Safe Haskell	Safe
Language	Haskell98

Lens.Family2

Contents

Lenses
Traversals
Documentation
Pseudo-imperatives
Types
Re-exports

Description

This is the main module for end-users of lens-families. If you are not building your own lenses or traversals, but just using functional references made by others, this is the only module you need.

Synopsis

Lenses

This module provides ^. for accessing fields and .~ and %~ for setting and modifying fields. Lenses are composed with . from the Prelude and id is the identity lens.

Lens composition in this library enjoys the following identities.

```
x^.l1.l2 === x^.l1^.l2
```
```
l1.l2 %~ f === l1 %~ l2 %~ f
```

The identity lens behaves as follows.

```
x^.id === x
```
```
id %~ f === f
```

The & operator, allows for a convenient way to sequence record updating:

record & l1 .~ value1 & l2 .~ value2

Lenses are implemented in van Laarhoven style. Lenses have type Functor f => (b -> f b) -> a -> f a and lens families have type Functor f => (b i -> f (b j)) -> a i -> f (a j).

Keep in mind that lenses and lens families can be used directly for functorial updates. For example, _2 id gives you strength.

_2 id :: Functor f => (a, f b) -> f (a, b)

Here is an example of code that uses the Maybe functor to preserves sharing during update when possible.

-- | 'sharedUpdate' returns the *identical* object if the update doesn't change anything.
-- This is useful for preserving sharing.
sharedUpdate :: Eq b => LensLike' Maybe a b -> (b -> b) -> a -> a
sharedUpdate l f a = fromMaybe a (l f' a)
 where
  f' b | fb == b  = Nothing
       | otherwise = Just fb
   where
    fb = f b

Traversals

^. can be used with traversals to access monoidal fields. The result will be a mconcat of all the fields referenced. The various fooOf functions can be used to access different monoidal summaries of some kinds of values.

^? can be used to access the first value of a traversal. Nothing is returned when the traversal has no references.

^.. can be used with a traversals and will return a list of all fields referenced.

When .~ is used with a traversal, all referenced fields will be set to the same value, and when %~ is used with a traversal, all referenced fields will be modified with the same function.

Like lenses, traversals can be composed with ., and because every lens is automatically a traversal, lenses and traversals can be composed with . yielding a traversal.

Traversals are implemented in van Laarhoven style. Traversals have type Applicative f => (b -> f b) -> a -> f a and traversal families have type Applicative f => (b i -> f (b j)) -> a i -> f (a j).

For stock lenses and traversals, see Lens.Family2.Stock.

To build your own lenses and traversals, see Lens.Family2.Unchecked.

References:

Documentation

to :: (a -> b) -> Getter a a' b b' Source #

to promotes a projection function to a read-only lens called a getter. To demote a lens to a projection function, use the section (^.l) or view l.

>>> (3 :+ 4, "example")^._1.to(abs)
5.0 :+ 0.0

view :: FoldLike b a a' b b' -> a -> b #

view :: Getter a a' b b' -> a -> b

Demote a lens or getter to a projection function.

view :: Monoid b => Fold a a' b b' -> a -> b

Returns the monoidal summary of a traversal or a fold.

(^.) :: a -> FoldLike b a a' b b' -> b infixl 8 #

(^.) :: a -> Getter a a' b b' -> b

Access the value referenced by a getter or lens.

(^.) :: Monoid b => a -> Fold a a' b b' -> b

Access the monoidal summary referenced by a getter or lens.

folding :: Foldable f => (a -> f b) -> Fold a a' b b' Source #

folding promotes a "toList" function to a read-only traversal called a fold.

To demote a traversal or fold to a "toList" function use the section (^..l) or toListOf l.

views :: FoldLike r a a' b b' -> (b -> r) -> a -> r #

views :: Monoid r => Fold a a' b b' -> (b -> r) -> a -> r

Given a fold or traversal, return the foldMap of all the values using the given function.

views :: Getter a a' b b' -> (b -> r) -> a -> r

views is not particularly useful for getters or lenses, but given a getter or lens, it returns the referenced value passed through the given function.

views l f a = f (view l a)

(^..) :: a -> Fold a a' b b' -> [b] infixl 8 Source #

Returns a list of all of the referenced values in order.

(^?) :: a -> Fold a a' b b' -> Maybe b infixl 8 Source #

Returns Just the first referenced value. Returns Nothing if there are no referenced values.

toListOf :: Fold a a' b b' -> a -> [b] Source #

Returns a list of all of the referenced values in order.

allOf :: Fold a a' b b' -> (b -> Bool) -> a -> Bool Source #

Returns true if all of the referenced values satisfy the given predicate.

anyOf :: Fold a a' b b' -> (b -> Bool) -> a -> Bool Source #

Returns true if any of the referenced values satisfy the given predicate.

firstOf :: Fold a a' b b' -> a -> Maybe b Source #

Returns Just the first referenced value. Returns Nothing if there are no referenced values. See ^? for an infix version of firstOf

lastOf :: Fold a a' b b' -> a -> Maybe b Source #

Returns Just the last referenced value. Returns Nothing if there are no referenced values.

sumOf :: Num b => Fold a a' b b' -> a -> b Source #

Returns the sum of all the referenced values.

productOf :: Num b => Fold a a' b b' -> a -> b Source #

Returns the product of all the referenced values.

lengthOf :: Num r => Fold a a' b b' -> a -> r Source #

Counts the number of references in a traversal or fold for the input.

nullOf :: Fold a a' b b' -> a -> Bool Source #

Returns true if the number of references in the input is zero.

backwards :: LensLike (Backwards * f) a a' b b' -> LensLike f a a' b b' #

backwards :: Traversal a a' b b' -> Traversal a a' b b'
backwards :: Fold a a' b b' -> Fold a a' b b'

Given a traversal or fold, reverse the order that elements are traversed.

backwards :: Lens a a' b b' -> Lens a a' b b'
backwards :: Getter a a' b b' -> Getter a a' b b'
backwards :: Setter a a' b b' -> Setter a a' b b'

No effect on lenses, getters or setters.

over :: Setter a a' b b' -> (b -> b') -> a -> a' Source #

Demote a setter to a semantic editor combinator.

(%~) :: Setter a a' b b' -> (b -> b') -> a -> a' infixr 4 Source #

Modify all referenced fields.

set :: Setter a a' b b' -> b' -> a -> a' Source #

Set all referenced fields to the given value.

(.~) :: Setter a a' b b' -> b' -> a -> a' infixr 4 Source #

Set all referenced fields to the given value.

(&) :: a -> (a -> b) -> b infixl 1 #

A flipped version of ($).

Pseudo-imperatives

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

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

(-~) :: Num b => Setter' a b -> b -> a -> a infixr 4 Source #

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

(&&~) :: Setter' a Bool -> Bool -> a -> a infixr 4 Source #

(||~) :: Setter' a Bool -> Bool -> a -> a infixr 4 Source #

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

Monoidally append a value to all referenced fields.

Types

type Lens a a' b b' = forall f. Functor f => LensLike f a a' b b' Source #

type Lens' a b = forall f. Functor f => LensLike' f a b Source #

type Traversal a a' b b' = forall f. Applicative f => LensLike f a a' b b' Source #

type Traversal' a b = forall f. Applicative f => LensLike' f a b Source #

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 #

type Getter a a' b b' = forall f. Phantom f => LensLike f a a' b b' Source #

type Getter' a b = forall f. Phantom f => LensLike' f a b Source #

type Fold a a' b b' = forall f. (Phantom f, Applicative f) => LensLike f a a' b b' Source #

type Fold' a b = forall f. (Phantom f, Applicative f) => LensLike' f a b Source #

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' #

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

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

Constant functor.

