Copyright	(c) Andy Gill 2001 (c) Oregon Graduate Institute of Science and Technology 2001
License	BSD-style (see the file libraries/base/LICENSE)
Maintainer	libraries@haskell.org
Stability	experimental
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell2010

Data.Monoid

Contents

Description

A class for monoids (types with an associative binary operation that has an identity) with various general-purpose instances.

Synopsis

classSemigroup a =>Monoid awhere
- mempty :: a
- mappend :: a -> a -> a
- mconcat :: [a] -> a
(<>) ::Semigroup a => a -> a -> a
newtypeDual a =Dual {
- getDual :: a
}
newtypeEndo a =Endo {
- appEndo :: a -> a
}
newtypeAll =All {
- getAll ::Bool
}
newtypeAny =Any {
- getAny ::Bool
}
newtypeSum a =Sum {
- getSum :: a
}
newtypeProduct a =Product {
- getProduct :: a
}
newtypeFirst a =First {
- getFirst ::Maybe a
}
newtypeLast a =Last {
- getLast ::Maybe a
}
newtypeAlt f a =Alt {
- getAlt :: f a
}
newtypeAp f a =Ap {
- getAp :: f a
}

`Monoid` typeclass

classSemigroup a =>Monoid awhereSource #

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 definenewtypes and make those instances ofMonoid, e.g.Sum andProduct.

NOTE:Semigroup is a superclass ofMonoid sincebase-4.11.0.0.

Minimal complete definition

mempty

Methods

mempty :: aSource #

Identity ofmappend

mappend :: a -> a -> aSource #

An associative operation

NOTE: This method is redundant and has the default implementationmappend = '(<>)' sincebase-4.11.0.0.

mconcat :: [a] -> aSource #

Fold a list using the monoid.

For most types, the default definition formconcat will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.

