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Language	Haskell98

Lens.Family2.State.Strict

Contents

Compound Assignments
Strict Assignments
Types
Re-exports

Description

Lenses allow you to use fields of the state of a state monad as if they were variables in an imperative language. use is used to retrieve the value of a variable, and .= and %= allow you to set and modify a variable. C-style compound assignments are also provided.

Synopsis

zoom :: Monad m => LensLike' (Zooming m c) a b -> StateT b m c -> StateT a m c
use :: MonadState a m => FoldLike b a a' b b' -> m b
uses :: MonadState a m => FoldLike r a a' b b' -> (b -> r) -> m r
(%=) :: MonadState a m => Setter a a b b' -> (b -> b') -> m ()
assign :: MonadState a m => Setter a a b b' -> b' -> m ()
(.=) :: MonadState a m => Setter a a b b' -> b' -> m ()
(%%=) :: MonadState a m => LensLike (Writer c) a a b b' -> (b -> (c, b')) -> m c
(<~) :: MonadState a m => Setter a a b b' -> m b' -> m ()
(+=) :: (MonadState a m, Num b) => Setter' a b -> b -> m ()
(-=) :: (MonadState a m, Num b) => Setter' a b -> b -> m ()
(*=) :: (MonadState a m, Num b) => Setter' a b -> b -> m ()
(//=) :: (MonadState a m, Fractional b) => Setter' a b -> b -> m ()
(&&=) :: MonadState a m => Setter' a Bool -> Bool -> m ()
(||=) :: MonadState a m => Setter' a Bool -> Bool -> m ()
(<>=) :: (Monoid o, MonadState a m) => Setter' a o -> o -> m ()
(%!=) :: MonadState a m => Setter a a b b' -> (b -> b') -> m ()
(+!=) :: (MonadState a m, Num b) => Setter' a b -> b -> m ()
(-!=) :: (MonadState a m, Num b) => Setter' a b -> b -> m ()
(*!=) :: (MonadState a m, Num b) => Setter' a b -> b -> m ()
(//!=) :: (MonadState a m, Fractional b) => Setter' a b -> b -> m ()
(&&!=) :: MonadState a m => Setter' a Bool -> Bool -> m ()
(||!=) :: MonadState a m => Setter' a Bool -> Bool -> m ()
(<>!=) :: (Monoid o, MonadState a m) => Setter' a o -> o -> m ()
data Zooming (m :: * -> *) c a
type LensLike (f :: * -> *) a a' b b' = (b -> f b') -> a -> f a'
type LensLike' (f :: * -> *) a b = (b -> f b) -> a -> f a
type FoldLike r a a' b b' = LensLike (Constant r :: * -> *) a a' b b'
data Constant a (b :: k) :: forall k. * -> k -> *
type Setter a a' b b' = forall f. Identical f => LensLike f a a' b b'
type Setter' a b = forall f. Identical f => LensLike' f a b
class Applicative f => Identical (f :: * -> *)
data StateT s (m :: * -> *) a
class Monad m => MonadState s (m :: * -> *) | m -> s
type Writer w = WriterT w Identity
class Semigroup a => Monoid a

Documentation

zoom :: Monad m => LensLike' (Zooming m c) a b -> StateT b m c -> StateT a m c #

zoom :: Monad m => Lens' a b -> StateT b m c -> StateT a m c

Lift a stateful operation on a field to a stateful operation on the whole state. This is a good way to call a "subroutine" that only needs access to part of the state.

zoom :: (Monoid c, Monad m) => Traversal' a b -> StateT b m c -> StateT a m c

Run the "subroutine" on each element of the traversal in turn and mconcat all the results together.

zoom :: Monad m => Traversal' a b -> StateT b m () -> StateT a m ()

Run the "subroutine" on each element the traversal in turn.

use :: MonadState a m => FoldLike b a a' b b' -> m b Source #

use :: MonadState a m => Getter a a' b b' -> m b

Retrieve a field of the state

use :: (Monoid b, MonadState a m) => Fold a a' b b' -> m b

Retrieve a monoidal summary of all the referenced fields from the state

uses :: MonadState a m => FoldLike r a a' b b' -> (b -> r) -> m r Source #

uses :: (MonadState a m, Monoid r) => Fold a a' b b' -> (b -> r) -> m r

Retrieve all the referenced fields from the state and foldMap the results together with f :: b -> r.

uses :: MonadState a m => Getter a a' b b' -> (b -> r) -> m r

Retrieve a field of the state and pass it through the function f :: b -> r.

uses l f = f <$> use l

(%=) :: MonadState a m => Setter a a b b' -> (b -> b') -> m () infix 4 Source #

Modify a field of the state.

assign :: MonadState a m => Setter a a b b' -> b' -> m () Source #

Set a field of the state.

