up / Add dependencies

  • More documentation

0.1.2 September 2014

  • Expose HList module

  • Add haddocks

0.1.1 June 2014

  • First version published on hackage