Instances

Eq2 (Constant *)
Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Constant * a c -> Constant * b d -> Bool #
Ord2 (Constant *)
Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Constant * a c -> Constant * b d -> Ordering #
Read2 (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] #
Show2 (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 #
Bifunctor (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 #
Functor (Constant * a)
Methods fmap :: (a -> b) -> Constant * a a -> Constant * a b # (<$) :: a -> Constant * a b -> Constant * a a #
Monoid a => Applicative (Constant * a)
Methods pure :: a -> Constant * a a # (<>) :: Constant a (a -> b) -> Constant * a a -> Constant * a b # (>) :: Constant a a -> Constant * a b -> Constant * a b # (<) :: Constant a a -> Constant * a b -> Constant * a a #
Foldable (Constant * a)
Methods fold :: Monoid m => Constant * a m -> m # foldMap :: Monoid m => (a -> m) -> Constant * a a -> m # foldr :: (a -> b -> b) -> b -> Constant * a a -> b # foldr' :: (a -> b -> b) -> b -> Constant * a a -> b # foldl :: (b -> a -> b) -> b -> Constant * a a -> b # foldl' :: (b -> a -> b) -> b -> Constant * a a -> b # foldr1 :: (a -> a -> a) -> Constant * a a -> a # foldl1 :: (a -> a -> a) -> Constant * a a -> a # toList :: Constant * a a -> [a] # null :: Constant * a a -> Bool # length :: Constant * a a -> Int # elem :: Eq a => a -> Constant * a a -> Bool # maximum :: Ord a => Constant * a a -> a # minimum :: Ord a => Constant * a a -> a # sum :: Num a => Constant * a a -> a # product :: Num a => Constant * a a -> a #
Traversable (Constant * a)
Methods traverse :: Applicative f => (a -> f b) -> Constant * a a -> f (Constant * a b) # sequenceA :: Applicative f => Constant * a (f a) -> f (Constant * a a) # mapM :: Monad m => (a -> m b) -> Constant * a a -> m (Constant * a b) # sequence :: Monad m => Constant * a (m a) -> m (Constant * a a) #
Eq a => Eq1 (Constant * a)
Methods liftEq :: (a -> b -> Bool) -> Constant * a a -> Constant * a b -> Bool #
Ord a => Ord1 (Constant * a)
Methods liftCompare :: (a -> b -> Ordering) -> Constant * a a -> Constant * a b -> Ordering #
Read a => Read1 (Constant * a)
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Constant * a a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Constant * a a] #
Show a => Show1 (Constant * a)
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Constant * a a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Constant * a a] -> ShowS #
Phantom (Constant * a)
Methods coerce :: Constant * a a -> Constant * a b
Eq a => Eq (Constant k a b)
Methods (==) :: Constant k a b -> Constant k a b -> Bool # (/=) :: Constant k a b -> Constant k a b -> Bool #
Ord a => Ord (Constant k a b)
Methods compare :: Constant k a b -> Constant k a b -> Ordering # (<) :: Constant k a b -> Constant k a b -> Bool # (<=) :: Constant k a b -> Constant k a b -> Bool # (>) :: Constant k a b -> Constant k a b -> Bool # (>=) :: Constant k a b -> Constant k a b -> Bool # max :: Constant k a b -> Constant k a b -> Constant k a b # min :: Constant k a b -> Constant k a b -> Constant k a b #
Read a => Read (Constant k a b)
Methods readsPrec :: Int -> ReadS (Constant k a b) # readList :: ReadS [Constant k a b] # readPrec :: ReadPrec (Constant k a b) # readListPrec :: ReadPrec [Constant k a b] #
Show a => Show (Constant k a b)
Methods showsPrec :: Int -> Constant k a b -> ShowS # show :: Constant k a b -> String # showList :: [Constant k a b] -> ShowS #
Monoid a => Monoid (Constant k a b)
Methods mempty :: Constant k a b # mappend :: Constant k a b -> Constant k a b -> Constant k a b # mconcat :: [Constant k a b] -> Constant k a b #

class Functor f => Phantom f #

Minimal complete definition

coerce

Instances

Phantom (Const * a)
Methods coerce :: Const * a a -> Const * a b
Phantom f => Phantom (AlongsideLeft f a)
Methods coerce :: AlongsideLeft f a a -> AlongsideLeft f a b
Phantom f => Phantom (AlongsideRight f a)
Methods coerce :: AlongsideRight f a a -> AlongsideRight f a b
Phantom (Constant * a)
Methods coerce :: Constant * a a -> Constant * a b
Phantom f => Phantom (Backwards * f)
Methods coerce :: Backwards * f a -> Backwards * f b
(Phantom f, Functor g) => Phantom (Compose * * f g)
Methods coerce :: Compose * * f g a -> Compose * * f g b

class Applicative f => Identical f #

Minimal complete definition

extract

Instances

Identical Identity
Methods extract :: Identity a -> a
Identical f => Identical (Backwards * f)
Methods extract :: Backwards * f a -> a
(Identical f, Identical g) => Identical (Compose * * f g)
Methods extract :: Compose * * f g a -> a

Re-exports

class Functor f => Applicative f #

A functor with application, providing operations to

embed pure expressions (pure), and
sequence computations and combine their results (<*>).

A minimal complete definition must include implementations of these functions satisfying the following laws:

identity

pure id <*> v = v

composition

pure (.) <*> u <*> v <*> w = u <*> (v <*> w)

homomorphism

pure f <*> pure x = pure (f x)

interchange

u <*> pure y = pure ($ y) <*> u

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

```
u *> v = pure (const id) <*> u <*> v
```
```
u <* v = pure const <*> u <*> v
```

As a consequence of these laws, the Functor instance for f will satisfy

```
fmap f x = pure f <*> x
```

If f is also a Monad, it should satisfy

```
pure = return
```
```
(<*>) = ap
```

(which implies that pure and <*> satisfy the applicative functor laws).

Minimal complete definition

pure, (<*>)