Instances

Monoid OrderingSource #	Since: 2.1
Instance details Defined inGHC.Base Methods mempty ::Ordering Source # mappend ::Ordering ->Ordering ->Ordering Source # mconcat :: [Ordering] ->Ordering Source #
Monoid ()Source #	Since: 2.1
Instance details Defined inGHC.Base Methods mempty :: ()Source # mappend :: () -> () -> ()Source # mconcat :: [()] -> ()Source #
Monoid AnySource #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods mempty ::Any Source # mappend ::Any ->Any ->Any Source # mconcat :: [Any] ->Any Source #
Monoid AllSource #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods mempty ::All Source # mappend ::All ->All ->All Source # mconcat :: [All] ->All Source #
Monoid LifetimeSource #	`mappend` takes the longer of two lifetimes. Since: 4.8.0.0
Instance details Defined inGHC.Event.Internal Methods mempty ::Lifetime Source # mappend ::Lifetime ->Lifetime ->Lifetime Source # mconcat :: [Lifetime] ->Lifetime Source #
Monoid EventSource #	Since: 4.4.0.0
Instance details Defined inGHC.Event.Internal Methods mempty ::Event Source # mappend ::Event ->Event ->Event Source # mconcat :: [Event] ->Event Source #
Monoid [a]Source #	Since: 2.1
Instance details Defined inGHC.Base Methods mempty :: [a]Source # mappend :: [a] -> [a] -> [a]Source # mconcat :: [[a]] -> [a]Source #
Semigroup a =>Monoid (Maybe a)Source #	Lift a semigroup into`Maybe` forming a`Monoid` according tohttp://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: 2.1*
Instance details Defined inGHC.Base Methods mempty ::Maybe aSource # mappend ::Maybe a ->Maybe a ->Maybe aSource # mconcat :: [Maybe a] ->Maybe aSource #
Monoid a =>Monoid (IO a)Source #	Since: 4.9.0.0
Instance details Defined inGHC.Base Methods mempty ::IO aSource # mappend ::IO a ->IO a ->IO aSource # mconcat :: [IO a] ->IO aSource #
Monoid p =>Monoid (Par1 p)Source #	Since: 4.12.0.0
Instance details Defined inGHC.Generics Methods mempty ::Par1 pSource # mappend ::Par1 p ->Par1 p ->Par1 pSource # mconcat :: [Par1 p] ->Par1 pSource #
Monoid a =>Monoid (Down a)Source #	Since: 4.11.0.0
Instance details Defined inData.Ord Methods mempty ::Down aSource # mappend ::Down a ->Down a ->Down aSource # mconcat :: [Down a] ->Down aSource #
Num a =>Monoid (Product a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods mempty ::Product aSource # mappend ::Product a ->Product a ->Product aSource # mconcat :: [Product a] ->Product aSource #
Num a =>Monoid (Sum a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods mempty ::Sum aSource # mappend ::Sum a ->Sum a ->Sum aSource # mconcat :: [Sum a] ->Sum aSource #
Monoid (Endo a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods mempty ::Endo aSource # mappend ::Endo a ->Endo a ->Endo aSource # mconcat :: [Endo a] ->Endo aSource #
Monoid a =>Monoid (Dual a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods mempty ::Dual aSource # mappend ::Dual a ->Dual a ->Dual aSource # mconcat :: [Dual a] ->Dual aSource #
Monoid (Last a)Source #	Since: 2.1
Instance details Defined inData.Monoid Methods mempty ::Last aSource # mappend ::Last a ->Last a ->Last aSource # mconcat :: [Last a] ->Last aSource #
Monoid (First a)Source #	Since: 2.1
Instance details Defined inData.Monoid Methods mempty ::First aSource # mappend ::First a ->First a ->First aSource # mconcat :: [First a] ->First aSource #
Monoid a =>Monoid (Identity a)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Identity Methods mempty ::Identity aSource # mappend ::Identity a ->Identity a ->Identity aSource # mconcat :: [Identity a] ->Identity aSource #
Semigroup a =>Monoid (Option a)Source #	Since: 4.9.0.0
Instance details Defined inData.Semigroup Methods mempty ::Option aSource # mappend ::Option a ->Option a ->Option aSource # mconcat :: [Option a] ->Option aSource #
Monoid m =>Monoid (WrappedMonoid m)Source #	Since: 4.9.0.0
Instance details Defined inData.Semigroup Methods mempty ::WrappedMonoid mSource # mappend ::WrappedMonoid m ->WrappedMonoid m ->WrappedMonoid mSource # mconcat :: [WrappedMonoid m] ->WrappedMonoid mSource #
(Ord a,Bounded a) =>Monoid (Max a)Source #	Since: 4.9.0.0
Instance details Defined inData.Semigroup Methods mempty ::Max aSource # mappend ::Max a ->Max a ->Max aSource # mconcat :: [Max a] ->Max aSource #
(Ord a,Bounded a) =>Monoid (Min a)Source #	Since: 4.9.0.0
Instance details Defined inData.Semigroup Methods mempty ::Min aSource # mappend ::Min a ->Min a ->Min aSource # mconcat :: [Min a] ->Min aSource #
Monoid (Equivalence a)Source #
Instance details Defined inData.Functor.Contravariant Methods mempty ::Equivalence aSource # mappend ::Equivalence a ->Equivalence a ->Equivalence aSource # mconcat :: [Equivalence a] ->Equivalence aSource #
Monoid (Comparison a)Source #
Instance details Defined inData.Functor.Contravariant Methods mempty ::Comparison aSource # mappend ::Comparison a ->Comparison a ->Comparison aSource # mconcat :: [Comparison a] ->Comparison aSource #
Monoid (Predicate a)Source #
Instance details Defined inData.Functor.Contravariant Methods mempty ::Predicate aSource # mappend ::Predicate a ->Predicate a ->Predicate aSource # mconcat :: [Predicate a] ->Predicate aSource #
Monoid b =>Monoid (a -> b)Source #	Since: 2.1
Instance details Defined inGHC.Base Methods mempty :: a -> bSource # mappend :: (a -> b) -> (a -> b) -> a -> bSource # mconcat :: [a -> b] -> a -> bSource #
Monoid (U1 p)Source #	Since: 4.12.0.0
Instance details Defined inGHC.Generics Methods mempty ::U1 pSource # mappend ::U1 p ->U1 p ->U1 pSource # mconcat :: [U1 p] ->U1 pSource #
(Monoid a,Monoid b) =>Monoid (a, b)Source #	Since: 2.1
Instance details Defined inGHC.Base Methods mempty :: (a, b)Source # mappend :: (a, b) -> (a, b) -> (a, b)Source # mconcat :: [(a, b)] -> (a, b)Source #
Monoid a =>Monoid (ST s a)Source #	Since: 4.11.0.0
Instance details Defined inGHC.ST Methods mempty ::ST s aSource # mappend ::ST s a ->ST s a ->ST s aSource # mconcat :: [ST s a] ->ST s aSource #
Monoid (Proxy s)Source #	Since: 4.7.0.0
Instance details Defined inData.Proxy Methods mempty ::Proxy sSource # mappend ::Proxy s ->Proxy s ->Proxy sSource # mconcat :: [Proxy s] ->Proxy sSource #
Monoid a =>Monoid (Op a b)Source #
Instance details Defined inData.Functor.Contravariant Methods mempty ::Op a bSource # mappend ::Op a b ->Op a b ->Op a bSource # mconcat :: [Op a b] ->Op a bSource #
Monoid (f p) =>Monoid (Rec1 f p)Source #	Since: 4.12.0.0
Instance details Defined inGHC.Generics Methods mempty ::Rec1 f pSource # mappend ::Rec1 f p ->Rec1 f p ->Rec1 f pSource # mconcat :: [Rec1 f p] ->Rec1 f pSource #
(Monoid a,Monoid b,Monoid c) =>Monoid (a, b, c)Source #	Since: 2.1
Instance details Defined inGHC.Base Methods mempty :: (a, b, c)Source # mappend :: (a, b, c) -> (a, b, c) -> (a, b, c)Source # mconcat :: [(a, b, c)] -> (a, b, c)Source #
Alternative f =>Monoid (Alt f a)Source #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods mempty ::Alt f aSource # mappend ::Alt f a ->Alt f a ->Alt f aSource # mconcat :: [Alt f a] ->Alt f aSource #
(Applicative f,Monoid a) =>Monoid (Ap f a)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid Methods mempty ::Ap f aSource # mappend ::Ap f a ->Ap f a ->Ap f aSource # mconcat :: [Ap f a] ->Ap f aSource #
Monoid a =>Monoid (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const Methods mempty ::Const a bSource # mappend ::Const a b ->Const a b ->Const a bSource # mconcat :: [Const a b] ->Const a bSource #
Monoid c =>Monoid (K1 i c p)Source #	Since: 4.12.0.0
Instance details Defined inGHC.Generics Methods mempty ::K1 i c pSource # mappend ::K1 i c p ->K1 i c p ->K1 i c pSource # mconcat :: [K1 i c p] ->K1 i c pSource #
(Monoid (f p),Monoid (g p)) =>Monoid ((f:*: g) p)Source #	Since: 4.12.0.0
Instance details Defined inGHC.Generics Methods mempty :: (f:: g) pSource # mappend :: (f:: g) p -> (f:: g) p -> (f:: g) pSource # mconcat :: [(f:: g) p] -> (f:: g) pSource #
(Monoid a,Monoid b,Monoid c,Monoid d) =>Monoid (a, b, c, d)Source #	Since: 2.1
Instance details Defined inGHC.Base Methods mempty :: (a, b, c, d)Source # mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d)Source # mconcat :: [(a, b, c, d)] -> (a, b, c, d)Source #
Monoid (f p) =>Monoid (M1 i c f p)Source #	Since: 4.12.0.0
Instance details Defined inGHC.Generics Methods mempty ::M1 i c f pSource # mappend ::M1 i c f p ->M1 i c f p ->M1 i c f pSource # mconcat :: [M1 i c f p] ->M1 i c f pSource #
Monoid (f (g p)) =>Monoid ((f:.: g) p)Source #	Since: 4.12.0.0
Instance details Defined inGHC.Generics Methods mempty :: (f:.: g) pSource # mappend :: (f:.: g) p -> (f:.: g) p -> (f:.: g) pSource # mconcat :: [(f:.: g) p] -> (f:.: g) pSource #
(Monoid a,Monoid b,Monoid c,Monoid d,Monoid e) =>Monoid (a, b, c, d, e)Source #	Since: 2.1
Instance details Defined inGHC.Base Methods mempty :: (a, b, c, d, e)Source # mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e)Source # mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e)Source #

(<>) ::Semigroup a => a -> a -> ainfixr 6Source #

An associative operation.

newtypeDual aSource #

The dual of aMonoid, obtained by swapping the arguments ofmappend.