(.=) :: MonadState a m => Setter a a b b' -> b' -> m () infix 4 Source #

Set a field of the state.

(%%=) :: MonadState a m => LensLike (Writer c) a a b b' -> (b -> (c, b')) -> m c infix 4 Source #

(%%=) :: MonadState a m => Lens a a b b' -> (b -> (c, b')) -> m c

Modify a field of the state while returning another value.

(%%=) :: (MonadState a m, Monoid c) => Traversal a a b b' -> (b -> (c, b')) -> m c

Modify each field of the state and return the mconcat of the other values.

(<~) :: MonadState a m => Setter a a b b' -> m b' -> m () infixr 2 Source #

Set a field of the state using the result of executing a stateful command.

Compound Assignments

(+=) :: (MonadState a m, Num b) => Setter' a b -> b -> m () infixr 4 Source #

(-=) :: (MonadState a m, Num b) => Setter' a b -> b -> m () infixr 4 Source #

(*=) :: (MonadState a m, Num b) => Setter' a b -> b -> m () infixr 4 Source #

(//=) :: (MonadState a m, Fractional b) => Setter' a b -> b -> m () infixr 4 Source #

(&&=) :: MonadState a m => Setter' a Bool -> Bool -> m () infixr 4 Source #

(||=) :: MonadState a m => Setter' a Bool -> Bool -> m () infixr 4 Source #

(<>=) :: (Monoid o, MonadState a m) => Setter' a o -> o -> m () infixr 4 Source #

Monoidally append a value to all referenced fields of the state.

Strict Assignments

(%!=) :: MonadState a m => Setter a a b b' -> (b -> b') -> m () infix 4 Source #

Strictly modify a field of the state.

(+!=) :: (MonadState a m, Num b) => Setter' a b -> b -> m () infixr 4 Source #

(-!=) :: (MonadState a m, Num b) => Setter' a b -> b -> m () infixr 4 Source #

(*!=) :: (MonadState a m, Num b) => Setter' a b -> b -> m () infixr 4 Source #

(//!=) :: (MonadState a m, Fractional b) => Setter' a b -> b -> m () infixr 4 Source #

(&&!=) :: MonadState a m => Setter' a Bool -> Bool -> m () infixr 4 Source #

(||!=) :: MonadState a m => Setter' a Bool -> Bool -> m () infixr 4 Source #

(<>!=) :: (Monoid o, MonadState a m) => Setter' a o -> o -> m () infixr 4 Source #

Types

data Zooming (m :: * -> *) c a #

Instances

Monad m => Functor (Zooming m c)
Instance details Defined in Lens.Family.State.Zoom Methods fmap :: (a -> b) -> Zooming m c a -> Zooming m c b # (<$) :: a -> Zooming m c b -> Zooming m c a #
(Monoid c, Monad m) => Applicative (Zooming m c)
Instance details Defined in Lens.Family.State.Zoom Methods pure :: a -> Zooming m c a # (<>) :: Zooming m c (a -> b) -> Zooming m c a -> Zooming m c b # liftA2 :: (a -> b -> c0) -> Zooming m c a -> Zooming m c b -> Zooming m c c0 # (>) :: Zooming m c a -> Zooming m c b -> Zooming m c b # (<*) :: Zooming m c a -> Zooming m c b -> Zooming m c a #

Re-exports

type LensLike (f :: * -> *) a a' b b' = (b -> f b') -> a -> f a' #

type LensLike' (f :: * -> *) a b = (b -> f b) -> a -> f a #

type FoldLike r a a' b b' = LensLike (Constant r :: * -> *) a a' b b' #

data Constant a (b :: k) :: forall k. * -> k -> * #

Constant functor.