Instances

Applicative []
Methods pure :: a -> [a] # (<>) :: [a -> b] -> [a] -> [b] # (>) :: [a] -> [b] -> [b] # (<*) :: [a] -> [b] -> [a] #
Applicative Maybe
Methods pure :: a -> Maybe a # (<>) :: Maybe (a -> b) -> Maybe a -> Maybe b # (>) :: Maybe a -> Maybe b -> Maybe b # (<*) :: Maybe a -> Maybe b -> Maybe a #
Applicative IO
Methods pure :: a -> IO a # (<>) :: IO (a -> b) -> IO a -> IO b # (>) :: IO a -> IO b -> IO b # (<*) :: IO a -> IO b -> IO a #
Applicative U1
Methods pure :: a -> U1 a # (<>) :: U1 (a -> b) -> U1 a -> U1 b # (>) :: U1 a -> U1 b -> U1 b # (<*) :: U1 a -> U1 b -> U1 a #
Applicative Par1
Methods pure :: a -> Par1 a # (<>) :: Par1 (a -> b) -> Par1 a -> Par1 b # (>) :: Par1 a -> Par1 b -> Par1 b # (<*) :: Par1 a -> Par1 b -> Par1 a #
Applicative Identity
Methods pure :: a -> Identity a # (<>) :: Identity (a -> b) -> Identity a -> Identity b # (>) :: Identity a -> Identity b -> Identity b # (<*) :: Identity a -> Identity b -> Identity a #
Applicative ZipList
Methods pure :: a -> ZipList a # (<>) :: ZipList (a -> b) -> ZipList a -> ZipList b # (>) :: ZipList a -> ZipList b -> ZipList b # (<*) :: ZipList a -> ZipList b -> ZipList a #
Applicative Dual
Methods pure :: a -> Dual a # (<>) :: Dual (a -> b) -> Dual a -> Dual b # (>) :: Dual a -> Dual b -> Dual b # (<*) :: Dual a -> Dual b -> Dual a #
Applicative Sum
Methods pure :: a -> Sum a # (<>) :: Sum (a -> b) -> Sum a -> Sum b # (>) :: Sum a -> Sum b -> Sum b # (<*) :: Sum a -> Sum b -> Sum a #
Applicative Product
Methods pure :: a -> Product a # (<>) :: Product (a -> b) -> Product a -> Product b # (>) :: Product a -> Product b -> Product b # (<*) :: Product a -> Product b -> Product a #
Applicative First
Methods pure :: a -> First a # (<>) :: First (a -> b) -> First a -> First b # (>) :: First a -> First b -> First b # (<*) :: First a -> First b -> First a #
Applicative Last
Methods pure :: a -> Last a # (<>) :: Last (a -> b) -> Last a -> Last b # (>) :: Last a -> Last b -> Last b # (<*) :: Last a -> Last b -> Last a #
Applicative ((->) a)
Methods pure :: a -> a -> a # (<>) :: (a -> a -> b) -> (a -> a) -> a -> b # (>) :: (a -> a) -> (a -> b) -> a -> b # (<*) :: (a -> a) -> (a -> b) -> a -> a #
Applicative (Either e)
Methods pure :: a -> Either e a # (<>) :: Either e (a -> b) -> Either e a -> Either e b # (>) :: Either e a -> Either e b -> Either e b # (<*) :: Either e a -> Either e b -> Either e a #
Applicative f => Applicative (Rec1 f)
Methods pure :: a -> Rec1 f a # (<>) :: Rec1 f (a -> b) -> Rec1 f a -> Rec1 f b # (>) :: Rec1 f a -> Rec1 f b -> Rec1 f b # (<*) :: Rec1 f a -> Rec1 f b -> Rec1 f a #
Monoid a => Applicative ((,) a)
Methods pure :: a -> (a, a) # (<>) :: (a, a -> b) -> (a, a) -> (a, b) # (>) :: (a, a) -> (a, b) -> (a, b) # (<*) :: (a, a) -> (a, b) -> (a, a) #
Monad m => Applicative (WrappedMonad m)
Methods pure :: a -> WrappedMonad m a # (<>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b # (>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a #
Applicative (Proxy *)
Methods pure :: a -> Proxy * a # (<>) :: Proxy (a -> b) -> Proxy * a -> Proxy * b # (>) :: Proxy a -> Proxy * b -> Proxy * b # (<) :: Proxy a -> Proxy * b -> Proxy * a #
Applicative m => Applicative (ListT m)
Methods pure :: a -> ListT m a # (<>) :: ListT m (a -> b) -> ListT m a -> ListT m b # (>) :: ListT m a -> ListT m b -> ListT m b # (<*) :: ListT m a -> ListT m b -> ListT m a #
(Functor m, Monad m) => Applicative (MaybeT m)
Methods pure :: a -> MaybeT m a # (<>) :: MaybeT m (a -> b) -> MaybeT m a -> MaybeT m b # (>) :: MaybeT m a -> MaybeT m b -> MaybeT m b # (<*) :: MaybeT m a -> MaybeT m b -> MaybeT m a #
(Applicative f, Applicative g) => Applicative ((:*:) f g)
Methods pure :: a -> (f :: g) a # (<>) :: (f :: g) (a -> b) -> (f :: g) a -> (f :: g) b # (>) :: (f :: g) a -> (f :: g) b -> (f :: g) b # (<) :: (f :: g) a -> (f :: g) b -> (f :*: g) a #
(Applicative f, Applicative g) => Applicative ((:.:) f g)
Methods pure :: a -> (f :.: g) a # (<>) :: (f :.: g) (a -> b) -> (f :.: g) a -> (f :.: g) b # (>) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) b # (<*) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) a #
Arrow a => Applicative (WrappedArrow a b)
Methods pure :: a -> WrappedArrow a b a # (<>) :: WrappedArrow a b (a -> b) -> WrappedArrow a b a -> WrappedArrow a b b # (>) :: WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b b # (<*) :: WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b a #
Applicative f => Applicative (Alt * f)
Methods pure :: a -> Alt * f a # (<>) :: Alt f (a -> b) -> Alt * f a -> Alt * f b # (>) :: Alt f a -> Alt * f b -> Alt * f b # (<) :: Alt f a -> Alt * f b -> Alt * f a #
(Applicative f, Monad f) => Applicative (WhenMissing f x)	Equivalent to `ReaderT k (ReaderT x (MaybeT f))`.
Methods pure :: a -> WhenMissing f x a # (<>) :: WhenMissing f x (a -> b) -> WhenMissing f x a -> WhenMissing f x b # (>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b # (<*) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x a #
(Monoid c, Monad m) => Applicative (Zooming m c)
Methods pure :: a -> Zooming m c a # (<>) :: Zooming m c (a -> b) -> Zooming m c a -> Zooming m c b # (>) :: Zooming m c a -> Zooming m c b -> Zooming m c b # (<*) :: Zooming m c a -> Zooming m c b -> Zooming m c a #
Monoid a => Applicative (Constant * a)
Methods pure :: a -> Constant * a a # (<>) :: Constant a (a -> b) -> Constant * a a -> Constant * a b # (>) :: Constant a a -> Constant * a b -> Constant * a b # (<) :: Constant a a -> Constant * a b -> Constant * a a #
(Functor m, Monad m) => Applicative (StateT s m)
Methods pure :: a -> StateT s m a # (<>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b # (>) :: StateT s m a -> StateT s m b -> StateT s m b # (<*) :: StateT s m a -> StateT s m b -> StateT s m a #
(Functor m, Monad m) => Applicative (StateT s m)
Methods pure :: a -> StateT s m a # (<>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b # (>) :: StateT s m a -> StateT s m b -> StateT s m b # (<*) :: StateT s m a -> StateT s m b -> StateT s m a #
Applicative f => Applicative (Backwards * f)	Apply `f`-actions in the reverse order.
Methods pure :: a -> Backwards * f a # (<>) :: Backwards f (a -> b) -> Backwards * f a -> Backwards * f b # (>) :: Backwards f a -> Backwards * f b -> Backwards * f b # (<) :: Backwards f a -> Backwards * f b -> Backwards * f a #
(Functor m, Monad m) => Applicative (ErrorT e m)
Methods pure :: a -> ErrorT e m a # (<>) :: ErrorT e m (a -> b) -> ErrorT e m a -> ErrorT e m b # (>) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m b # (<*) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m a #
(Functor m, Monad m) => Applicative (ExceptT e m)
Methods pure :: a -> ExceptT e m a # (<>) :: ExceptT e m (a -> b) -> ExceptT e m a -> ExceptT e m b # (>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b # (<*) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m a #
(Monoid w, Applicative m) => Applicative (WriterT w m)
Methods pure :: a -> WriterT w m a # (<>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b # (>) :: WriterT w m a -> WriterT w m b -> WriterT w m b # (<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a #
(Monoid w, Applicative m) => Applicative (WriterT w m)
Methods pure :: a -> WriterT w m a # (<>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b # (>) :: WriterT w m a -> WriterT w m b -> WriterT w m b # (<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a #
Applicative m => Applicative (IdentityT * m)
Methods pure :: a -> IdentityT * m a # (<>) :: IdentityT m (a -> b) -> IdentityT * m a -> IdentityT * m b # (>) :: IdentityT m a -> IdentityT * m b -> IdentityT * m b # (<) :: IdentityT m a -> IdentityT * m b -> IdentityT * m a #
Applicative f => Applicative (M1 i c f)
Methods pure :: a -> M1 i c f a # (<>) :: M1 i c f (a -> b) -> M1 i c f a -> M1 i c f b # (>) :: M1 i c f a -> M1 i c f b -> M1 i c f b # (<*) :: M1 i c f a -> M1 i c f b -> M1 i c f a #
(Monad f, Applicative f) => Applicative (WhenMatched f x y)	Equivalent to `ReaderT Key (ReaderT x (ReaderT y (MaybeT f)))`
Methods pure :: a -> WhenMatched f x y a # (<>) :: WhenMatched f x y (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b # (>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b # (<*) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y a #
(Applicative f, Monad f) => Applicative (WhenMissing f k x)	Equivalent to `ReaderT k (ReaderT x (MaybeT f))` .
Methods pure :: a -> WhenMissing f k x a # (<>) :: WhenMissing f k x (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b # (>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b # (<*) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x a #
Applicative (ContT k r m)
Methods pure :: a -> ContT k r m a # (<>) :: ContT k r m (a -> b) -> ContT k r m a -> ContT k r m b # (>) :: ContT k r m a -> ContT k r m b -> ContT k r m b # (<*) :: ContT k r m a -> ContT k r m b -> ContT k r m a #
Applicative m => Applicative (ReaderT * r m)
Methods pure :: a -> ReaderT * r m a # (<>) :: ReaderT r m (a -> b) -> ReaderT * r m a -> ReaderT * r m b # (>) :: ReaderT r m a -> ReaderT * r m b -> ReaderT * r m b # (<) :: ReaderT r m a -> ReaderT * r m b -> ReaderT * r m a #
(Monad f, Applicative f) => Applicative (WhenMatched f k x y)	Equivalent to `ReaderT k (ReaderT x (ReaderT y (MaybeT f)))`
Methods pure :: a -> WhenMatched f k x y a # (<>) :: WhenMatched f k x y (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b # (>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b # (<*) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y a #
(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m)
Methods pure :: a -> RWST r w s m a # (<>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b # (>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b # (<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a #
(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m)
Methods pure :: a -> RWST r w s m a # (<>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b # (>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b # (<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a #

class Foldable t #

Data structures that can be folded.

For example, given a data type

data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be

instance Foldable Tree where
   foldMap f Empty = mempty
   foldMap f (Leaf x) = f x
   foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r

This is suitable even for abstract types, as the monoid is assumed to satisfy the monoid laws. Alternatively, one could define foldr:

instance Foldable Tree where
   foldr f z Empty = z
   foldr f z (Leaf x) = f x z
   foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l

Foldable instances are expected to satisfy the following laws:

foldr f z t = appEndo (foldMap (Endo . f) t ) z

foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z

fold = foldMap id

sum, product, maximum, and minimum should all be essentially equivalent to foldMap forms, such as

sum = getSum . foldMap Sum

but may be less defined.

