Control.Monad.Accum

mtl-2.3.1: Monad classes for transformers, using functional dependencies

Copyright | (C) Koz Ross 2022 Manuel Bärenz 2021
License | BSD-3-Clause (see the LICENSE file)
Maintainer | koz.ross@retro-freedom.nz
Stability | Experimental
Portability | GHC only
Safe Haskell | Trustworthy
Language | Haskell2010

Control.Monad.Accum

Contents

- Type class
- Lifting helper type
- Other functions

Description

Computation type:
  Accumulation (either append-only state, or writer with the ability to read all previous input).
Binding strategy:
  Binding a function to a monadic value monoidally accumulates the subcomputations (that is, using `<>`).
Useful for:
  Logging, patch-style tracking.
Zero and plus:
  None.
Example type:
  ``Accum` w a`

# A note on commutativity

Some effects are commutative: it doesn't matter which you resolve first, as all possible orderings of commutative effects are isomorphic. Consider, for example, the reader and state effects, as exemplified by `ReaderT` and `StateT` respectively. If we have ``ReaderT` r (`State` s) a`, this is effectively `r -> `State` s a ~ r -> s -> (a, s)`; if we instead have ``StateT` s (`Reader` r) a`, this is effectively `s -> `Reader` r (a, s) ~ s -> r -> (a, s)`. Since we can always reorder function arguments (for example, using `flip`, as in this case) without changing the result, these are isomorphic, showing that reader and state are commutative, or, more precisely, commute with each other.

However, this isn't generally the case. Consider instead the error and state effects, as exemplified by `MaybeT` and `StateT` respectively. If we have ``MaybeT` (`State` s) a`, this is effectively ``State` s (`Maybe` a) ~ s -> (`Maybe` a, s)`: put simply, the error can occur only in the result, but not the state, which always 'survives'. On the other hand, if we have ``StateT` s `Maybe` a`, this is instead `s -> `Maybe` (a, s)`: here, if we error, we lose both the state and the result! Thus, error and state effects do not commute with each other.

As the MTL is capability-based, we support any ordering of non-commutative effects on an equal footing. Indeed, if you wish to use `MonadState`, for example, whether your final monadic stack ends up being ``MaybeT` (`State` s) a`, ``StateT` s `Maybe` a`, or anything else, you will be able to write your desired code without having to consider such differences. However, the way we implement these capabilities for any given transformer (or rather, any given transformed stack) is affected by this ordering unless the effects in question are commutative.

We note in this module which effects the accumulation effect does and doesn't commute with; we also note on implementations with non-commutative transformers what the outcome will be. Note that, depending on how the 'inner monad' is structured, this may be more complex than we note: we describe only what impact the 'outer effect' has, not what else might be in the stack.

# Commutativity of accumulation

The accumulation effect commutes with the identity effect (`IdentityT`), reader, writer or state effects (`ReaderT`, `WriterT`, `StateT` and any combination, including `RWST` for example) and with itself. It does not commute with anything else.

Synopsis

- class (Monoid w, Monad m) => MonadAccum w (m :: Type -> Type) | m -> w where
  - look :: m w
  - add :: w -> m ()
  - accum :: (w -> (a, w)) -> m a
- newtype LiftingAccum (t :: (Type -> Type) -> Type -> Type) (m :: Type -> Type) a = LiftingAccum (t m a)
- looks :: forall a m w. MonadAccum w m => (w -> a) -> m a

# Type class

class (Monoid w, Monad m) => MonadAccum w (m :: Type -> Type) | m -> w where Source #

The capability to accumulate. This can be seen in one of two ways:

- A `MonadState` which can only append (using `<>`); or
- A `MonadWriter` (limited to `tell`) with the ability to view the result of all previous `tell`s.

# Laws

`accum` should obey the following:

1. ``accum` (`const` (x, `mempty`))` `=` ``pure` x`
2. ``accum` f `*>` `accum` g` `=` ``accum` `$` acc -> let (_, v) = f acc (res, w) = g (acc `<>` v) in (res, v `<>` w)`

If you choose to define `look` and `add` instead, their definitions must obey the following:

1. ``look` `*>` `look`` `=` ``look``
2. ``add` `mempty`` `=` ``pure` ()`
3. ``add` x `*>` `add` y` `=` ``add` (x `<>` y)`
4. ``add` x `*>` `look`` `=` ``look` `>>=` w -> `add` x `$>` w `<>` x`

If you want to define both, the relationship between them is as follows. These are also the default definitions.

1. ``look`` `=` ``accum` `$` acc -> (acc, mempty)`
2. ``add` x` `=` ``accum` `$` acc -> (`()`, x)`
3. ``accum` f` `=` ``look` >>= acc -> let (res, v) = f acc in `add` v `$>` res`

Since: mtl-2.3

Minimal complete definition

accum | look, add

Methods

look :: m w Source #

Retrieve the accumulated result so far.

add :: w -> m () Source #

Append a value to the result.

accum :: (w -> (a, w)) -> m a Source #

Embed a simple accumulation action into the monad.