Instances

Bitraversable (Constant :: * -> * -> *)
Instance details Defined in Data.Functor.Constant Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Constant a b -> f (Constant c d) #
Bifoldable (Constant :: * -> * -> *)
Instance details Defined in Data.Functor.Constant Methods bifold :: Monoid m => Constant m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Constant a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Constant a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Constant a b -> c #
Bifunctor (Constant :: * -> * -> *)
Instance details Defined in Data.Functor.Constant Methods bimap :: (a -> b) -> (c -> d) -> Constant a c -> Constant b d # first :: (a -> b) -> Constant a c -> Constant b c # second :: (b -> c) -> Constant a b -> Constant a c #
Eq2 (Constant :: * -> * -> *)
Instance details Defined in Data.Functor.Constant Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Constant a c -> Constant b d -> Bool #
Ord2 (Constant :: * -> * -> *)
Instance details Defined in Data.Functor.Constant Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Constant a c -> Constant b d -> Ordering #
Read2 (Constant :: * -> * -> *)
Instance details Defined in Data.Functor.Constant Methods liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Constant a b) # liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Constant a b] # liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Constant a b) # liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Constant a b] #
Show2 (Constant :: * -> * -> *)
Instance details Defined in Data.Functor.Constant Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Constant a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Constant a b] -> ShowS #
Functor (Constant a :: * -> *)
Instance details Defined in Data.Functor.Constant Methods fmap :: (a0 -> b) -> Constant a a0 -> Constant a b # (<$) :: a0 -> Constant a b -> Constant a a0 #
Monoid a => Applicative (Constant a :: * -> *)
Instance details Defined in Data.Functor.Constant Methods pure :: a0 -> Constant a a0 # (<>) :: Constant a (a0 -> b) -> Constant a a0 -> Constant a b # liftA2 :: (a0 -> b -> c) -> Constant a a0 -> Constant a b -> Constant a c # (>) :: Constant a a0 -> Constant a b -> Constant a b # (<*) :: Constant a a0 -> Constant a b -> Constant a a0 #
Foldable (Constant a :: * -> *)
Instance details Defined in Data.Functor.Constant Methods fold :: Monoid m => Constant a m -> m # foldMap :: Monoid m => (a0 -> m) -> Constant a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Constant a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Constant a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Constant a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Constant a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Constant a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Constant a a0 -> a0 # toList :: Constant a a0 -> [a0] # null :: Constant a a0 -> Bool # length :: Constant a a0 -> Int # elem :: Eq a0 => a0 -> Constant a a0 -> Bool # maximum :: Ord a0 => Constant a a0 -> a0 # minimum :: Ord a0 => Constant a a0 -> a0 # sum :: Num a0 => Constant a a0 -> a0 # product :: Num a0 => Constant a a0 -> a0 #
Traversable (Constant a :: * -> *)
Instance details Defined in Data.Functor.Constant Methods traverse :: Applicative f => (a0 -> f b) -> Constant a a0 -> f (Constant a b) # sequenceA :: Applicative f => Constant a (f a0) -> f (Constant a a0) # mapM :: Monad m => (a0 -> m b) -> Constant a a0 -> m (Constant a b) # sequence :: Monad m => Constant a (m a0) -> m (Constant a a0) #
Eq a => Eq1 (Constant a :: * -> *)
Instance details Defined in Data.Functor.Constant Methods liftEq :: (a0 -> b -> Bool) -> Constant a a0 -> Constant a b -> Bool #
Ord a => Ord1 (Constant a :: * -> *)
Instance details Defined in Data.Functor.Constant Methods liftCompare :: (a0 -> b -> Ordering) -> Constant a a0 -> Constant a b -> Ordering #
Read a => Read1 (Constant a :: * -> *)
Instance details Defined in Data.Functor.Constant Methods liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Constant a a0) # liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Constant a a0] # liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Constant a a0) # liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Constant a a0] #
Show a => Show1 (Constant a :: * -> *)
Instance details Defined in Data.Functor.Constant Methods liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> Constant a a0 -> ShowS # liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [Constant a a0] -> ShowS #
Phantom (Constant a :: * -> *)
Instance details Defined in Lens.Family.Phantom Methods coerce :: Constant a a0 -> Constant a b
Eq a => Eq (Constant a b)
Instance details Defined in Data.Functor.Constant Methods (==) :: Constant a b -> Constant a b -> Bool # (/=) :: Constant a b -> Constant a b -> Bool #
Ord a => Ord (Constant a b)
Instance details Defined in Data.Functor.Constant Methods compare :: Constant a b -> Constant a b -> Ordering # (<) :: Constant a b -> Constant a b -> Bool # (<=) :: Constant a b -> Constant a b -> Bool # (>) :: Constant a b -> Constant a b -> Bool # (>=) :: Constant a b -> Constant a b -> Bool # max :: Constant a b -> Constant a b -> Constant a b # min :: Constant a b -> Constant a b -> Constant a b #
Read a => Read (Constant a b)
Instance details Defined in Data.Functor.Constant Methods readsPrec :: Int -> ReadS (Constant a b) # readList :: ReadS [Constant a b] # readPrec :: ReadPrec (Constant a b) # readListPrec :: ReadPrec [Constant a b] #
Show a => Show (Constant a b)
Instance details Defined in Data.Functor.Constant Methods showsPrec :: Int -> Constant a b -> ShowS # show :: Constant a b -> String # showList :: [Constant a b] -> ShowS #
Semigroup a => Semigroup (Constant a b)
Instance details Defined in Data.Functor.Constant Methods (<>) :: Constant a b -> Constant a b -> Constant a b # sconcat :: NonEmpty (Constant a b) -> Constant a b # stimes :: Integral b0 => b0 -> Constant a b -> Constant a b #
Monoid a => Monoid (Constant a b)
Instance details Defined in Data.Functor.Constant Methods mempty :: Constant a b # mappend :: Constant a b -> Constant a b -> Constant a b # mconcat :: [Constant a b] -> Constant a b #