If the type is also a Functor instance, it should satisfy

foldMap f = fold . fmap f

which implies that

foldMap f . fmap g = foldMap (f . g)

Minimal complete definition

foldMap | foldr

Instances

Foldable []
Methods fold :: Monoid m => [m] -> m # foldMap :: Monoid m => (a -> m) -> [a] -> m # foldr :: (a -> b -> b) -> b -> [a] -> b # foldr' :: (a -> b -> b) -> b -> [a] -> b # foldl :: (b -> a -> b) -> b -> [a] -> b # foldl' :: (b -> a -> b) -> b -> [a] -> b # foldr1 :: (a -> a -> a) -> [a] -> a # foldl1 :: (a -> a -> a) -> [a] -> a # toList :: [a] -> [a] # null :: [a] -> Bool # length :: [a] -> Int # elem :: Eq a => a -> [a] -> Bool # maximum :: Ord a => [a] -> a # minimum :: Ord a => [a] -> a # sum :: Num a => [a] -> a # product :: Num a => [a] -> a #
Foldable Maybe
Methods fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> m # foldr :: (a -> b -> b) -> b -> Maybe a -> b # foldr' :: (a -> b -> b) -> b -> Maybe a -> b # foldl :: (b -> a -> b) -> b -> Maybe a -> b # foldl' :: (b -> a -> b) -> b -> Maybe a -> b # foldr1 :: (a -> a -> a) -> Maybe a -> a # foldl1 :: (a -> a -> a) -> Maybe a -> a # toList :: Maybe a -> [a] # null :: Maybe a -> Bool # length :: Maybe a -> Int # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # sum :: Num a => Maybe a -> a # product :: Num a => Maybe a -> a #
Foldable V1
Methods fold :: Monoid m => V1 m -> m # foldMap :: Monoid m => (a -> m) -> V1 a -> m # foldr :: (a -> b -> b) -> b -> V1 a -> b # foldr' :: (a -> b -> b) -> b -> V1 a -> b # foldl :: (b -> a -> b) -> b -> V1 a -> b # foldl' :: (b -> a -> b) -> b -> V1 a -> b # foldr1 :: (a -> a -> a) -> V1 a -> a # foldl1 :: (a -> a -> a) -> V1 a -> a # toList :: V1 a -> [a] # null :: V1 a -> Bool # length :: V1 a -> Int # elem :: Eq a => a -> V1 a -> Bool # maximum :: Ord a => V1 a -> a # minimum :: Ord a => V1 a -> a # sum :: Num a => V1 a -> a # product :: Num a => V1 a -> a #
Foldable U1
Methods fold :: Monoid m => U1 m -> m # foldMap :: Monoid m => (a -> m) -> U1 a -> m # foldr :: (a -> b -> b) -> b -> U1 a -> b # foldr' :: (a -> b -> b) -> b -> U1 a -> b # foldl :: (b -> a -> b) -> b -> U1 a -> b # foldl' :: (b -> a -> b) -> b -> U1 a -> b # foldr1 :: (a -> a -> a) -> U1 a -> a # foldl1 :: (a -> a -> a) -> U1 a -> a # toList :: U1 a -> [a] # null :: U1 a -> Bool # length :: U1 a -> Int # elem :: Eq a => a -> U1 a -> Bool # maximum :: Ord a => U1 a -> a # minimum :: Ord a => U1 a -> a # sum :: Num a => U1 a -> a # product :: Num a => U1 a -> a #
Foldable Par1
Methods fold :: Monoid m => Par1 m -> m # foldMap :: Monoid m => (a -> m) -> Par1 a -> m # foldr :: (a -> b -> b) -> b -> Par1 a -> b # foldr' :: (a -> b -> b) -> b -> Par1 a -> b # foldl :: (b -> a -> b) -> b -> Par1 a -> b # foldl' :: (b -> a -> b) -> b -> Par1 a -> b # foldr1 :: (a -> a -> a) -> Par1 a -> a # foldl1 :: (a -> a -> a) -> Par1 a -> a # toList :: Par1 a -> [a] # null :: Par1 a -> Bool # length :: Par1 a -> Int # elem :: Eq a => a -> Par1 a -> Bool # maximum :: Ord a => Par1 a -> a # minimum :: Ord a => Par1 a -> a # sum :: Num a => Par1 a -> a # product :: Num a => Par1 a -> a #
Foldable Identity
Methods fold :: Monoid m => Identity m -> m # foldMap :: Monoid m => (a -> m) -> Identity a -> m # foldr :: (a -> b -> b) -> b -> Identity a -> b # foldr' :: (a -> b -> b) -> b -> Identity a -> b # foldl :: (b -> a -> b) -> b -> Identity a -> b # foldl' :: (b -> a -> b) -> b -> Identity a -> b # foldr1 :: (a -> a -> a) -> Identity a -> a # foldl1 :: (a -> a -> a) -> Identity a -> a # toList :: Identity a -> [a] # null :: Identity a -> Bool # length :: Identity a -> Int # elem :: Eq a => a -> Identity a -> Bool # maximum :: Ord a => Identity a -> a # minimum :: Ord a => Identity a -> a # sum :: Num a => Identity a -> a # product :: Num a => Identity a -> a #
Foldable ZipList
Methods fold :: Monoid m => ZipList m -> m # foldMap :: Monoid m => (a -> m) -> ZipList a -> m # foldr :: (a -> b -> b) -> b -> ZipList a -> b # foldr' :: (a -> b -> b) -> b -> ZipList a -> b # foldl :: (b -> a -> b) -> b -> ZipList a -> b # foldl' :: (b -> a -> b) -> b -> ZipList a -> b # foldr1 :: (a -> a -> a) -> ZipList a -> a # foldl1 :: (a -> a -> a) -> ZipList a -> a # toList :: ZipList a -> [a] # null :: ZipList a -> Bool # length :: ZipList a -> Int # elem :: Eq a => a -> ZipList a -> Bool # maximum :: Ord a => ZipList a -> a # minimum :: Ord a => ZipList a -> a # sum :: Num a => ZipList a -> a # product :: Num a => ZipList a -> a #
Foldable Dual
Methods fold :: Monoid m => Dual m -> m # foldMap :: Monoid m => (a -> m) -> Dual a -> m # foldr :: (a -> b -> b) -> b -> Dual a -> b # foldr' :: (a -> b -> b) -> b -> Dual a -> b # foldl :: (b -> a -> b) -> b -> Dual a -> b # foldl' :: (b -> a -> b) -> b -> Dual a -> b # foldr1 :: (a -> a -> a) -> Dual a -> a # foldl1 :: (a -> a -> a) -> Dual a -> a # toList :: Dual a -> [a] # null :: Dual a -> Bool # length :: Dual a -> Int # elem :: Eq a => a -> Dual a -> Bool # maximum :: Ord a => Dual a -> a # minimum :: Ord a => Dual a -> a # sum :: Num a => Dual a -> a # product :: Num a => Dual a -> a #
Foldable Sum
Methods fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> m # foldr :: (a -> b -> b) -> b -> Sum a -> b # foldr' :: (a -> b -> b) -> b -> Sum a -> b # foldl :: (b -> a -> b) -> b -> Sum a -> b # foldl' :: (b -> a -> b) -> b -> Sum a -> b # foldr1 :: (a -> a -> a) -> Sum a -> a # foldl1 :: (a -> a -> a) -> Sum a -> a # toList :: Sum a -> [a] # null :: Sum a -> Bool # length :: Sum a -> Int # elem :: Eq a => a -> Sum a -> Bool # maximum :: Ord a => Sum a -> a # minimum :: Ord a => Sum a -> a # sum :: Num a => Sum a -> a # product :: Num a => Sum a -> a #
Foldable Product
Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # toList :: Product a -> [a] # null :: Product a -> Bool # length :: Product a -> Int # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # sum :: Num a => Product a -> a # product :: Num a => Product a -> a #
Foldable First
Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # toList :: First a -> [a] # null :: First a -> Bool # length :: First a -> Int # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # sum :: Num a => First a -> a # product :: Num a => First a -> a #
Foldable Last
Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # toList :: Last a -> [a] # null :: Last a -> Bool # length :: Last a -> Int # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # minimum :: Ord a => Last a -> a # sum :: Num a => Last a -> a # product :: Num a => Last a -> a #