>>>getDual (mappend (Dual "Hello") (Dual "World"))"WorldHello"

Constructors

Dual
Fields getDual :: a

Instances

Monad DualSource #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods (>>=) ::Dual a -> (a ->Dual b) ->Dual bSource # (>>) ::Dual a ->Dual b ->Dual bSource # return :: a ->Dual aSource # fail ::String ->Dual aSource #
Functor DualSource #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods fmap :: (a -> b) ->Dual a ->Dual bSource # (<$) :: a ->Dual b ->Dual aSource #
MonadFix DualSource #	Since: 4.8.0.0
Instance details Defined inControl.Monad.Fix Methods mfix :: (a ->Dual a) ->Dual aSource #
Applicative DualSource #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods pure :: a ->Dual aSource # (<>) ::Dual (a -> b) ->Dual a ->Dual bSource # liftA2 :: (a -> b -> c) ->Dual a ->Dual b ->Dual cSource # (>) ::Dual a ->Dual b ->Dual bSource # (<*) ::Dual a ->Dual b ->Dual aSource #
Foldable DualSource #	Since: 4.8.0.0
Instance details Defined inData.Foldable Methods fold ::Monoid m =>Dual m -> mSource # foldMap ::Monoid m => (a -> m) ->Dual a -> mSource # foldr :: (a -> b -> b) -> b ->Dual a -> bSource # foldr' :: (a -> b -> b) -> b ->Dual a -> bSource # foldl :: (b -> a -> b) -> b ->Dual a -> bSource # foldl' :: (b -> a -> b) -> b ->Dual a -> bSource # foldr1 :: (a -> a -> a) ->Dual a -> aSource # foldl1 :: (a -> a -> a) ->Dual a -> aSource # toList ::Dual a -> [a]Source # null ::Dual a ->Bool Source # length ::Dual a ->Int Source # elem ::Eq a => a ->Dual a ->Bool Source # maximum ::Ord a =>Dual a -> aSource # minimum ::Ord a =>Dual a -> aSource # sum ::Num a =>Dual a -> aSource # product ::Num a =>Dual a -> aSource #
Traversable DualSource #	Since: 4.8.0.0
Instance details Defined inData.Traversable Methods traverse ::Applicative f => (a -> f b) ->Dual a -> f (Dual b)Source # sequenceA ::Applicative f =>Dual (f a) -> f (Dual a)Source # mapM ::Monad m => (a -> m b) ->Dual a -> m (Dual b)Source # sequence ::Monad m =>Dual (m a) -> m (Dual a)Source #
MonadZip DualSource #	Since: 4.8.0.0
Instance details Defined inControl.Monad.Zip Methods mzip ::Dual a ->Dual b ->Dual (a, b)Source # mzipWith :: (a -> b -> c) ->Dual a ->Dual b ->Dual cSource # munzip ::Dual (a, b) -> (Dual a,Dual b)Source #
Bounded a =>Bounded (Dual a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods minBound ::Dual aSource # maxBound ::Dual aSource #
Eq a =>Eq (Dual a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods (==) ::Dual a ->Dual a ->Bool # (/=) ::Dual a ->Dual a ->Bool #
Data a =>Data (Dual a)Source #	Since: 4.8.0.0
Instance details Defined inData.Data Methods gfoldl :: (forall d b.Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) ->Dual a -> c (Dual a)Source # gunfold :: (forall b r.Data b => c (b -> r) -> c r) -> (forall r. r -> c r) ->Constr -> c (Dual a)Source # toConstr ::Dual a ->Constr Source # dataTypeOf ::Dual a ->DataType Source # dataCast1 ::Typeable t => (forall d.Data d => c (t d)) ->Maybe (c (Dual a))Source # dataCast2 ::Typeable t => (forall d e. (Data d,Data e) => c (t d e)) ->Maybe (c (Dual a))Source # gmapT :: (forall b.Data b => b -> b) ->Dual a ->Dual aSource # gmapQl :: (r -> r' -> r) -> r -> (forall d.Data d => d -> r') ->Dual a -> rSource # gmapQr :: (r' -> r -> r) -> r -> (forall d.Data d => d -> r') ->Dual a -> rSource # gmapQ :: (forall d.Data d => d -> u) ->Dual a -> [u]Source # gmapQi ::Int -> (forall d.Data d => d -> u) ->Dual a -> uSource # gmapM ::Monad m => (forall d.Data d => d -> m d) ->Dual a -> m (Dual a)Source # gmapMp ::MonadPlus m => (forall d.Data d => d -> m d) ->Dual a -> m (Dual a)Source # gmapMo ::MonadPlus m => (forall d.Data d => d -> m d) ->Dual a -> m (Dual a)Source #
Ord a =>Ord (Dual a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods compare ::Dual a ->Dual a ->Ordering # (<) ::Dual a ->Dual a ->Bool # (<=) ::Dual a ->Dual a ->Bool # (>) ::Dual a ->Dual a ->Bool # (>=) ::Dual a ->Dual a ->Bool # max ::Dual a ->Dual a ->Dual a# min ::Dual a ->Dual a ->Dual a#
Read a =>Read (Dual a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods readsPrec ::Int ->ReadS (Dual a)Source # readList ::ReadS [Dual a]Source # readPrec ::ReadPrec (Dual a)Source # readListPrec ::ReadPrec [Dual a]Source #
Show a =>Show (Dual a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods showsPrec ::Int ->Dual a ->ShowS Source # show ::Dual a ->String Source # showList :: [Dual a] ->ShowS Source #
Generic (Dual a)Source #
Instance details Defined inData.Semigroup.Internal Associated Types typeRep (Dual a) ::Type ->Type Source # Methods from ::Dual a ->Rep (Dual a) xSource # to ::Rep (Dual a) x ->Dual aSource #
Semigroup a =>Semigroup (Dual a)Source #	Since: 4.9.0.0
Instance details Defined inData.Semigroup.Internal Methods (<>) ::Dual a ->Dual a ->Dual aSource # sconcat ::NonEmpty (Dual a) ->Dual aSource # stimes ::Integral b => b ->Dual a ->Dual aSource #
Monoid a =>Monoid (Dual a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods mempty ::Dual aSource # mappend ::Dual a ->Dual a ->Dual aSource # mconcat :: [Dual a] ->Dual aSource #
Generic1 DualSource #
Instance details Defined inData.Semigroup.Internal Associated Types typeRep1 Dual :: k ->Type Source # Methods from1 ::Dual a ->Rep1 Dual aSource # to1 ::Rep1 Dual a ->Dual aSource #
typeRep (Dual a)Source #	Since: 4.7.0.0
Instance details Defined inData.Semigroup.Internal typeRep (Dual a) =D1 (MetaData "Dual" "Data.Semigroup.Internal" "base"True) (C1 (MetaCons "Dual"PrefixI True) (S1 (MetaSel (Just "getDual")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
typeRep1 DualSource #	Since: 4.7.0.0
Instance details Defined inData.Semigroup.Internal typeRep1 Dual =D1 (MetaData "Dual" "Data.Semigroup.Internal" "base"True) (C1 (MetaCons "Dual"PrefixI True) (S1 (MetaSel (Just "getDual")NoSourceUnpackedness NoSourceStrictness DecidedLazy)Par1))

