Safe Haskell	Safe
Language	Haskell2010

Reader

Contents

Reader
ReaderT
MonadReader
Magnify

Synopsis

type Reader r = ReaderT r Identity
runReader :: Reader r a -> r -> a
mapReader :: (a -> b) -> Reader r a -> Reader r b
withReader :: (r' -> r) -> Reader r a -> Reader r' a
newtype ReaderT r (m :: k -> *) (a :: k) :: forall k. * -> (k -> *) -> k -> * = ReaderT {
- runReaderT :: r -> m a
}
mapReaderT :: (m a -> n b) -> ReaderT r m a -> ReaderT r n b
withReaderT :: (r' -> r) -> ReaderT r m a -> ReaderT r' m a
class Monad m => MonadReader r (m :: * -> *) | m -> r where
class (Magnified m ~ Magnified n, MonadReader b m, MonadReader a n) => Magnify (m :: * -> *) (n :: * -> *) b a | m -> b, n -> a, m a -> n, n b -> m
magnify :: Magnify m n b a => LensLike' (Magnified m c) a b -> m c -> n c

Reader

type Reader r = ReaderT r Identity #

The parameterizable reader monad.

Computations are functions of a shared environment.

The return function ignores the environment, while >>= passes the inherited environment to both subcomputations.

runReader #

Arguments

:: Reader r a	A `Reader` to run.
-> r	An initial environment.
-> a

Runs a Reader and extracts the final value from it. (The inverse of reader.)

mapReader :: (a -> b) -> Reader r a -> Reader r b #

Transform the value returned by a Reader.

runReader (mapReader f m) = f . runReader m

withReader #

Arguments

:: (r' -> r)	The function to modify the environment.
-> Reader r a	Computation to run in the modified environment.
-> Reader r' a

Execute a computation in a modified environment (a specialization of withReaderT).

runReader (withReader f m) = runReader m . f

ReaderT

newtype ReaderT r (m :: k -> *) (a :: k) :: forall k. * -> (k -> *) -> k -> * #

The reader monad transformer, which adds a read-only environment to the given monad.

The return function ignores the environment, while >>= passes the inherited environment to both subcomputations.