Foldable IntMap
Methods fold :: Monoid m => IntMap m -> m # foldMap :: Monoid m => (a -> m) -> IntMap a -> m # foldr :: (a -> b -> b) -> b -> IntMap a -> b # foldr' :: (a -> b -> b) -> b -> IntMap a -> b # foldl :: (b -> a -> b) -> b -> IntMap a -> b # foldl' :: (b -> a -> b) -> b -> IntMap a -> b # foldr1 :: (a -> a -> a) -> IntMap a -> a # foldl1 :: (a -> a -> a) -> IntMap a -> a # toList :: IntMap a -> [a] # null :: IntMap a -> Bool # length :: IntMap a -> Int # elem :: Eq a => a -> IntMap a -> Bool # maximum :: Ord a => IntMap a -> a # minimum :: Ord a => IntMap a -> a # sum :: Num a => IntMap a -> a # product :: Num a => IntMap a -> a #
Foldable Set
Methods fold :: Monoid m => Set m -> m # foldMap :: Monoid m => (a -> m) -> Set a -> m # foldr :: (a -> b -> b) -> b -> Set a -> b # foldr' :: (a -> b -> b) -> b -> Set a -> b # foldl :: (b -> a -> b) -> b -> Set a -> b # foldl' :: (b -> a -> b) -> b -> Set a -> b # foldr1 :: (a -> a -> a) -> Set a -> a # foldl1 :: (a -> a -> a) -> Set a -> a # toList :: Set a -> [a] # null :: Set a -> Bool # length :: Set a -> Int # elem :: Eq a => a -> Set a -> Bool # maximum :: Ord a => Set a -> a # minimum :: Ord a => Set a -> a # sum :: Num a => Set a -> a # product :: Num a => Set a -> a #
Foldable (Either a)
Methods fold :: Monoid m => Either a m -> m # foldMap :: Monoid m => (a -> m) -> Either a a -> m # foldr :: (a -> b -> b) -> b -> Either a a -> b # foldr' :: (a -> b -> b) -> b -> Either a a -> b # foldl :: (b -> a -> b) -> b -> Either a a -> b # foldl' :: (b -> a -> b) -> b -> Either a a -> b # foldr1 :: (a -> a -> a) -> Either a a -> a # foldl1 :: (a -> a -> a) -> Either a a -> a # toList :: Either a a -> [a] # null :: Either a a -> Bool # length :: Either a a -> Int # elem :: Eq a => a -> Either a a -> Bool # maximum :: Ord a => Either a a -> a # minimum :: Ord a => Either a a -> a # sum :: Num a => Either a a -> a # product :: Num a => Either a a -> a #
Foldable f => Foldable (Rec1 f)
Methods fold :: Monoid m => Rec1 f m -> m # foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m # foldr :: (a -> b -> b) -> b -> Rec1 f a -> b # foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b # foldl :: (b -> a -> b) -> b -> Rec1 f a -> b # foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b # foldr1 :: (a -> a -> a) -> Rec1 f a -> a # foldl1 :: (a -> a -> a) -> Rec1 f a -> a # toList :: Rec1 f a -> [a] # null :: Rec1 f a -> Bool # length :: Rec1 f a -> Int # elem :: Eq a => a -> Rec1 f a -> Bool # maximum :: Ord a => Rec1 f a -> a # minimum :: Ord a => Rec1 f a -> a # sum :: Num a => Rec1 f a -> a # product :: Num a => Rec1 f a -> a #
Foldable (URec Char)
Methods fold :: Monoid m => URec Char m -> m # foldMap :: Monoid m => (a -> m) -> URec Char a -> m # foldr :: (a -> b -> b) -> b -> URec Char a -> b # foldr' :: (a -> b -> b) -> b -> URec Char a -> b # foldl :: (b -> a -> b) -> b -> URec Char a -> b # foldl' :: (b -> a -> b) -> b -> URec Char a -> b # foldr1 :: (a -> a -> a) -> URec Char a -> a # foldl1 :: (a -> a -> a) -> URec Char a -> a # toList :: URec Char a -> [a] # null :: URec Char a -> Bool # length :: URec Char a -> Int # elem :: Eq a => a -> URec Char a -> Bool # maximum :: Ord a => URec Char a -> a # minimum :: Ord a => URec Char a -> a # sum :: Num a => URec Char a -> a # product :: Num a => URec Char a -> a #
Foldable (URec Double)
Methods fold :: Monoid m => URec Double m -> m # foldMap :: Monoid m => (a -> m) -> URec Double a -> m # foldr :: (a -> b -> b) -> b -> URec Double a -> b # foldr' :: (a -> b -> b) -> b -> URec Double a -> b # foldl :: (b -> a -> b) -> b -> URec Double a -> b # foldl' :: (b -> a -> b) -> b -> URec Double a -> b # foldr1 :: (a -> a -> a) -> URec Double a -> a # foldl1 :: (a -> a -> a) -> URec Double a -> a # toList :: URec Double a -> [a] # null :: URec Double a -> Bool # length :: URec Double a -> Int # elem :: Eq a => a -> URec Double a -> Bool # maximum :: Ord a => URec Double a -> a # minimum :: Ord a => URec Double a -> a # sum :: Num a => URec Double a -> a # product :: Num a => URec Double a -> a #
Foldable (URec Float)
Methods fold :: Monoid m => URec Float m -> m # foldMap :: Monoid m => (a -> m) -> URec Float a -> m # foldr :: (a -> b -> b) -> b -> URec Float a -> b # foldr' :: (a -> b -> b) -> b -> URec Float a -> b # foldl :: (b -> a -> b) -> b -> URec Float a -> b # foldl' :: (b -> a -> b) -> b -> URec Float a -> b # foldr1 :: (a -> a -> a) -> URec Float a -> a # foldl1 :: (a -> a -> a) -> URec Float a -> a # toList :: URec Float a -> [a] # null :: URec Float a -> Bool # length :: URec Float a -> Int # elem :: Eq a => a -> URec Float a -> Bool # maximum :: Ord a => URec Float a -> a # minimum :: Ord a => URec Float a -> a # sum :: Num a => URec Float a -> a # product :: Num a => URec Float a -> a #
Foldable (URec Int)
Methods fold :: Monoid m => URec Int m -> m # foldMap :: Monoid m => (a -> m) -> URec Int a -> m # foldr :: (a -> b -> b) -> b -> URec Int a -> b # foldr' :: (a -> b -> b) -> b -> URec Int a -> b # foldl :: (b -> a -> b) -> b -> URec Int a -> b # foldl' :: (b -> a -> b) -> b -> URec Int a -> b # foldr1 :: (a -> a -> a) -> URec Int a -> a # foldl1 :: (a -> a -> a) -> URec Int a -> a # toList :: URec Int a -> [a] # null :: URec Int a -> Bool # length :: URec Int a -> Int # elem :: Eq a => a -> URec Int a -> Bool # maximum :: Ord a => URec Int a -> a # minimum :: Ord a => URec Int a -> a # sum :: Num a => URec Int a -> a # product :: Num a => URec Int a -> a #
Foldable (URec Word)
Methods fold :: Monoid m => URec Word m -> m # foldMap :: Monoid m => (a -> m) -> URec Word a -> m # foldr :: (a -> b -> b) -> b -> URec Word a -> b # foldr' :: (a -> b -> b) -> b -> URec Word a -> b # foldl :: (b -> a -> b) -> b -> URec Word a -> b # foldl' :: (b -> a -> b) -> b -> URec Word a -> b # foldr1 :: (a -> a -> a) -> URec Word a -> a # foldl1 :: (a -> a -> a) -> URec Word a -> a # toList :: URec Word a -> [a] # null :: URec Word a -> Bool # length :: URec Word a -> Int # elem :: Eq a => a -> URec Word a -> Bool # maximum :: Ord a => URec Word a -> a # minimum :: Ord a => URec Word a -> a # sum :: Num a => URec Word a -> a # product :: Num a => URec Word a -> a #
Foldable (URec (Ptr ()))