newtypeEndo aSource #

The monoid of endomorphisms under composition.

>>>let computation = Endo ("Hello, " ++) <> Endo (++ "!")>>>appEndo computation "Haskell""Hello, Haskell!"

Constructors

Endo
Fields appEndo :: a -> a

Instances

Generic (Endo a)Source #
Instance details Defined inData.Semigroup.Internal Associated Types typeRep (Endo a) ::Type ->Type Source # Methods from ::Endo a ->Rep (Endo a) xSource # to ::Rep (Endo a) x ->Endo aSource #
Semigroup (Endo a)Source #	Since: 4.9.0.0
Instance details Defined inData.Semigroup.Internal Methods (<>) ::Endo a ->Endo a ->Endo aSource # sconcat ::NonEmpty (Endo a) ->Endo aSource # stimes ::Integral b => b ->Endo a ->Endo aSource #
Monoid (Endo a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods mempty ::Endo aSource # mappend ::Endo a ->Endo a ->Endo aSource # mconcat :: [Endo a] ->Endo aSource #
typeRep (Endo a)Source #	Since: 4.7.0.0
Instance details Defined inData.Semigroup.Internal typeRep (Endo a) =D1 (MetaData "Endo" "Data.Semigroup.Internal" "base"True) (C1 (MetaCons "Endo"PrefixI True) (S1 (MetaSel (Just "appEndo")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (a -> a))))

`Bool` wrappers

newtypeAll Source #

Boolean monoid under conjunction (&&).

>>>getAll (All True <> mempty <> All False)False

>>>getAll (mconcat (map (\x -> All (even x)) [2,4,6,7,8]))False

Constructors

All
Fields getAll ::Bool

Instances

Bounded AllSource #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods minBound ::All Source # maxBound ::All Source #
Eq AllSource #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods (==) ::All ->All ->Bool # (/=) ::All ->All ->Bool #
Data AllSource #	Since: 4.8.0.0
Instance details Defined inData.Data Methods gfoldl :: (forall d b.Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) ->All -> cAll Source # gunfold :: (forall b r.Data b => c (b -> r) -> c r) -> (forall r. r -> c r) ->Constr -> cAll Source # toConstr ::All ->Constr Source # dataTypeOf ::All ->DataType Source # dataCast1 ::Typeable t => (forall d.Data d => c (t d)) ->Maybe (cAll)Source # dataCast2 ::Typeable t => (forall d e. (Data d,Data e) => c (t d e)) ->Maybe (cAll)Source # gmapT :: (forall b.Data b => b -> b) ->All ->All Source # gmapQl :: (r -> r' -> r) -> r -> (forall d.Data d => d -> r') ->All -> rSource # gmapQr :: (r' -> r -> r) -> r -> (forall d.Data d => d -> r') ->All -> rSource # gmapQ :: (forall d.Data d => d -> u) ->All -> [u]Source # gmapQi ::Int -> (forall d.Data d => d -> u) ->All -> uSource # gmapM ::Monad m => (forall d.Data d => d -> m d) ->All -> mAll Source # gmapMp ::MonadPlus m => (forall d.Data d => d -> m d) ->All -> mAll Source # gmapMo ::MonadPlus m => (forall d.Data d => d -> m d) ->All -> mAll Source #
Ord AllSource #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods compare ::All ->All ->Ordering # (<) ::All ->All ->Bool # (<=) ::All ->All ->Bool # (>) ::All ->All ->Bool # (>=) ::All ->All ->Bool # max ::All ->All ->All # min ::All ->All ->All #
Read AllSource #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods readsPrec ::Int ->ReadS All Source # readList ::ReadS [All]Source # readPrec ::ReadPrec All Source # readListPrec ::ReadPrec [All]Source #
Show AllSource #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods showsPrec ::Int ->All ->ShowS Source # show ::All ->String Source # showList :: [All] ->ShowS Source #
Generic AllSource #
Instance details Defined inData.Semigroup.Internal Associated Types typeRep All ::Type ->Type Source # Methods from ::All ->Rep All xSource # to ::Rep All x ->All Source #
Semigroup AllSource #	Since: 4.9.0.0
Instance details Defined inData.Semigroup.Internal Methods (<>) ::All ->All ->All Source # sconcat ::NonEmpty All ->All Source # stimes ::Integral b => b ->All ->All Source #
Monoid AllSource #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods mempty ::All Source # mappend ::All ->All ->All Source # mconcat :: [All] ->All Source #
typeRep AllSource #	Since: 4.7.0.0
Instance details Defined inData.Semigroup.Internal typeRep All =D1 (MetaData "All" "Data.Semigroup.Internal" "base"True) (C1 (MetaCons "All"PrefixI True) (S1 (MetaSel (Just "getAll")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Bool)))

newtypeAny Source #

Boolean monoid under disjunction (||).