Constructors

ReaderT
Fields runReaderT :: r -> m a

Instances

MonadParsec e s m => MonadParsec e s (ReaderT r m)
Instance details Defined in Text.Megaparsec.Class Methods failure :: Maybe (ErrorItem (Token s)) -> Set (ErrorItem (Token s)) -> ReaderT r m a # fancyFailure :: Set (ErrorFancy e) -> ReaderT r m a # label :: String -> ReaderT r m a -> ReaderT r m a # hidden :: ReaderT r m a -> ReaderT r m a # try :: ReaderT r m a -> ReaderT r m a # lookAhead :: ReaderT r m a -> ReaderT r m a # notFollowedBy :: ReaderT r m a -> ReaderT r m () # withRecovery :: (ParseError (Token s) e -> ReaderT r m a) -> ReaderT r m a -> ReaderT r m a # observing :: ReaderT r m a -> ReaderT r m (Either (ParseError (Token s) e) a) # eof :: ReaderT r m () # token :: (Token s -> Either (Maybe (ErrorItem (Token s)), Set (ErrorItem (Token s))) a) -> Maybe (Token s) -> ReaderT r m a # tokens :: (Tokens s -> Tokens s -> Bool) -> Tokens s -> ReaderT r m (Tokens s) # takeWhileP :: Maybe String -> (Token s -> Bool) -> ReaderT r m (Tokens s) # takeWhile1P :: Maybe String -> (Token s -> Bool) -> ReaderT r m (Tokens s) # takeP :: Maybe String -> Int -> ReaderT r m (Tokens s) # getParserState :: ReaderT r m (State s) # updateParserState :: (State s -> State s) -> ReaderT r m () #
Monad m => MonadReader r (ReaderT r m)
Instance details Defined in Control.Monad.Reader.Class Methods ask :: ReaderT r m r # local :: (r -> r) -> ReaderT r m a -> ReaderT r m a # reader :: (r -> a) -> ReaderT r m a #
MonadState s m => MonadState s (ReaderT r m)
Instance details Defined in Control.Monad.State.Class Methods get :: ReaderT r m s # put :: s -> ReaderT r m () # state :: (s -> (a, s)) -> ReaderT r m a #
(Functor f, MonadFree f m) => MonadFree f (ReaderT e m)
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (ReaderT e m a) -> ReaderT e m a #
MonadError e m => MonadError e (ReaderT r m)
Instance details Defined in Control.Monad.Error.Class Methods throwError :: e -> ReaderT r m a # catchError :: ReaderT r m a -> (e -> ReaderT r m a) -> ReaderT r m a #
MonadWriter w m => MonadWriter w (ReaderT r m)
Instance details Defined in Control.Monad.Writer.Class Methods writer :: (a, w) -> ReaderT r m a # tell :: w -> ReaderT r m () # listen :: ReaderT r m a -> ReaderT r m (a, w) # pass :: ReaderT r m (a, w -> w) -> ReaderT r m a #
MonadBase b m => MonadBase b (ReaderT r m)
Instance details Defined in Control.Monad.Base Methods liftBase :: b α -> ReaderT r m α #
MFunctor (ReaderT r :: (* -> ) -> -> *)
Instance details Defined in Control.Monad.Morph Methods hoist :: Monad m => (forall a. m a -> n a) -> ReaderT r m b -> ReaderT r n b #
MonadTrans (ReaderT r :: (* -> ) -> -> *)
Instance details Defined in Control.Monad.Trans.Reader Methods lift :: Monad m => m a -> ReaderT r m a #
MMonad (ReaderT r :: (* -> ) -> -> *)
Instance details Defined in Control.Monad.Morph Methods embed :: Monad n => (forall a. m a -> ReaderT r n a) -> ReaderT r m b -> ReaderT r n b #
Monad m => Monad (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods (>>=) :: ReaderT r m a -> (a -> ReaderT r m b) -> ReaderT r m b # (>>) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m b # return :: a -> ReaderT r m a # fail :: String -> ReaderT r m a #
Functor m => Functor (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods fmap :: (a -> b) -> ReaderT r m a -> ReaderT r m b # (<$) :: a -> ReaderT r m b -> ReaderT r m a #
