Control.Monad.Accum

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.

Type class

class (Monoid w, Monad m) => MonadAccum w m | m -> w where

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 tells.

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: 2.3

Minimal complete definition

accum | look, add

Methods

look :: m w

Retrieve the accumulated result so far.

add :: w -> m ()

Append a value to the result.

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

Embed a simple accumulation action into the monad.

Instances

MonadAccum w m => MonadAccum w (MaybeT m)

The accumulated value 'survives' an error: even if the computation fails to deliver a result, we still have an accumulated value.

Since: 2.3

Defined in Control.Monad.Accum

Methods

look :: MaybeT m w

add :: w -> MaybeT m ()

accum :: (w -> (a, w)) -> MaybeT m a

(MonadTrans t, Monad (t m), MonadAccum w m) => MonadAccum w (LiftingAccum t m)

Since: 2.3

Defined in Control.Monad.Accum

Methods

look :: LiftingAccum t m w

add :: w -> LiftingAccum t m ()

accum :: (w -> (a, w)) -> LiftingAccum t m a

Monoid w => MonadAccum w (AccumT w Identity)

Since: 2.3

Defined in Control.Monad.Accum

Methods

look :: AccumT w Identity w

add :: w -> AccumT w Identity ()

accum :: (w -> (a, w)) -> AccumT w Identity a

MonadAccum w m => MonadAccum w (ExceptT e m)

The accumulated value 'survives' an exception: even if the computation fails to deliver a result, we still have an accumulated value.

Since: 2.3

Defined in Control.Monad.Accum

Methods

look :: ExceptT e m w

add :: w -> ExceptT e m ()

accum :: (w -> (a, w)) -> ExceptT e m a

MonadAccum w m => MonadAccum w (IdentityT m)

Since: 2.3

Defined in Control.Monad.Accum

Methods

look :: IdentityT m w

add :: w -> IdentityT m ()

accum :: (w -> (a, w)) -> IdentityT m a

MonadAccum w m => MonadAccum w (ReaderT r m)

Since: 2.3

Defined in Control.Monad.Accum

Methods

look :: ReaderT r m w

add :: w -> ReaderT r m ()

accum :: (w -> (a, w)) -> ReaderT r m a

MonadAccum w m => MonadAccum w (SelectT r m)

The 'ranking' function gains the ability to accumulate ws each time it is called. The final result will include the entire log of all such calls.

Since: 2.3

Defined in Control.Monad.Accum

Methods

look :: SelectT r m w

add :: w -> SelectT r m ()

accum :: (w -> (a, w)) -> SelectT r m a

MonadAccum w m => MonadAccum w (StateT s m)

Since: 2.3

Defined in Control.Monad.Accum

Methods

look :: StateT s m w

add :: w -> StateT s m ()

accum :: (w -> (a, w)) -> StateT s m a

MonadAccum w m => MonadAccum w (StateT s m)

Since: 2.3

Defined in Control.Monad.Accum

Methods

look :: StateT s m w

add :: w -> StateT s m ()

accum :: (w -> (a, w)) -> StateT s m a

MonadAccum w' m => MonadAccum w' (WriterT w m)

Since: 2.3

Defined in Control.Monad.Accum

Methods

look :: WriterT w m w'

add :: w' -> WriterT w m ()

accum :: (w' -> (a, w')) -> WriterT w m a

(MonadAccum w' m, Monoid w) => MonadAccum w' (WriterT w m)

Since: 2.3

Defined in Control.Monad.Accum

Methods

look :: WriterT w m w'

add :: w' -> WriterT w m ()

accum :: (w' -> (a, w')) -> WriterT w m a

(MonadAccum w' m, Monoid w) => MonadAccum w' (WriterT w m)

Since: 2.3

Defined in Control.Monad.Accum

Methods

look :: WriterT w m w'

add :: w' -> WriterT w m ()

accum :: (w' -> (a, w')) -> WriterT w m a

MonadAccum w m => MonadAccum w (ContT r m)

The continuation can see, and interact with, the accumulated value.

Since: 2.3

Defined in Control.Monad.Accum

Methods

look :: ContT r m w

add :: w -> ContT r m ()

accum :: (w -> (a, w)) -> ContT r m a

MonadAccum w' m => MonadAccum w' (RWST r w s m)

Since: 2.3

Defined in Control.Monad.Accum

Methods

look :: RWST r w s m w'

add :: w' -> RWST r w s m ()

accum :: (w' -> (a, w')) -> RWST r w s m a

(MonadAccum w' m, Monoid w) => MonadAccum w' (RWST r w s m)

Since: 2.3

Defined in Control.Monad.Accum

Methods

look :: RWST r w s m w'

add :: w' -> RWST r w s m ()

accum :: (w' -> (a, w')) -> RWST r w s m a

(MonadAccum w' m, Monoid w) => MonadAccum w' (RWST r w s m)

Since: 2.3

Defined in Control.Monad.Accum

Methods

look :: RWST r w s m w'

add :: w' -> RWST r w s m ()

accum :: (w' -> (a, w')) -> RWST r w s m a

Lifting helper type

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

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: 2.3

Constructors

LiftingAccum (t m a)

Instances

(MonadTrans t, Monad (t m), MonadAccum w m) => MonadAccum w (LiftingAccum t m)

Since: 2.3

Defined in Control.Monad.Accum

Methods

look :: LiftingAccum t m w

add :: w -> LiftingAccum t m ()

accum :: (w -> (a, w)) -> LiftingAccum t m a

Applicative (t m) => Applicative (LiftingAccum t m)

Since: 2.3

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)

Since: 2.3

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)

Since: 2.3

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 :: Type) (m :: Type -> Type) (w :: Type). MonadAccum w m => (w -> a) -> m a

Retrieve a function of the accumulated value.

Since: 2.3