type Setter a a' b b' = forall f. Identical f => LensLike f a a' b b' Source #

type Setter' a b = forall f. Identical f => LensLike' f a b Source #

class Applicative f => Identical (f :: * -> *) #

Minimal complete definition

extract

Instances

Identical Identity
Instance details Defined in Lens.Family.Identical Methods extract :: Identity a -> a
Identical f => Identical (Backwards f)
Instance details Defined in Lens.Family.Identical Methods extract :: Backwards f a -> a
(Identical f, Identical g) => Identical (Compose f g)
Instance details Defined in Lens.Family.Identical Methods extract :: Compose f g a -> a

data StateT s (m :: * -> *) a #

A state transformer monad parameterized by:

s - The state.
m - The inner monad.

The return function leaves the state unchanged, while >>= uses the final state of the first computation as the initial state of the second.

Instances

Monad m => MonadState s (StateT s m)
Instance details Defined in Control.Monad.State.Class Methods get :: StateT s m s # put :: s -> StateT s m () # state :: (s -> (a, s)) -> StateT s m a #
MonadTrans (StateT s)
Instance details Defined in Control.Monad.Trans.State.Strict Methods lift :: Monad m => m a -> StateT s m a #
Monad m => Monad (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods (>>=) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b # (>>) :: StateT s m a -> StateT s m b -> StateT s m b # return :: a -> StateT s m a # fail :: String -> StateT s m a #
Functor m => Functor (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods fmap :: (a -> b) -> StateT s m a -> StateT s m b # (<$) :: a -> StateT s m b -> StateT s m a #
MonadFix m => MonadFix (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods mfix :: (a -> StateT s m a) -> StateT s m a #
MonadFail m => MonadFail (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods fail :: String -> StateT s m a #
(Functor m, Monad m) => Applicative (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods pure :: a -> StateT s m a # (<>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b # liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c # (>) :: StateT s m a -> StateT s m b -> StateT s m b # (<*) :: StateT s m a -> StateT s m b -> StateT s m a #
MonadIO m => MonadIO (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods liftIO :: IO a -> StateT s m a #
(Functor m, MonadPlus m) => Alternative (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods empty :: StateT s m a # (<\|>) :: StateT s m a -> StateT s m a -> StateT s m a # some :: StateT s m a -> StateT s m [a] # many :: StateT s m a -> StateT s m [a] #
MonadPlus m => MonadPlus (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods mzero :: StateT s m a # mplus :: StateT s m a -> StateT s m a -> StateT s m a #