MonadFix m => MonadFix (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods mfix :: (a -> ReaderT r m a) -> ReaderT r m a #
MonadFail m => MonadFail (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods fail :: String -> ReaderT r m a #
Applicative m => Applicative (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods pure :: a -> ReaderT r m a # (<>) :: ReaderT r m (a -> b) -> ReaderT r m a -> ReaderT r m b # liftA2 :: (a -> b -> c) -> ReaderT r m a -> ReaderT r m b -> ReaderT r m c # (>) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m b # (<*) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m a #
Alternative m => Alternative (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods empty :: ReaderT r m a # (<\|>) :: ReaderT r m a -> ReaderT r m a -> ReaderT r m a # some :: ReaderT r m a -> ReaderT r m [a] # many :: ReaderT r m a -> ReaderT r m [a] #
Distributive g => Distributive (ReaderT e g)
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f (ReaderT e g a) -> ReaderT e g (f a) # collect :: Functor f => (a -> ReaderT e g b) -> f a -> ReaderT e g (f b) # distributeM :: Monad m => m (ReaderT e g a) -> ReaderT e g (m a) # collectM :: Monad m => (a -> ReaderT e g b) -> m a -> ReaderT e g (m b) #
Contravariant m => Contravariant (ReaderT r m)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> ReaderT r m b -> ReaderT r m a # (>$) :: b -> ReaderT r m b -> ReaderT r m a #
Representable m => Representable (ReaderT e m)
Instance details Defined in Data.Functor.Rep Associated Types type Rep (ReaderT e m) :: * # Methods tabulate :: (Rep (ReaderT e m) -> a) -> ReaderT e m a # index :: ReaderT e m a -> Rep (ReaderT e m) -> a #
MonadPlus m => MonadPlus (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods mzero :: ReaderT r m a # mplus :: ReaderT r m a -> ReaderT r m a -> ReaderT r m a #
MonadZip m => MonadZip (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods mzip :: ReaderT r m a -> ReaderT r m b -> ReaderT r m (a, b) # mzipWith :: (a -> b -> c) -> ReaderT r m a -> ReaderT r m b -> ReaderT r m c # munzip :: ReaderT r m (a, b) -> (ReaderT r m a, ReaderT r m b) #
MonadIO m => MonadIO (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods liftIO :: IO a -> ReaderT r m a #
Divisible m => Divisible (ReaderT r m)
Instance details Defined in Data.Functor.Contravariant.Divisible Methods divide :: (a -> (b, c)) -> ReaderT r m b -> ReaderT r m c -> ReaderT r m a # conquer :: ReaderT r m a #
Decidable m => Decidable (ReaderT r m)
Instance details Defined in Data.Functor.Contravariant.Divisible Methods lose :: (a -> Void) -> ReaderT r m a # choose :: (a -> Either b c) -> ReaderT r m b -> ReaderT r m c -> ReaderT r m a #
MonadThrow m => MonadThrow (ReaderT r m)
Instance details Defined in Control.Monad.Catch Methods throwM :: Exception e => e -> ReaderT r m a #
MonadCatch m => MonadCatch (ReaderT r m)
Instance details Defined in Control.Monad.Catch Methods catch :: Exception e => ReaderT r m a -> (e -> ReaderT r m a) -> ReaderT r m a #
MonadMask m => MonadMask (ReaderT r m)
Instance details Defined in Control.Monad.Catch Methods mask :: ((forall a. ReaderT r m a -> ReaderT r m a) -> ReaderT r m b) -> ReaderT r m b # uninterruptibleMask :: ((forall a. ReaderT r m a -> ReaderT r m a) -> ReaderT r m b) -> ReaderT r m b # generalBracket :: ReaderT r m a -> (a -> ExitCase b -> ReaderT r m c) -> (a -> ReaderT r m b) -> ReaderT r m (b, c) #