#### Instances

Instances details

MonadAccum w m => MonadAccum w (MaybeT m) Source # | The accumulated value 'survives' an error: even if the computation fails to deliver a result, we still have an accumulated value. Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods look :: MaybeT m w Source # add :: w -> MaybeT m () Source # accum :: (w -> (a, w)) -> MaybeT m a Source #
(MonadTrans t, Monad (t m), MonadAccum w m) => MonadAccum w (LiftingAccum t m) Source # | Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods look :: LiftingAccum t m w Source # add :: w -> LiftingAccum t m () Source # accum :: (w -> (a, w)) -> LiftingAccum t m a Source #
Monoid w => MonadAccum w (AccumT w Identity) Source # | Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods look :: AccumT w Identity w Source # add :: w -> AccumT w Identity () Source # accum :: (w -> (a, w)) -> AccumT w Identity a Source #
MonadAccum w m => MonadAccum w (ExceptT e m) Source # | The accumulated value 'survives' an exception: even if the computation fails to deliver a result, we still have an accumulated value. Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods look :: ExceptT e m w Source # add :: w -> ExceptT e m () Source # accum :: (w -> (a, w)) -> ExceptT e m a Source #
MonadAccum w m => MonadAccum w (IdentityT m) Source # | Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods look :: IdentityT m w Source # add :: w -> IdentityT m () Source # accum :: (w -> (a, w)) -> IdentityT m a Source #
MonadAccum w m => MonadAccum w (ReaderT r m) Source # | Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods look :: ReaderT r m w Source # add :: w -> ReaderT r m () Source # accum :: (w -> (a, w)) -> ReaderT r m a Source #
MonadAccum w m => MonadAccum w (SelectT r m) Source # | The 'ranking' function gains the ability to accumulate `w`s each time it is called. The final result will include the entire log of all such calls. Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods look :: SelectT r m w Source # add :: w -> SelectT r m () Source # accum :: (w -> (a, w)) -> SelectT r m a Source #
MonadAccum w m => MonadAccum w (StateT s m) Source # | Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods look :: StateT s m w Source # add :: w -> StateT s m () Source # accum :: (w -> (a, w)) -> StateT s m a Source #
MonadAccum w m => MonadAccum w (StateT s m) Source # | Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods look :: StateT s m w Source # add :: w -> StateT s m () Source # accum :: (w -> (a, w)) -> StateT s m a Source #
MonadAccum w' m => MonadAccum w' (WriterT w m) Source # | Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods look :: WriterT w m w' Source # add :: w' -> WriterT w m () Source # accum :: (w' -> (a, w')) -> WriterT w m a Source #
(MonadAccum w' m, Monoid w) => MonadAccum w' (WriterT w m) Source # | Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods look :: WriterT w m w' Source # add :: w' -> WriterT w m () Source # accum :: (w' -> (a, w')) -> WriterT w m a Source #
(MonadAccum w' m, Monoid w) => MonadAccum w' (WriterT w m) Source # | Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods look :: WriterT w m w' Source # add :: w' -> WriterT w m () Source # accum :: (w' -> (a, w')) -> WriterT w m a Source #
MonadAccum w m => MonadAccum w (ContT r m) Source # | The continuation can see, and interact with, the accumulated value. Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods look :: ContT r m w Source # add :: w -> ContT r m () Source # accum :: (w -> (a, w)) -> ContT r m a Source #
MonadAccum w' m => MonadAccum w' (RWST r w s m) Source # | Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods look :: RWST r w s m w' Source # add :: w' -> RWST r w s m () Source # accum :: (w' -> (a, w')) -> RWST r w s m a Source #
(MonadAccum w' m, Monoid w) => MonadAccum w' (RWST r w s m) Source # | Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods look :: RWST r w s m w' Source # add :: w' -> RWST r w s m () Source # accum :: (w' -> (a, w')) -> RWST r w s m a Source #
(MonadAccum w' m, Monoid w) => MonadAccum w' (RWST r w s m) Source # | Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods look :: RWST r w s m w' Source # add :: w' -> RWST r w s m () Source # accum :: (w' -> (a, w')) -> RWST r w s m a Source #

# Lifting helper type

newtype LiftingAccum (t :: (Type -> Type) -> Type -> Type) (m :: Type -> Type) a Source #

A helper type to decrease boilerplate when defining new transformer instances of `MonadAccum`.

Most of the instances in this module are derived using this method; for example, our instance of `ExceptT` is derived as follows:

    deriving via (LiftingAccum (ExceptT e) m) instance (MonadAccum w m) =>
     MonadAccum w (ExceptT e m)

Since: mtl-2.3

Constructors

LiftingAccum (t m a) |

#### Instances

Instances details

(MonadTrans t, Monad (t m), MonadAccum w m) => MonadAccum w (LiftingAccum t m) Source # | Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods look :: LiftingAccum t m w Source # add :: w -> LiftingAccum t m () Source # accum :: (w -> (a, w)) -> LiftingAccum t m a Source #
Applicative (t m) => Applicative (LiftingAccum t m) Source # | Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods pure :: a -> LiftingAccum t m a # (<*>) :: LiftingAccum t m (a -> b) -> LiftingAccum t m a -> LiftingAccum t m b # liftA2 :: (a -> b -> c) -> LiftingAccum t m a -> LiftingAccum t m b -> LiftingAccum t m c # (*>) :: LiftingAccum t m a -> LiftingAccum t m b -> LiftingAccum t m b # (<*) :: LiftingAccum t m a -> LiftingAccum t m b -> LiftingAccum t m a #
Functor (t m) => Functor (LiftingAccum t m) Source # | Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods fmap :: (a -> b) -> LiftingAccum t m a -> LiftingAccum t m b # (<$) :: a -> LiftingAccum t m b -> LiftingAccum t m a #
Monad (t m) => Monad (LiftingAccum t m) Source # | Since: mtl-2.3
Instance details Defined in Control.Monad.Accum Methods (>>=) :: LiftingAccum t m a -> (a -> LiftingAccum t m b) -> LiftingAccum t m b # (>>) :: LiftingAccum t m a -> LiftingAccum t m b -> LiftingAccum t m b # return :: a -> LiftingAccum t m a #

# Other functions

looks :: forall a m w. MonadAccum w m => (w -> a) -> m a Source #

Retrieve a function of the accumulated value.

Since: mtl-2.3