>>>getAny (Any True <> mempty <> Any False)True

>>>getAny (mconcat (map (\x -> Any (even x)) [2,4,6,7,8]))True

Constructors

Any
Fields getAny ::Bool

Instances

Bounded AnySource #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods minBound ::Any Source # maxBound ::Any Source #
Eq AnySource #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods (==) ::Any ->Any ->Bool # (/=) ::Any ->Any ->Bool #
Data AnySource #	Since: 4.8.0.0
Instance details Defined inData.Data Methods gfoldl :: (forall d b.Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) ->Any -> cAny Source # gunfold :: (forall b r.Data b => c (b -> r) -> c r) -> (forall r. r -> c r) ->Constr -> cAny Source # toConstr ::Any ->Constr Source # dataTypeOf ::Any ->DataType Source # dataCast1 ::Typeable t => (forall d.Data d => c (t d)) ->Maybe (cAny)Source # dataCast2 ::Typeable t => (forall d e. (Data d,Data e) => c (t d e)) ->Maybe (cAny)Source # gmapT :: (forall b.Data b => b -> b) ->Any ->Any Source # gmapQl :: (r -> r' -> r) -> r -> (forall d.Data d => d -> r') ->Any -> rSource # gmapQr :: (r' -> r -> r) -> r -> (forall d.Data d => d -> r') ->Any -> rSource # gmapQ :: (forall d.Data d => d -> u) ->Any -> [u]Source # gmapQi ::Int -> (forall d.Data d => d -> u) ->Any -> uSource # gmapM ::Monad m => (forall d.Data d => d -> m d) ->Any -> mAny Source # gmapMp ::MonadPlus m => (forall d.Data d => d -> m d) ->Any -> mAny Source # gmapMo ::MonadPlus m => (forall d.Data d => d -> m d) ->Any -> mAny Source #
Ord AnySource #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods compare ::Any ->Any ->Ordering # (<) ::Any ->Any ->Bool # (<=) ::Any ->Any ->Bool # (>) ::Any ->Any ->Bool # (>=) ::Any ->Any ->Bool # max ::Any ->Any ->Any # min ::Any ->Any ->Any #
Read AnySource #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods readsPrec ::Int ->ReadS Any Source # readList ::ReadS [Any]Source # readPrec ::ReadPrec Any Source # readListPrec ::ReadPrec [Any]Source #
Show AnySource #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods showsPrec ::Int ->Any ->ShowS Source # show ::Any ->String Source # showList :: [Any] ->ShowS Source #
Generic AnySource #
Instance details Defined inData.Semigroup.Internal Associated Types typeRep Any ::Type ->Type Source # Methods from ::Any ->Rep Any xSource # to ::Rep Any x ->Any Source #
Semigroup AnySource #	Since: 4.9.0.0
Instance details Defined inData.Semigroup.Internal Methods (<>) ::Any ->Any ->Any Source # sconcat ::NonEmpty Any ->Any Source # stimes ::Integral b => b ->Any ->Any Source #
Monoid AnySource #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods mempty ::Any Source # mappend ::Any ->Any ->Any Source # mconcat :: [Any] ->Any Source #
typeRep AnySource #	Since: 4.7.0.0
Instance details Defined inData.Semigroup.Internal typeRep Any =D1 (MetaData "Any" "Data.Semigroup.Internal" "base"True) (C1 (MetaCons "Any"PrefixI True) (S1 (MetaSel (Just "getAny")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Bool)))

`Num` wrappers

newtypeSum aSource #

Monoid under addition.