PrimMonad m => PrimMonad (ReaderT r m)
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState (ReaderT r m) :: * # Methods primitive :: (State# (PrimState (ReaderT r m)) -> (#State# (PrimState (ReaderT r m)), a#)) -> ReaderT r m a #
Apply m => Apply (ReaderT e m)
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: ReaderT e m (a -> b) -> ReaderT e m a -> ReaderT e m b # (.>) :: ReaderT e m a -> ReaderT e m b -> ReaderT e m b # (<.) :: ReaderT e m a -> ReaderT e m b -> ReaderT e m a # liftF2 :: (a -> b -> c) -> ReaderT e m a -> ReaderT e m b -> ReaderT e m c #
MonadLogic m => MonadLogic (ReaderT e m)
Instance details Defined in Control.Monad.Logic.Class Methods msplit :: ReaderT e m a -> ReaderT e m (Maybe (a, ReaderT e m a)) # interleave :: ReaderT e m a -> ReaderT e m a -> ReaderT e m a # (>>-) :: ReaderT e m a -> (a -> ReaderT e m b) -> ReaderT e m b # ifte :: ReaderT e m a -> (a -> ReaderT e m b) -> ReaderT e m b -> ReaderT e m b # once :: ReaderT e m a -> ReaderT e m a #
MonadManaged m => MonadManaged (ReaderT r m)
Instance details Defined in Control.Monad.Managed Methods using :: Managed a -> ReaderT r m a #
MonadCont m => MonadCont (ReaderT r m)
Instance details Defined in Control.Monad.Cont.Class Methods callCC :: ((a -> ReaderT r m b) -> ReaderT r m a) -> ReaderT r m a #
Pointed m => Pointed (ReaderT r m)
Instance details Defined in Data.Pointed Methods point :: a -> ReaderT r m a #
Plus f => Plus (ReaderT e f)
Instance details Defined in Data.Functor.Plus Methods zero :: ReaderT e f a #
Alt f => Alt (ReaderT e f)
Instance details Defined in Data.Functor.Alt Methods (<!>) :: ReaderT e f a -> ReaderT e f a -> ReaderT e f a # some :: Applicative (ReaderT e f) => ReaderT e f a -> ReaderT e f [a] # many :: Applicative (ReaderT e f) => ReaderT e f a -> ReaderT e f [a] #
Bind m => Bind (ReaderT e m)
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: ReaderT e m a -> (a -> ReaderT e m b) -> ReaderT e m b # join :: ReaderT e m (ReaderT e m a) -> ReaderT e m a #
MonadUnliftIO m => MonadUnliftIO (ReaderT r m)
Instance details Defined in Control.Monad.IO.Unlift Methods askUnliftIO :: ReaderT r m (UnliftIO (ReaderT r m)) # withRunInIO :: ((forall a. ReaderT r m a -> IO a) -> IO b) -> ReaderT r m b #
Zoom m n s t => Zoom (ReaderT e m) (ReaderT e n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (ReaderT e m) c) t s -> ReaderT e m c -> ReaderT e n c #
Monad m => Magnify (ReaderT b m) (ReaderT a m) b a
Instance details Defined in Control.Lens.Zoom Methods magnify :: LensLike' (Magnified (ReaderT b m) c) a b -> ReaderT b m c -> ReaderT a m c #
Wrapped (ReaderT r m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ReaderT r m a) :: * # Methods _Wrapped' :: Iso' (ReaderT r m a) (Unwrapped (ReaderT r m a)) #
t ~ ReaderT s n b => Rewrapped (ReaderT r m a) t
Instance details Defined in Control.Lens.Wrapped
type Rep (ReaderT e m)
Instance details Defined in Data.Functor.Rep type Rep (ReaderT e m) = (e, Rep m)
type Zoomed (ReaderT e m)
Instance details Defined in Control.Lens.Zoom type Zoomed (ReaderT e m) = Zoomed m
type Magnified (ReaderT b m)
Instance details Defined in Control.Lens.Zoom type Magnified (ReaderT b m) = Effect m
type PrimState (ReaderT r m)
Instance details Defined in Control.Monad.Primitive type PrimState (ReaderT r m) = PrimState m
type Unwrapped (ReaderT r m a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (ReaderT r m a) = r -> m a