Methods fold :: Monoid m => URec (Ptr ()) m -> m # foldMap :: Monoid m => (a -> m) -> URec (Ptr ()) a -> m # foldr :: (a -> b -> b) -> b -> URec (Ptr ()) a -> b # foldr' :: (a -> b -> b) -> b -> URec (Ptr ()) a -> b # foldl :: (b -> a -> b) -> b -> URec (Ptr ()) a -> b # foldl' :: (b -> a -> b) -> b -> URec (Ptr ()) a -> b # foldr1 :: (a -> a -> a) -> URec (Ptr ()) a -> a # foldl1 :: (a -> a -> a) -> URec (Ptr ()) a -> a # toList :: URec (Ptr ()) a -> [a] # null :: URec (Ptr ()) a -> Bool # length :: URec (Ptr ()) a -> Int # elem :: Eq a => a -> URec (Ptr ()) a -> Bool # maximum :: Ord a => URec (Ptr ()) a -> a # minimum :: Ord a => URec (Ptr ()) a -> a # sum :: Num a => URec (Ptr ()) a -> a # product :: Num a => URec (Ptr ()) a -> a #
Foldable ((,) a)
Methods fold :: Monoid m => (a, m) -> m # foldMap :: Monoid m => (a -> m) -> (a, a) -> m # foldr :: (a -> b -> b) -> b -> (a, a) -> b # foldr' :: (a -> b -> b) -> b -> (a, a) -> b # foldl :: (b -> a -> b) -> b -> (a, a) -> b # foldl' :: (b -> a -> b) -> b -> (a, a) -> b # foldr1 :: (a -> a -> a) -> (a, a) -> a # foldl1 :: (a -> a -> a) -> (a, a) -> a # toList :: (a, a) -> [a] # null :: (a, a) -> Bool # length :: (a, a) -> Int # elem :: Eq a => a -> (a, a) -> Bool # maximum :: Ord a => (a, a) -> a # minimum :: Ord a => (a, a) -> a # sum :: Num a => (a, a) -> a # product :: Num a => (a, a) -> a #
Foldable (Array i)
Methods fold :: Monoid m => Array i m -> m # foldMap :: Monoid m => (a -> m) -> Array i a -> m # foldr :: (a -> b -> b) -> b -> Array i a -> b # foldr' :: (a -> b -> b) -> b -> Array i a -> b # foldl :: (b -> a -> b) -> b -> Array i a -> b # foldl' :: (b -> a -> b) -> b -> Array i a -> b # foldr1 :: (a -> a -> a) -> Array i a -> a # foldl1 :: (a -> a -> a) -> Array i a -> a # toList :: Array i a -> [a] # null :: Array i a -> Bool # length :: Array i a -> Int # elem :: Eq a => a -> Array i a -> Bool # maximum :: Ord a => Array i a -> a # minimum :: Ord a => Array i a -> a # sum :: Num a => Array i a -> a # product :: Num a => Array i a -> a #
Foldable (Proxy *)
Methods fold :: Monoid m => Proxy * m -> m # foldMap :: Monoid m => (a -> m) -> Proxy * a -> m # foldr :: (a -> b -> b) -> b -> Proxy * a -> b # foldr' :: (a -> b -> b) -> b -> Proxy * a -> b # foldl :: (b -> a -> b) -> b -> Proxy * a -> b # foldl' :: (b -> a -> b) -> b -> Proxy * a -> b # foldr1 :: (a -> a -> a) -> Proxy * a -> a # foldl1 :: (a -> a -> a) -> Proxy * a -> a # toList :: Proxy * a -> [a] # null :: Proxy * a -> Bool # length :: Proxy * a -> Int # elem :: Eq a => a -> Proxy * a -> Bool # maximum :: Ord a => Proxy * a -> a # minimum :: Ord a => Proxy * a -> a # sum :: Num a => Proxy * a -> a # product :: Num a => Proxy * a -> a #
Foldable (Map k)
Methods fold :: Monoid m => Map k m -> m # foldMap :: Monoid m => (a -> m) -> Map k a -> m # foldr :: (a -> b -> b) -> b -> Map k a -> b # foldr' :: (a -> b -> b) -> b -> Map k a -> b # foldl :: (b -> a -> b) -> b -> Map k a -> b # foldl' :: (b -> a -> b) -> b -> Map k a -> b # foldr1 :: (a -> a -> a) -> Map k a -> a # foldl1 :: (a -> a -> a) -> Map k a -> a # toList :: Map k a -> [a] # null :: Map k a -> Bool # length :: Map k a -> Int # elem :: Eq a => a -> Map k a -> Bool # maximum :: Ord a => Map k a -> a # minimum :: Ord a => Map k a -> a # sum :: Num a => Map k a -> a # product :: Num a => Map k a -> a #
Foldable f => Foldable (ListT f)
Methods fold :: Monoid m => ListT f m -> m # foldMap :: Monoid m => (a -> m) -> ListT f a -> m # foldr :: (a -> b -> b) -> b -> ListT f a -> b # foldr' :: (a -> b -> b) -> b -> ListT f a -> b # foldl :: (b -> a -> b) -> b -> ListT f a -> b # foldl' :: (b -> a -> b) -> b -> ListT f a -> b # foldr1 :: (a -> a -> a) -> ListT f a -> a # foldl1 :: (a -> a -> a) -> ListT f a -> a # toList :: ListT f a -> [a] # null :: ListT f a -> Bool # length :: ListT f a -> Int # elem :: Eq a => a -> ListT f a -> Bool # maximum :: Ord a => ListT f a -> a # minimum :: Ord a => ListT f a -> a # sum :: Num a => ListT f a -> a # product :: Num a => ListT f a -> a #
Foldable f => Foldable (MaybeT f)
Methods fold :: Monoid m => MaybeT f m -> m # foldMap :: Monoid m => (a -> m) -> MaybeT f a -> m # foldr :: (a -> b -> b) -> b -> MaybeT f a -> b # foldr' :: (a -> b -> b) -> b -> MaybeT f a -> b # foldl :: (b -> a -> b) -> b -> MaybeT f a -> b # foldl' :: (b -> a -> b) -> b -> MaybeT f a -> b # foldr1 :: (a -> a -> a) -> MaybeT f a -> a # foldl1 :: (a -> a -> a) -> MaybeT f a -> a # toList :: MaybeT f a -> [a] # null :: MaybeT f a -> Bool # length :: MaybeT f a -> Int # elem :: Eq a => a -> MaybeT f a -> Bool # maximum :: Ord a => MaybeT f a -> a # minimum :: Ord a => MaybeT f a -> a # sum :: Num a => MaybeT f a -> a # product :: Num a => MaybeT f a -> a #
Foldable (K1 i c)
Methods fold :: Monoid m => K1 i c m -> m # foldMap :: Monoid m => (a -> m) -> K1 i c a -> m # foldr :: (a -> b -> b) -> b -> K1 i c a -> b # foldr' :: (a -> b -> b) -> b -> K1 i c a -> b # foldl :: (b -> a -> b) -> b -> K1 i c a -> b # foldl' :: (b -> a -> b) -> b -> K1 i c a -> b # foldr1 :: (a -> a -> a) -> K1 i c a -> a # foldl1 :: (a -> a -> a) -> K1 i c a -> a # toList :: K1 i c a -> [a] # null :: K1 i c a -> Bool # length :: K1 i c a -> Int # elem :: Eq a => a -> K1 i c a -> Bool # maximum :: Ord a => K1 i c a -> a # minimum :: Ord a => K1 i c a -> a # sum :: Num a => K1 i c a -> a # product :: Num a => K1 i c a -> a #
(Foldable f, Foldable g) => Foldable ((:+:) f g)
Methods fold :: Monoid m => (f :+: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldr1 :: (a -> a -> a) -> (f :+: g) a -> a # foldl1 :: (a -> a -> a) -> (f :+: g) a -> a # toList :: (f :+: g) a -> [a] # null :: (f :+: g) a -> Bool # length :: (f :+: g) a -> Int # elem :: Eq a => a -> (f :+: g) a -> Bool # maximum :: Ord a => (f :+: g) a -> a # minimum :: Ord a => (f :+: g) a -> a # sum :: Num a => (f :+: g) a -> a # product :: Num a => (f :+: g) a -> a #
(Foldable f, Foldable g) => Foldable ((:*:) f g)
Methods fold :: Monoid m => (f :: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :: g) a -> b # foldr1 :: (a -> a -> a) -> (f :: g) a -> a # foldl1 :: (a -> a -> a) -> (f :: g) a -> a # toList :: (f :: g) a -> [a] # null :: (f :: g) a -> Bool # length :: (f :: g) a -> Int # elem :: Eq a => a -> (f :: g) a -> Bool # maximum :: Ord a => (f :: g) a -> a # minimum :: Ord a => (f :: g) a -> a # sum :: Num a => (f :: g) a -> a # product :: Num a => (f :: g) a -> a #
(Foldable f, Foldable g) => Foldable ((:.:) f g)