class Monad m => MonadState s (m :: * -> *) | m -> s #

Minimal definition is either both of get and put or just state

Minimal complete definition

state | get, put

Instances

MonadState s m => MonadState s (MaybeT m)
Instance details Defined in Control.Monad.State.Class Methods get :: MaybeT m s # put :: s -> MaybeT m () # state :: (s -> (a, s)) -> MaybeT m a #
MonadState s m => MonadState s (ListT m)
Instance details Defined in Control.Monad.State.Class Methods get :: ListT m s # put :: s -> ListT m () # state :: (s -> (a, s)) -> ListT m a #
(Monoid w, MonadState s m) => MonadState s (WriterT w m)
Instance details Defined in Control.Monad.State.Class Methods get :: WriterT w m s # put :: s -> WriterT w m () # state :: (s -> (a, s)) -> WriterT w m a #
(Monoid w, MonadState s m) => MonadState s (WriterT w m)
Instance details Defined in Control.Monad.State.Class Methods get :: WriterT w m s # put :: s -> WriterT w m () # state :: (s -> (a, s)) -> WriterT w m a #
Monad m => MonadState s (StateT s m)
Instance details Defined in Control.Monad.State.Class Methods get :: StateT s m s # put :: s -> StateT s m () # state :: (s -> (a, s)) -> StateT s m a #
Monad m => MonadState s (StateT s m)
Instance details Defined in Control.Monad.State.Class Methods get :: StateT s m s # put :: s -> StateT s m () # state :: (s -> (a, s)) -> StateT s m a #
MonadState s m => MonadState s (IdentityT m)
Instance details Defined in Control.Monad.State.Class Methods get :: IdentityT m s # put :: s -> IdentityT m () # state :: (s -> (a, s)) -> IdentityT m a #
MonadState s m => MonadState s (ExceptT e m)	Since: mtl-2.2
Instance details Defined in Control.Monad.State.Class Methods get :: ExceptT e m s # put :: s -> ExceptT e m () # state :: (s -> (a, s)) -> ExceptT e m a #
(Error e, MonadState s m) => MonadState s (ErrorT e m)
Instance details Defined in Control.Monad.State.Class Methods get :: ErrorT e m s # put :: s -> ErrorT e m () # state :: (s -> (a, s)) -> ErrorT e 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 #
MonadState s m => MonadState s (ContT r m)
Instance details Defined in Control.Monad.State.Class Methods get :: ContT r m s # put :: s -> ContT r m () # state :: (s -> (a, s)) -> ContT r m a #
(Monad m, Monoid w) => MonadState s (RWST r w s m)
Instance details Defined in Control.Monad.State.Class Methods get :: RWST r w s m s # put :: s -> RWST r w s m () # state :: (s -> (a, s)) -> RWST r w s m a #
(Monad m, Monoid w) => MonadState s (RWST r w s m)
Instance details Defined in Control.Monad.State.Class Methods get :: RWST r w s m s # put :: s -> RWST r w s m () # state :: (s -> (a, s)) -> RWST r w s m a #

type Writer w = WriterT w Identity #

A writer monad parameterized by the type w of output to accumulate.

The return function produces the output mempty, while >>= combines the outputs of the subcomputations using mappend.

class Semigroup a => Monoid a #

The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:

```
x <> mempty = x
```
```
mempty <> x = x
```
x <> (y <> z) = (x <> y) <> z (Semigroup law)
```
mconcat = foldr '(<>)' mempty
```

The method names refer to the monoid of lists under concatenation, but there are many other instances.

Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product.

NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.