>>>getSum (Sum 1 <> Sum 2 <> mempty)3

Constructors

Sum
Fields getSum :: a

Instances

Monad SumSource #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods (>>=) ::Sum a -> (a ->Sum b) ->Sum bSource # (>>) ::Sum a ->Sum b ->Sum bSource # return :: a ->Sum aSource # fail ::String ->Sum aSource #
Functor SumSource #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods fmap :: (a -> b) ->Sum a ->Sum bSource # (<$) :: a ->Sum b ->Sum aSource #
MonadFix SumSource #	Since: 4.8.0.0
Instance details Defined inControl.Monad.Fix Methods mfix :: (a ->Sum a) ->Sum aSource #
Applicative SumSource #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods pure :: a ->Sum aSource # (<>) ::Sum (a -> b) ->Sum a ->Sum bSource # liftA2 :: (a -> b -> c) ->Sum a ->Sum b ->Sum cSource # (>) ::Sum a ->Sum b ->Sum bSource # (<*) ::Sum a ->Sum b ->Sum aSource #
Foldable SumSource #	Since: 4.8.0.0
Instance details Defined inData.Foldable Methods fold ::Monoid m =>Sum m -> mSource # foldMap ::Monoid m => (a -> m) ->Sum a -> mSource # foldr :: (a -> b -> b) -> b ->Sum a -> bSource # foldr' :: (a -> b -> b) -> b ->Sum a -> bSource # foldl :: (b -> a -> b) -> b ->Sum a -> bSource # foldl' :: (b -> a -> b) -> b ->Sum a -> bSource # foldr1 :: (a -> a -> a) ->Sum a -> aSource # foldl1 :: (a -> a -> a) ->Sum a -> aSource # toList ::Sum a -> [a]Source # null ::Sum a ->Bool Source # length ::Sum a ->Int Source # elem ::Eq a => a ->Sum a ->Bool Source # maximum ::Ord a =>Sum a -> aSource # minimum ::Ord a =>Sum a -> aSource # sum ::Num a =>Sum a -> aSource # product ::Num a =>Sum a -> aSource #
Traversable SumSource #	Since: 4.8.0.0
Instance details Defined inData.Traversable Methods traverse ::Applicative f => (a -> f b) ->Sum a -> f (Sum b)Source # sequenceA ::Applicative f =>Sum (f a) -> f (Sum a)Source # mapM ::Monad m => (a -> m b) ->Sum a -> m (Sum b)Source # sequence ::Monad m =>Sum (m a) -> m (Sum a)Source #
MonadZip SumSource #	Since: 4.8.0.0
Instance details Defined inControl.Monad.Zip Methods mzip ::Sum a ->Sum b ->Sum (a, b)Source # mzipWith :: (a -> b -> c) ->Sum a ->Sum b ->Sum cSource # munzip ::Sum (a, b) -> (Sum a,Sum b)Source #
Bounded a =>Bounded (Sum a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods minBound ::Sum aSource # maxBound ::Sum aSource #
Eq a =>Eq (Sum a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods (==) ::Sum a ->Sum a ->Bool # (/=) ::Sum a ->Sum a ->Bool #
Data a =>Data (Sum a)Source #	Since: 4.8.0.0
Instance details Defined inData.Data Methods gfoldl :: (forall d b.Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) ->Sum a -> c (Sum a)Source # gunfold :: (forall b r.Data b => c (b -> r) -> c r) -> (forall r. r -> c r) ->Constr -> c (Sum a)Source # toConstr ::Sum a ->Constr Source # dataTypeOf ::Sum a ->DataType Source # dataCast1 ::Typeable t => (forall d.Data d => c (t d)) ->Maybe (c (Sum a))Source # dataCast2 ::Typeable t => (forall d e. (Data d,Data e) => c (t d e)) ->Maybe (c (Sum a))Source # gmapT :: (forall b.Data b => b -> b) ->Sum a ->Sum aSource # gmapQl :: (r -> r' -> r) -> r -> (forall d.Data d => d -> r') ->Sum a -> rSource # gmapQr :: (r' -> r -> r) -> r -> (forall d.Data d => d -> r') ->Sum a -> rSource # gmapQ :: (forall d.Data d => d -> u) ->Sum a -> [u]Source # gmapQi ::Int -> (forall d.Data d => d -> u) ->Sum a -> uSource # gmapM ::Monad m => (forall d.Data d => d -> m d) ->Sum a -> m (Sum a)Source # gmapMp ::MonadPlus m => (forall d.Data d => d -> m d) ->Sum a -> m (Sum a)Source # gmapMo ::MonadPlus m => (forall d.Data d => d -> m d) ->Sum a -> m (Sum a)Source #
Num a =>Num (Sum a)Source #	Since: 4.7.0.0
Instance details Defined inData.Semigroup.Internal Methods (+) ::Sum a ->Sum a ->Sum aSource # (-) ::Sum a ->Sum a ->Sum aSource # (*) ::Sum a ->Sum a ->Sum aSource # negate ::Sum a ->Sum aSource # abs ::Sum a ->Sum aSource # signum ::Sum a ->Sum aSource # fromInteger ::Integer ->Sum aSource #
Ord a =>Ord (Sum a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods compare ::Sum a ->Sum a ->Ordering # (<) ::Sum a ->Sum a ->Bool # (<=) ::Sum a ->Sum a ->Bool # (>) ::Sum a ->Sum a ->Bool # (>=) ::Sum a ->Sum a ->Bool # max ::Sum a ->Sum a ->Sum a# min ::Sum a ->Sum a ->Sum a#
Read a =>Read (Sum a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods readsPrec ::Int ->ReadS (Sum a)Source # readList ::ReadS [Sum a]Source # readPrec ::ReadPrec (Sum a)Source # readListPrec ::ReadPrec [Sum a]Source #
Show a =>Show (Sum a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods showsPrec ::Int ->Sum a ->ShowS Source # show ::Sum a ->String Source # showList :: [Sum a] ->ShowS Source #
Generic (Sum a)Source #
Instance details Defined inData.Semigroup.Internal Associated Types typeRep (Sum a) ::Type ->Type Source # Methods from ::Sum a ->Rep (Sum a) xSource # to ::Rep (Sum a) x ->Sum aSource #
Num a =>Semigroup (Sum a)Source #	Since: 4.9.0.0
Instance details Defined inData.Semigroup.Internal Methods (<>) ::Sum a ->Sum a ->Sum aSource # sconcat ::NonEmpty (Sum a) ->Sum aSource # stimes ::Integral b => b ->Sum a ->Sum aSource #
Num a =>Monoid (Sum a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods mempty ::Sum aSource # mappend ::Sum a ->Sum a ->Sum aSource # mconcat :: [Sum a] ->Sum aSource #
Generic1 SumSource #
Instance details Defined inData.Semigroup.Internal Associated Types typeRep1 Sum :: k ->Type Source # Methods from1 ::Sum a ->Rep1 Sum aSource # to1 ::Rep1 Sum a ->Sum aSource #
typeRep (Sum a)Source #	Since: 4.7.0.0
Instance details Defined inData.Semigroup.Internal typeRep (Sum a) =D1 (MetaData "Sum" "Data.Semigroup.Internal" "base"True) (C1 (MetaCons "Sum"PrefixI True) (S1 (MetaSel (Just "getSum")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
typeRep1 SumSource #	Since: 4.7.0.0
Instance details Defined inData.Semigroup.Internal typeRep1 Sum =D1 (MetaData "Sum" "Data.Semigroup.Internal" "base"True) (C1 (MetaCons "Sum"PrefixI True) (S1 (MetaSel (Just "getSum")NoSourceUnpackedness NoSourceStrictness DecidedLazy)Par1))

newtypeProduct aSource #

Monoid under multiplication.