mapReaderT :: (m a -> n b) -> ReaderT r m a -> ReaderT r n b #

Transform the computation inside a ReaderT.

runReaderT (mapReaderT f m) = f . runReaderT m

withReaderT #

Arguments

:: (r' -> r)	The function to modify the environment.
-> ReaderT r m a	Computation to run in the modified environment.
-> ReaderT r' m a

Execute a computation in a modified environment (a more general version of local).

runReaderT (withReaderT f m) = runReaderT m . f

MonadReader

class Monad m => MonadReader r (m :: * -> *) | m -> r where #

See examples in Control.Monad.Reader. Note, the partially applied function type (->) r is a simple reader monad. See the instance declaration below.

Minimal complete definition

(ask | reader), local

Methods

ask :: m r #

Retrieves the monad environment.

local #

Arguments

:: (r -> r)	The function to modify the environment.
-> m a	`Reader` to run in the modified environment.
-> m a

Executes a computation in a modified environment.

reader #

Arguments

:: (r -> a)	The selector function to apply to the environment.
-> m a

Retrieves a function of the current environment.

Instances

MonadReader r m => MonadReader r (MaybeT m)
Instance details Defined in Control.Monad.Reader.Class Methods ask :: MaybeT m r # local :: (r -> r) -> MaybeT m a -> MaybeT m a # reader :: (r -> a) -> MaybeT m a #
MonadReader r m => MonadReader r (ListT m)
Instance details Defined in Control.Monad.Reader.Class Methods ask :: ListT m r # local :: (r -> r) -> ListT m a -> ListT m a # reader :: (r -> a) -> ListT m a #
MonadReader r m => MonadReader r (LogicT m)
Instance details Defined in Control.Monad.Logic Methods ask :: LogicT m r # local :: (r -> r) -> LogicT m a -> LogicT m a # reader :: (r -> a) -> LogicT m a #
MonadReader i m => MonadReader i (ListT m)
Instance details Defined in List.Transformer Methods ask :: ListT m i # local :: (i -> i) -> ListT m a -> ListT m a # reader :: (i -> a) -> ListT m a #
MonadReader s (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods ask :: ReifiedGetter s s # local :: (s -> s) -> ReifiedGetter s a -> ReifiedGetter s a # reader :: (s -> a) -> ReifiedGetter s a #
MonadReader s (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods ask :: ReifiedFold s s # local :: (s -> s) -> ReifiedFold s a -> ReifiedFold s a # reader :: (s -> a) -> ReifiedFold s a #
(Functor m, MonadReader e m) => MonadReader e (Free m)
Instance details Defined in Control.Monad.Free Methods ask :: Free m e # local :: (e -> e) -> Free m a -> Free m a # reader :: (e -> a) -> Free m a #
(Representable f, Rep f ~ a) => MonadReader a (Co f)
Instance details Defined in Data.Functor.Rep Methods ask :: Co f a # local :: (a -> a) -> Co f a0 -> Co f a0 # reader :: (a -> a0) -> Co f a0 #
(Monoid w, MonadReader r m) => MonadReader r (WriterT w m)
Instance details Defined in Control.Monad.Reader.Class Methods ask :: WriterT w m r # local :: (r -> r) -> WriterT w m a -> WriterT w m a # reader :: (r -> a) -> WriterT w m a #
(Monoid w, MonadReader r m) => MonadReader r (WriterT w m)
Instance details Defined in Control.Monad.Reader.Class Methods ask :: WriterT w m r # local :: (r -> r) -> WriterT w m a -> WriterT w m a # reader :: (r -> a) -> WriterT w m a #
MonadReader r m => MonadReader r (StateT s m)
Instance details Defined in Control.Monad.Reader.Class Methods ask :: StateT s m r # local :: (r -> r) -> StateT s m a -> StateT s m a # reader :: (r -> a) -> StateT s m a #
MonadReader r m => MonadReader r (StateT s m)
Instance details Defined in Control.Monad.Reader.Class Methods ask :: StateT s m r # local :: (r -> r) -> StateT s m a -> StateT s m a # reader :: (r -> a) -> StateT s m a #
MonadReader r m => MonadReader r (IdentityT m)
Instance details Defined in Control.Monad.Reader.Class Methods ask :: IdentityT m r # local :: (r -> r) -> IdentityT m a -> IdentityT m a # reader :: (r -> a) -> IdentityT m a #
MonadReader r m => MonadReader r (ExceptT e m)	Since: mtl-2.2
Instance details Defined in Control.Monad.Reader.Class Methods ask :: ExceptT e m r # local :: (r -> r) -> ExceptT e m a -> ExceptT e m a # reader :: (r -> a) -> ExceptT e m a #
(Error e, MonadReader r m) => MonadReader r (ErrorT e m)
Instance details Defined in Control.Monad.Reader.Class Methods ask :: ErrorT e m r # local :: (r -> r) -> ErrorT e m a -> ErrorT e m a # reader :: (r -> a) -> ErrorT e m a #
(Functor f, MonadReader r m) => MonadReader r (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods ask :: FreeT f m r # local :: (r -> r) -> FreeT f m a -> FreeT f m a # reader :: (r -> a) -> FreeT f m a #
(Stream s, MonadReader r m) => MonadReader r (ParsecT e s m)
Instance details Defined in Text.Megaparsec.Internal Methods ask :: ParsecT e s m r # local :: (r -> r) -> ParsecT e s m a -> ParsecT e s m a # reader :: (r -> a) -> ParsecT e s m a #
Monad m => MonadReader r (ReaderT r m)
Instance details Defined in Control.Monad.Reader.Class Methods ask :: ReaderT r m r # local :: (r -> r) -> ReaderT r m a -> ReaderT r m a # reader :: (r -> a) -> ReaderT r m a #
MonadReader r ((->) r :: * -> *)
Instance details Defined in Control.Monad.Reader.Class Methods ask :: r -> r # local :: (r -> r) -> (r -> a) -> r -> a # reader :: (r -> a) -> r -> a #
MonadReader r' m => MonadReader r' (ContT r m)
Instance details Defined in Control.Monad.Reader.Class Methods ask :: ContT r m r' # local :: (r' -> r') -> ContT r m a -> ContT r m a # reader :: (r' -> a) -> ContT r m a #
(Monad m, Monoid w) => MonadReader r (RWST r w s m)
Instance details Defined in Control.Monad.Reader.Class Methods ask :: RWST r w s m r # local :: (r -> r) -> RWST r w s m a -> RWST r w s m a # reader :: (r -> a) -> RWST r w s m a #
(Monad m, Monoid w) => MonadReader r (RWST r w s m)
Instance details Defined in Control.Monad.Reader.Class Methods ask :: RWST r w s m r # local :: (r -> r) -> RWST r w s m a -> RWST r w s m a # reader :: (r -> a) -> RWST r w s m a #