Minimal complete definition

mempty

Instances

Monoid Ordering	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering # mappend :: Ordering -> Ordering -> Ordering # mconcat :: [Ordering] -> Ordering #
Monoid ()	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: () # mappend :: () -> () -> () # mconcat :: [()] -> () #
Monoid All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All # mappend :: All -> All -> All # mconcat :: [All] -> All #
Monoid Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any # mappend :: Any -> Any -> Any # mconcat :: [Any] -> Any #
Monoid IntSet
Instance details Defined in Data.IntSet.Internal Methods mempty :: IntSet # mappend :: IntSet -> IntSet -> IntSet # mconcat :: [IntSet] -> IntSet #
Monoid [a]	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: [a] # mappend :: [a] -> [a] -> [a] # mconcat :: [[a]] -> [a] #
Semigroup a => Monoid (Maybe a)	Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `ee = e` and `es = s = se` for all `s ∈ S`." Since 4.11.0: constraint on inner `a` value generalised from `Monoid` to `Semigroup`. Since: base-2.1*
Instance details Defined in GHC.Base Methods mempty :: Maybe a # mappend :: Maybe a -> Maybe a -> Maybe a # mconcat :: [Maybe a] -> Maybe a #
Monoid a => Monoid (IO a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mempty :: IO a # mappend :: IO a -> IO a -> IO a # mconcat :: [IO a] -> IO a #
Monoid a => Monoid (Identity a)
Instance details Defined in Data.Functor.Identity Methods mempty :: Identity a # mappend :: Identity a -> Identity a -> Identity a # mconcat :: [Identity a] -> Identity a #
Monoid (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: First a # mappend :: First a -> First a -> First a # mconcat :: [First a] -> First a #
Monoid (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: Last a # mappend :: Last a -> Last a -> Last a # mconcat :: [Last a] -> Last a #
Monoid a => Monoid (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a # mappend :: Dual a -> Dual a -> Dual a # mconcat :: [Dual a] -> Dual a #
Monoid (Endo a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a # mappend :: Endo a -> Endo a -> Endo a # mconcat :: [Endo a] -> Endo a #
Num a => Monoid (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a # mappend :: Sum a -> Sum a -> Sum a # mconcat :: [Sum a] -> Sum a #
Num a => Monoid (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a # mappend :: Product a -> Product a -> Product a # mconcat :: [Product a] -> Product a #
Monoid (IntMap a)
Instance details Defined in Data.IntMap.Internal Methods mempty :: IntMap a # mappend :: IntMap a -> IntMap a -> IntMap a # mconcat :: [IntMap a] -> IntMap a #
Ord a => Monoid (Set a)
Instance details Defined in Data.Set.Internal Methods mempty :: Set a # mappend :: Set a -> Set a -> Set a # mconcat :: [Set a] -> Set a #
Monoid (MergeSet a)
Instance details Defined in Data.Set.Internal Methods mempty :: MergeSet a # mappend :: MergeSet a -> MergeSet a -> MergeSet a # mconcat :: [MergeSet a] -> MergeSet a #
Monoid b => Monoid (a -> b)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: a -> b # mappend :: (a -> b) -> (a -> b) -> a -> b # mconcat :: [a -> b] -> a -> b #
(Monoid a, Monoid b) => Monoid (a, b)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b) # mappend :: (a, b) -> (a, b) -> (a, b) # mconcat :: [(a, b)] -> (a, b) #
Monoid (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods mempty :: Proxy s # mappend :: Proxy s -> Proxy s -> Proxy s # mconcat :: [Proxy s] -> Proxy s #
Ord k => Monoid (Map k v)
Instance details Defined in Data.Map.Internal Methods mempty :: Map k v # mappend :: Map k v -> Map k v -> Map k v # mconcat :: [Map k v] -> Map k v #
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c) # mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) # mconcat :: [(a, b, c)] -> (a, b, c) #
Monoid a => Monoid (Const a b)
Instance details Defined in Data.Functor.Const Methods mempty :: Const a b # mappend :: Const a b -> Const a b -> Const a b # mconcat :: [Const a b] -> Const a b #
Alternative f => Monoid (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Alt f a # mappend :: Alt f a -> Alt f a -> Alt f a # mconcat :: [Alt f a] -> Alt f a #
Monoid a => Monoid (Constant a b)
Instance details Defined in Data.Functor.Constant Methods mempty :: Constant a b # mappend :: Constant a b -> Constant a b -> Constant a b # mconcat :: [Constant a b] -> Constant a b #
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d) # mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # mconcat :: [(a, b, c, d)] -> (a, b, c, d) #
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d, e) # mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) #