>>>getProduct (Product 3 <> Product 4 <> mempty)12

Constructors

Product
Fields getProduct :: a

Instances

Monad ProductSource #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods (>>=) ::Product a -> (a ->Product b) ->Product bSource # (>>) ::Product a ->Product b ->Product bSource # return :: a ->Product aSource # fail ::String ->Product aSource #
Functor ProductSource #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods fmap :: (a -> b) ->Product a ->Product bSource # (<$) :: a ->Product b ->Product aSource #
MonadFix ProductSource #	Since: 4.8.0.0
Instance details Defined inControl.Monad.Fix Methods mfix :: (a ->Product a) ->Product aSource #
Applicative ProductSource #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods pure :: a ->Product aSource # (<>) ::Product (a -> b) ->Product a ->Product bSource # liftA2 :: (a -> b -> c) ->Product a ->Product b ->Product cSource # (>) ::Product a ->Product b ->Product bSource # (<*) ::Product a ->Product b ->Product aSource #
Foldable ProductSource #	Since: 4.8.0.0
Instance details Defined inData.Foldable Methods fold ::Monoid m =>Product m -> mSource # foldMap ::Monoid m => (a -> m) ->Product a -> mSource # foldr :: (a -> b -> b) -> b ->Product a -> bSource # foldr' :: (a -> b -> b) -> b ->Product a -> bSource # foldl :: (b -> a -> b) -> b ->Product a -> bSource # foldl' :: (b -> a -> b) -> b ->Product a -> bSource # foldr1 :: (a -> a -> a) ->Product a -> aSource # foldl1 :: (a -> a -> a) ->Product a -> aSource # toList ::Product a -> [a]Source # null ::Product a ->Bool Source # length ::Product a ->Int Source # elem ::Eq a => a ->Product a ->Bool Source # maximum ::Ord a =>Product a -> aSource # minimum ::Ord a =>Product a -> aSource # sum ::Num a =>Product a -> aSource # product ::Num a =>Product a -> aSource #
Traversable ProductSource #	Since: 4.8.0.0
Instance details Defined inData.Traversable Methods traverse ::Applicative f => (a -> f b) ->Product a -> f (Product b)Source # sequenceA ::Applicative f =>Product (f a) -> f (Product a)Source # mapM ::Monad m => (a -> m b) ->Product a -> m (Product b)Source # sequence ::Monad m =>Product (m a) -> m (Product a)Source #
MonadZip ProductSource #	Since: 4.8.0.0
Instance details Defined inControl.Monad.Zip Methods mzip ::Product a ->Product b ->Product (a, b)Source # mzipWith :: (a -> b -> c) ->Product a ->Product b ->Product cSource # munzip ::Product (a, b) -> (Product a,Product b)Source #
Bounded a =>Bounded (Product a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods minBound ::Product aSource # maxBound ::Product aSource #
Eq a =>Eq (Product a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods (==) ::Product a ->Product a ->Bool # (/=) ::Product a ->Product a ->Bool #
Data a =>Data (Product a)Source #	Since: 4.8.0.0
Instance details Defined inData.Data Methods gfoldl :: (forall d b.Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) ->Product a -> c (Product a)Source # gunfold :: (forall b r.Data b => c (b -> r) -> c r) -> (forall r. r -> c r) ->Constr -> c (Product a)Source # toConstr ::Product a ->Constr Source # dataTypeOf ::Product a ->DataType Source # dataCast1 ::Typeable t => (forall d.Data d => c (t d)) ->Maybe (c (Product a))Source # dataCast2 ::Typeable t => (forall d e. (Data d,Data e) => c (t d e)) ->Maybe (c (Product a))Source # gmapT :: (forall b.Data b => b -> b) ->Product a ->Product aSource # gmapQl :: (r -> r' -> r) -> r -> (forall d.Data d => d -> r') ->Product a -> rSource # gmapQr :: (r' -> r -> r) -> r -> (forall d.Data d => d -> r') ->Product a -> rSource # gmapQ :: (forall d.Data d => d -> u) ->Product a -> [u]Source # gmapQi ::Int -> (forall d.Data d => d -> u) ->Product a -> uSource # gmapM ::Monad m => (forall d.Data d => d -> m d) ->Product a -> m (Product a)Source # gmapMp ::MonadPlus m => (forall d.Data d => d -> m d) ->Product a -> m (Product a)Source # gmapMo ::MonadPlus m => (forall d.Data d => d -> m d) ->Product a -> m (Product a)Source #
Num a =>Num (Product a)Source #	Since: 4.7.0.0
Instance details Defined inData.Semigroup.Internal Methods (+) ::Product a ->Product a ->Product aSource # (-) ::Product a ->Product a ->Product aSource # (*) ::Product a ->Product a ->Product aSource # negate ::Product a ->Product aSource # abs ::Product a ->Product aSource # signum ::Product a ->Product aSource # fromInteger ::Integer ->Product aSource #
Ord a =>Ord (Product a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods compare ::Product a ->Product a ->Ordering # (<) ::Product a ->Product a ->Bool # (<=) ::Product a ->Product a ->Bool # (>) ::Product a ->Product a ->Bool # (>=) ::Product a ->Product a ->Bool # max ::Product a ->Product a ->Product a# min ::Product a ->Product a ->Product a#
Read a =>Read (Product a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods readsPrec ::Int ->ReadS (Product a)Source # readList ::ReadS [Product a]Source # readPrec ::ReadPrec (Product a)Source # readListPrec ::ReadPrec [Product a]Source #
Show a =>Show (Product a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods showsPrec ::Int ->Product a ->ShowS Source # show ::Product a ->String Source # showList :: [Product a] ->ShowS Source #
Generic (Product a)Source #
Instance details Defined inData.Semigroup.Internal Associated Types typeRep (Product a) ::Type ->Type Source # Methods from ::Product a ->Rep (Product a) xSource # to ::Rep (Product a) x ->Product aSource #
Num a =>Semigroup (Product a)Source #	Since: 4.9.0.0
Instance details Defined inData.Semigroup.Internal Methods (<>) ::Product a ->Product a ->Product aSource # sconcat ::NonEmpty (Product a) ->Product aSource # stimes ::Integral b => b ->Product a ->Product aSource #
Num a =>Monoid (Product a)Source #	Since: 2.1
Instance details Defined inData.Semigroup.Internal Methods mempty ::Product aSource # mappend ::Product a ->Product a ->Product aSource # mconcat :: [Product a] ->Product aSource #
Generic1 ProductSource #
Instance details Defined inData.Semigroup.Internal Associated Types typeRep1 Product :: k ->Type Source # Methods from1 ::Product a ->Rep1 Product aSource # to1 ::Rep1 Product a ->Product aSource #
typeRep (Product a)Source #	Since: 4.7.0.0
Instance details Defined inData.Semigroup.Internal typeRep (Product a) =D1 (MetaData "Product" "Data.Semigroup.Internal" "base"True) (C1 (MetaCons "Product"PrefixI True) (S1 (MetaSel (Just "getProduct")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
typeRep1 ProductSource #	Since: 4.7.0.0
Instance details Defined inData.Semigroup.Internal typeRep1 Product =D1 (MetaData "Product" "Data.Semigroup.Internal" "base"True) (C1 (MetaCons "Product"PrefixI True) (S1 (MetaSel (Just "getProduct")NoSourceUnpackedness NoSourceStrictness DecidedLazy)Par1))

`Maybe` wrappers

To implementfind orfindLast on anyFoldable:

findLast :: Foldable t => (a -> Bool) -> t a -> Maybe afindLast pred = getLast . foldMap (x -> if pred x                                           then Last (Just x)                                           else Last Nothing)

Much of Data.Map's interface can be implemented with Data.Map.alter. Some of the rest can be implemented with a newalterA function and eitherFirst orLast:

alterA :: (Applicative f, Ord k) =>          (Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a)instance Monoid a => Applicative ((,) a)  -- from Control.Applicative

insertLookupWithKey :: Ord k => (k -> v -> v -> v) -> k -> v                    -> Map k v -> (Maybe v, Map k v)insertLookupWithKey combine key value =  Arrow.first getFirst . alterA doChange key  where  doChange Nothing = (First Nothing, Just value)  doChange (Just oldValue) =    (First (Just oldValue),     Just (combine key value oldValue))

newtypeFirst aSource #

Maybe monoid returning the leftmost non-Nothing value.