Magnify

class (Magnified m ~ Magnified n, MonadReader b m, MonadReader a n) => Magnify (m :: * -> *) (n :: * -> *) b a | m -> b, n -> a, m a -> n, n b -> m #

This class allows us to use magnify part of the environment, changing the environment supplied by many different Monad transformers. Unlike zoom this can change the environment of a deeply nested Monad transformer.

Also, unlike zoom, this can be used with any valid Getter, but cannot be used with a Traversal or Fold.

Minimal complete definition

magnify

Instances

Magnify m n b a => Magnify (IdentityT m) (IdentityT n) b a
Instance details Defined in Control.Lens.Zoom Methods magnify :: LensLike' (Magnified (IdentityT m) c) a b -> IdentityT m c -> IdentityT n c #
Magnify ((->) b :: * -> ) ((->) a :: -> *) b a	`magnify` = `views`
Instance details Defined in Control.Lens.Zoom Methods magnify :: LensLike' (Magnified ((->) b) c) a b -> (b -> c) -> a -> c #
Monad m => Magnify (ReaderT b m) (ReaderT a m) b a
Instance details Defined in Control.Lens.Zoom Methods magnify :: LensLike' (Magnified (ReaderT b m) c) a b -> ReaderT b m c -> ReaderT a m c #
(Monad m, Monoid w) => Magnify (RWST b w s m) (RWST a w s m) b a
Instance details Defined in Control.Lens.Zoom Methods magnify :: LensLike' (Magnified (RWST b w s m) c) a b -> RWST b w s m c -> RWST a w s m c #
(Monad m, Monoid w) => Magnify (RWST b w s m) (RWST a w s m) b a
Instance details Defined in Control.Lens.Zoom Methods magnify :: LensLike' (Magnified (RWST b w s m) c) a b -> RWST b w s m c -> RWST a w s m c #

magnify :: Magnify m n b a => LensLike' (Magnified m c) a b -> m c -> n c infixr 2 #

Run a monadic action in a larger environment than it was defined in, using a Getter.

This acts like local, but can in many cases change the type of the environment as well.

This is commonly used to lift actions in a simpler Reader Monad into a Monad with a larger environment type.

This can be used to edit pretty much any Monad transformer stack with an environment in it:

>>> (1,2) & magnify _2 (+1)
3

>>> flip Reader.runReader (1,2) $ magnify _1 Reader.ask
1

>>> flip Reader.runReader (1,2,[10..20]) $ magnify (_3._tail) Reader.ask
[11,12,13,14,15,16,17,18,19,20]

magnify :: Getter s a -> (a -> r) -> s -> r
magnify :: Monoid r => Fold s a   -> (a -> r) -> s -> r

magnify :: Monoid w                 => Getter s t -> RWS t w st c -> RWS s w st c
magnify :: (Monoid w, Monoid c) => Fold s a   -> RWS a w st c -> RWS s w st c
...