Methods fold :: Monoid m => (f :.: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldr1 :: (a -> a -> a) -> (f :.: g) a -> a # foldl1 :: (a -> a -> a) -> (f :.: g) a -> a # toList :: (f :.: g) a -> [a] # null :: (f :.: g) a -> Bool # length :: (f :.: g) a -> Int # elem :: Eq a => a -> (f :.: g) a -> Bool # maximum :: Ord a => (f :.: g) a -> a # minimum :: Ord a => (f :.: g) a -> a # sum :: Num a => (f :.: g) a -> a # product :: Num a => (f :.: g) a -> a #
Foldable (Constant * a)
Methods fold :: Monoid m => Constant * a m -> m # foldMap :: Monoid m => (a -> m) -> Constant * a a -> m # foldr :: (a -> b -> b) -> b -> Constant * a a -> b # foldr' :: (a -> b -> b) -> b -> Constant * a a -> b # foldl :: (b -> a -> b) -> b -> Constant * a a -> b # foldl' :: (b -> a -> b) -> b -> Constant * a a -> b # foldr1 :: (a -> a -> a) -> Constant * a a -> a # foldl1 :: (a -> a -> a) -> Constant * a a -> a # toList :: Constant * a a -> [a] # null :: Constant * a a -> Bool # length :: Constant * a a -> Int # elem :: Eq a => a -> Constant * a a -> Bool # maximum :: Ord a => Constant * a a -> a # minimum :: Ord a => Constant * a a -> a # sum :: Num a => Constant * a a -> a # product :: Num a => Constant * a a -> a #
Foldable f => Foldable (Backwards * f)	Derived instance.
Methods fold :: Monoid m => Backwards * f m -> m # foldMap :: Monoid m => (a -> m) -> Backwards * f a -> m # foldr :: (a -> b -> b) -> b -> Backwards * f a -> b # foldr' :: (a -> b -> b) -> b -> Backwards * f a -> b # foldl :: (b -> a -> b) -> b -> Backwards * f a -> b # foldl' :: (b -> a -> b) -> b -> Backwards * f a -> b # foldr1 :: (a -> a -> a) -> Backwards * f a -> a # foldl1 :: (a -> a -> a) -> Backwards * f a -> a # toList :: Backwards * f a -> [a] # null :: Backwards * f a -> Bool # length :: Backwards * f a -> Int # elem :: Eq a => a -> Backwards * f a -> Bool # maximum :: Ord a => Backwards * f a -> a # minimum :: Ord a => Backwards * f a -> a # sum :: Num a => Backwards * f a -> a # product :: Num a => Backwards * f a -> a #
Foldable f => Foldable (ErrorT e f)
Methods fold :: Monoid m => ErrorT e f m -> m # foldMap :: Monoid m => (a -> m) -> ErrorT e f a -> m # foldr :: (a -> b -> b) -> b -> ErrorT e f a -> b # foldr' :: (a -> b -> b) -> b -> ErrorT e f a -> b # foldl :: (b -> a -> b) -> b -> ErrorT e f a -> b # foldl' :: (b -> a -> b) -> b -> ErrorT e f a -> b # foldr1 :: (a -> a -> a) -> ErrorT e f a -> a # foldl1 :: (a -> a -> a) -> ErrorT e f a -> a # toList :: ErrorT e f a -> [a] # null :: ErrorT e f a -> Bool # length :: ErrorT e f a -> Int # elem :: Eq a => a -> ErrorT e f a -> Bool # maximum :: Ord a => ErrorT e f a -> a # minimum :: Ord a => ErrorT e f a -> a # sum :: Num a => ErrorT e f a -> a # product :: Num a => ErrorT e f a -> a #
Foldable f => Foldable (ExceptT e f)
Methods fold :: Monoid m => ExceptT e f m -> m # foldMap :: Monoid m => (a -> m) -> ExceptT e f a -> m # foldr :: (a -> b -> b) -> b -> ExceptT e f a -> b # foldr' :: (a -> b -> b) -> b -> ExceptT e f a -> b # foldl :: (b -> a -> b) -> b -> ExceptT e f a -> b # foldl' :: (b -> a -> b) -> b -> ExceptT e f a -> b # foldr1 :: (a -> a -> a) -> ExceptT e f a -> a # foldl1 :: (a -> a -> a) -> ExceptT e f a -> a # toList :: ExceptT e f a -> [a] # null :: ExceptT e f a -> Bool # length :: ExceptT e f a -> Int # elem :: Eq a => a -> ExceptT e f a -> Bool # maximum :: Ord a => ExceptT e f a -> a # minimum :: Ord a => ExceptT e f a -> a # sum :: Num a => ExceptT e f a -> a # product :: Num a => ExceptT e f a -> a #
Foldable f => Foldable (WriterT w f)
Methods fold :: Monoid m => WriterT w f m -> m # foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m # foldr :: (a -> b -> b) -> b -> WriterT w f a -> b # foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b # foldl :: (b -> a -> b) -> b -> WriterT w f a -> b # foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b # foldr1 :: (a -> a -> a) -> WriterT w f a -> a # foldl1 :: (a -> a -> a) -> WriterT w f a -> a # toList :: WriterT w f a -> [a] # null :: WriterT w f a -> Bool # length :: WriterT w f a -> Int # elem :: Eq a => a -> WriterT w f a -> Bool # maximum :: Ord a => WriterT w f a -> a # minimum :: Ord a => WriterT w f a -> a # sum :: Num a => WriterT w f a -> a # product :: Num a => WriterT w f a -> a #
Foldable f => Foldable (WriterT w f)
Methods fold :: Monoid m => WriterT w f m -> m # foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m # foldr :: (a -> b -> b) -> b -> WriterT w f a -> b # foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b # foldl :: (b -> a -> b) -> b -> WriterT w f a -> b # foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b # foldr1 :: (a -> a -> a) -> WriterT w f a -> a # foldl1 :: (a -> a -> a) -> WriterT w f a -> a # toList :: WriterT w f a -> [a] # null :: WriterT w f a -> Bool # length :: WriterT w f a -> Int # elem :: Eq a => a -> WriterT w f a -> Bool # maximum :: Ord a => WriterT w f a -> a # minimum :: Ord a => WriterT w f a -> a # sum :: Num a => WriterT w f a -> a # product :: Num a => WriterT w f a -> a #
Foldable f => Foldable (IdentityT * f)
Methods fold :: Monoid m => IdentityT * f m -> m # foldMap :: Monoid m => (a -> m) -> IdentityT * f a -> m # foldr :: (a -> b -> b) -> b -> IdentityT * f a -> b # foldr' :: (a -> b -> b) -> b -> IdentityT * f a -> b # foldl :: (b -> a -> b) -> b -> IdentityT * f a -> b # foldl' :: (b -> a -> b) -> b -> IdentityT * f a -> b # foldr1 :: (a -> a -> a) -> IdentityT * f a -> a # foldl1 :: (a -> a -> a) -> IdentityT * f a -> a # toList :: IdentityT * f a -> [a] # null :: IdentityT * f a -> Bool # length :: IdentityT * f a -> Int # elem :: Eq a => a -> IdentityT * f a -> Bool # maximum :: Ord a => IdentityT * f a -> a # minimum :: Ord a => IdentityT * f a -> a # sum :: Num a => IdentityT * f a -> a # product :: Num a => IdentityT * f a -> a #
Foldable f => Foldable (M1 i c f)
Methods fold :: Monoid m => M1 i c f m -> m # foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m # foldr :: (a -> b -> b) -> b -> M1 i c f a -> b # foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b # foldl :: (b -> a -> b) -> b -> M1 i c f a -> b # foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b # foldr1 :: (a -> a -> a) -> M1 i c f a -> a # foldl1 :: (a -> a -> a) -> M1 i c f a -> a # toList :: M1 i c f a -> [a] # null :: M1 i c f a -> Bool # length :: M1 i c f a -> Int # elem :: Eq a => a -> M1 i c f a -> Bool # maximum :: Ord a => M1 i c f a -> a # minimum :: Ord a => M1 i c f a -> a # sum :: Num a => M1 i c f a -> a # product :: Num a => M1 i c f a -> a #

class Monoid a #

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

```
mappend mempty x = x
```
```
mappend x mempty = x
```

mappend x (mappend y z) = mappend (mappend x y) z

```
mconcat = foldr mappend 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.

Minimal complete definition

mempty, mappend

Instances

Monoid Ordering
Methods mempty :: Ordering # mappend :: Ordering -> Ordering -> Ordering # mconcat :: [Ordering] -> Ordering #
Monoid ()
Methods mempty :: () # mappend :: () -> () -> () # mconcat :: [()] -> () #
Monoid All
Methods mempty :: All # mappend :: All -> All -> All # mconcat :: [All] -> All #
Monoid Any
Methods mempty :: Any # mappend :: Any -> Any -> Any # mconcat :: [Any] -> Any #
Monoid IntSet
Methods mempty :: IntSet # mappend :: IntSet -> IntSet -> IntSet # mconcat :: [IntSet] -> IntSet #
Monoid [a]
Methods mempty :: [a] # mappend :: [a] -> [a] -> [a] # mconcat :: [[a]] -> [a] #
Monoid 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 = s*e` for all `s ∈ S`." Since there is no "Semigroup" typeclass providing just `mappend`, we use `Monoid` instead.
Methods mempty :: Maybe a # mappend :: Maybe a -> Maybe a -> Maybe a # mconcat :: [Maybe a] -> Maybe a #
Monoid a => Monoid (IO a)
Methods mempty :: IO a # mappend :: IO a -> IO a -> IO a # mconcat :: [IO a] -> IO a #
Ord a => Monoid (Max a)
Methods mempty :: Max a # mappend :: Max a -> Max a -> Max a # mconcat :: [Max a] -> Max a #
Ord a => Monoid (Min a)
Methods mempty :: Min a # mappend :: Min a -> Min a -> Min a # mconcat :: [Min a] -> Min a #
Monoid a => Monoid (Identity a)
Methods mempty :: Identity a # mappend :: Identity a -> Identity a -> Identity a # mconcat :: [Identity a] -> Identity a #
Monoid a => Monoid (Dual a)
Methods mempty :: Dual a # mappend :: Dual a -> Dual a -> Dual a # mconcat :: [Dual a] -> Dual a #
Monoid (Endo a)
Methods mempty :: Endo a # mappend :: Endo a -> Endo a -> Endo a # mconcat :: [Endo a] -> Endo a #
Num a => Monoid (Sum a)
Methods mempty :: Sum a # mappend :: Sum a -> Sum a -> Sum a # mconcat :: [Sum a] -> Sum a #
Num a => Monoid (Product a)
Methods mempty :: Product a # mappend :: Product a -> Product a -> Product a # mconcat :: [Product a] -> Product a #
Monoid (First a)
Methods mempty :: First a # mappend :: First a -> First a -> First a # mconcat :: [First a] -> First a #
Monoid (Last a)
Methods mempty :: Last a # mappend :: Last a -> Last a -> Last a # mconcat :: [Last a] -> Last a #
Monoid (IntMap a)
Methods mempty :: IntMap a # mappend :: IntMap a -> IntMap a -> IntMap a # mconcat :: [IntMap a] -> IntMap a #
Ord a => Monoid (Set a)
Methods mempty :: Set a # mappend :: Set a -> Set a -> Set a # mconcat :: [Set a] -> Set a #
Monoid b => Monoid (a -> b)
Methods mempty :: a -> b # mappend :: (a -> b) -> (a -> b) -> a -> b # mconcat :: [a -> b] -> a -> b #
(Monoid a, Monoid b) => Monoid (a, b)
Methods mempty :: (a, b) # mappend :: (a, b) -> (a, b) -> (a, b) # mconcat :: [(a, b)] -> (a, b) #
Monoid (Proxy k s)
Methods mempty :: Proxy k s # mappend :: Proxy k s -> Proxy k s -> Proxy k s # mconcat :: [Proxy k s] -> Proxy k s #
Ord k => Monoid (Map k v)
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)
Methods mempty :: (a, b, c) # mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) # mconcat :: [(a, b, c)] -> (a, b, c) #
Alternative f => Monoid (Alt * f a)
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 k a b)
Methods mempty :: Constant k a b # mappend :: Constant k a b -> Constant k a b -> Constant k a b # mconcat :: [Constant k a b] -> Constant k a b #
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d)
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)
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) #

data Backwards k f a :: forall k. (k -> *) -> k -> * #

The same functor, but with an Applicative instance that performs actions in the reverse order.

Instances

Functor f => Functor (Backwards * f)	Derived instance.
Methods fmap :: (a -> b) -> Backwards * f a -> Backwards * f b # (<$) :: a -> Backwards * f b -> Backwards * f a #
Applicative f => Applicative (Backwards * f)	Apply `f`-actions in the reverse order.
Methods pure :: a -> Backwards * f a # (<>) :: Backwards f (a -> b) -> Backwards * f a -> Backwards * f b # (>) :: Backwards f a -> Backwards * f b -> Backwards * f b # (<) :: Backwards f a -> Backwards * f b -> Backwards * f a #
Foldable f => Foldable (Backwards * f)	Derived instance.
Methods fold :: Monoid m => Backwards * f m -> m # foldMap :: Monoid m => (a -> m) -> Backwards * f a -> m # foldr :: (a -> b -> b) -> b -> Backwards * f a -> b # foldr' :: (a -> b -> b) -> b -> Backwards * f a -> b # foldl :: (b -> a -> b) -> b -> Backwards * f a -> b # foldl' :: (b -> a -> b) -> b -> Backwards * f a -> b # foldr1 :: (a -> a -> a) -> Backwards * f a -> a # foldl1 :: (a -> a -> a) -> Backwards * f a -> a # toList :: Backwards * f a -> [a] # null :: Backwards * f a -> Bool # length :: Backwards * f a -> Int # elem :: Eq a => a -> Backwards * f a -> Bool # maximum :: Ord a => Backwards * f a -> a # minimum :: Ord a => Backwards * f a -> a # sum :: Num a => Backwards * f a -> a # product :: Num a => Backwards * f a -> a #
Traversable f => Traversable (Backwards * f)	Derived instance.
Methods traverse :: Applicative f => (a -> f b) -> Backwards * f a -> f (Backwards * f b) # sequenceA :: Applicative f => Backwards * f (f a) -> f (Backwards * f a) # mapM :: Monad m => (a -> m b) -> Backwards * f a -> m (Backwards * f b) # sequence :: Monad m => Backwards * f (m a) -> m (Backwards * f a) #
Eq1 f => Eq1 (Backwards * f)
Methods liftEq :: (a -> b -> Bool) -> Backwards * f a -> Backwards * f b -> Bool #
Ord1 f => Ord1 (Backwards * f)
Methods liftCompare :: (a -> b -> Ordering) -> Backwards * f a -> Backwards * f b -> Ordering #
Read1 f => Read1 (Backwards * f)
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Backwards * f a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Backwards * f a] #
Show1 f => Show1 (Backwards * f)
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Backwards * f a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Backwards * f a] -> ShowS #
Alternative f => Alternative (Backwards * f)	Try alternatives in the same order as `f`.
Methods empty :: Backwards * f a # (<\|>) :: Backwards * f a -> Backwards * f a -> Backwards * f a # some :: Backwards * f a -> Backwards * f [a] # many :: Backwards * f a -> Backwards * f [a] #
Identical f => Identical (Backwards * f)
Methods extract :: Backwards * f a -> a
Phantom f => Phantom (Backwards * f)
Methods coerce :: Backwards * f a -> Backwards * f b
(Eq1 f, Eq a) => Eq (Backwards * f a)
Methods (==) :: Backwards * f a -> Backwards * f a -> Bool # (/=) :: Backwards * f a -> Backwards * f a -> Bool #
(Ord1 f, Ord a) => Ord (Backwards * f a)
Methods compare :: Backwards * f a -> Backwards * f a -> Ordering # (<) :: Backwards * f a -> Backwards * f a -> Bool # (<=) :: Backwards * f a -> Backwards * f a -> Bool # (>) :: Backwards * f a -> Backwards * f a -> Bool # (>=) :: Backwards * f a -> Backwards * f a -> Bool # max :: Backwards * f a -> Backwards * f a -> Backwards * f a # min :: Backwards * f a -> Backwards * f a -> Backwards * f a #
(Read1 f, Read a) => Read (Backwards * f a)
Methods readsPrec :: Int -> ReadS (Backwards * f a) # readList :: ReadS [Backwards * f a] # readPrec :: ReadPrec (Backwards * f a) # readListPrec :: ReadPrec [Backwards * f a] #
(Show1 f, Show a) => Show (Backwards * f a)
Methods showsPrec :: Int -> Backwards * f a -> ShowS # show :: Backwards * f a -> String # showList :: [Backwards * f a] -> ShowS #