First a is isomorphic toAltMaybe a, but precedes it historically.

>>>getFirst (First (Just "hello") <> First Nothing <> First (Just "world"))Just "hello"

Use of this type is discouraged. Note the following equivalence:

Data.Monoid.First x === Maybe (Data.Semigroup.First x)

In addition to being equivalent in the structural sense, the two also haveMonoid instances that behave the same. This type will be marked deprecated in GHC 8.8, and removed in GHC 8.10. Users are advised to use the variant fromData.Semigroup and wrap it inMaybe.

Constructors

First
Fields getFirst ::Maybe a

Instances

Monad FirstSource #	Since: 4.8.0.0
Instance details Defined inData.Monoid Methods (>>=) ::First a -> (a ->First b) ->First bSource # (>>) ::First a ->First b ->First bSource # return :: a ->First aSource # fail ::String ->First aSource #
Functor FirstSource #	Since: 4.8.0.0
Instance details Defined inData.Monoid Methods fmap :: (a -> b) ->First a ->First bSource # (<$) :: a ->First b ->First aSource #
MonadFix FirstSource #	Since: 4.8.0.0
Instance details Defined inControl.Monad.Fix Methods mfix :: (a ->First a) ->First aSource #
Applicative FirstSource #	Since: 4.8.0.0
Instance details Defined inData.Monoid Methods pure :: a ->First aSource # (<>) ::First (a -> b) ->First a ->First bSource # liftA2 :: (a -> b -> c) ->First a ->First b ->First cSource # (>) ::First a ->First b ->First bSource # (<*) ::First a ->First b ->First aSource #
Foldable FirstSource #	Since: 4.8.0.0
Instance details Defined inData.Foldable Methods fold ::Monoid m =>First m -> mSource # foldMap ::Monoid m => (a -> m) ->First a -> mSource # foldr :: (a -> b -> b) -> b ->First a -> bSource # foldr' :: (a -> b -> b) -> b ->First a -> bSource # foldl :: (b -> a -> b) -> b ->First a -> bSource # foldl' :: (b -> a -> b) -> b ->First a -> bSource # foldr1 :: (a -> a -> a) ->First a -> aSource # foldl1 :: (a -> a -> a) ->First a -> aSource # toList ::First a -> [a]Source # null ::First a ->Bool Source # length ::First a ->Int Source # elem ::Eq a => a ->First a ->Bool Source # maximum ::Ord a =>First a -> aSource # minimum ::Ord a =>First a -> aSource # sum ::Num a =>First a -> aSource # product ::Num a =>First a -> aSource #
Traversable FirstSource #	Since: 4.8.0.0
Instance details Defined inData.Traversable Methods traverse ::Applicative f => (a -> f b) ->First a -> f (First b)Source # sequenceA ::Applicative f =>First (f a) -> f (First a)Source # mapM ::Monad m => (a -> m b) ->First a -> m (First b)Source # sequence ::Monad m =>First (m a) -> m (First a)Source #
MonadZip FirstSource #	Since: 4.8.0.0
Instance details Defined inControl.Monad.Zip Methods mzip ::First a ->First b ->First (a, b)Source # mzipWith :: (a -> b -> c) ->First a ->First b ->First cSource # munzip ::First (a, b) -> (First a,First b)Source #
Eq a =>Eq (First a)Source #	Since: 2.1
Instance details Defined inData.Monoid Methods (==) ::First a ->First a ->Bool # (/=) ::First a ->First a ->Bool #
Data a =>Data (First a)Source #	Since: 4.8.0.0
Instance details Defined inData.Data Methods gfoldl :: (forall d b.Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) ->First a -> c (First a)Source # gunfold :: (forall b r.Data b => c (b -> r) -> c r) -> (forall r. r -> c r) ->Constr -> c (First a)Source # toConstr ::First a ->Constr Source # dataTypeOf ::First a ->DataType Source # dataCast1 ::Typeable t => (forall d.Data d => c (t d)) ->Maybe (c (First a))Source # dataCast2 ::Typeable t => (forall d e. (Data d,Data e) => c (t d e)) ->Maybe (c (First a))Source # gmapT :: (forall b.Data b => b -> b) ->First a ->First aSource # gmapQl :: (r -> r' -> r) -> r -> (forall d.Data d => d -> r') ->First a -> rSource # gmapQr :: (r' -> r -> r) -> r -> (forall d.Data d => d -> r') ->First a -> rSource # gmapQ :: (forall d.Data d => d -> u) ->First a -> [u]Source # gmapQi ::Int -> (forall d.Data d => d -> u) ->First a -> uSource # gmapM ::Monad m => (forall d.Data d => d -> m d) ->First a -> m (First a)Source # gmapMp ::MonadPlus m => (forall d.Data d => d -> m d) ->First a -> m (First a)Source # gmapMo ::MonadPlus m => (forall d.Data d => d -> m d) ->First a -> m (First a)Source #
Ord a =>Ord (First a)Source #	Since: 2.1
Instance details Defined inData.Monoid Methods compare ::First a ->First a ->Ordering # (<) ::First a ->First a ->Bool # (<=) ::First a ->First a ->Bool # (>) ::First a ->First a ->Bool # (>=) ::First a ->First a ->Bool # max ::First a ->First a ->First a# min ::First a ->First a ->First a#
Read a =>Read (First a)Source #	Since: 2.1
Instance details Defined inData.Monoid Methods readsPrec ::Int ->ReadS (First a)Source # readList ::ReadS [First a]Source # readPrec ::ReadPrec (First a)Source # readListPrec ::ReadPrec [First a]Source #
Show a =>Show (First a)Source #	Since: 2.1
Instance details Defined inData.Monoid Methods showsPrec ::Int ->First a ->ShowS Source # show ::First a ->String Source # showList :: [First a] ->ShowS Source #
Generic (First a)Source #
Instance details Defined inData.Monoid Associated Types typeRep (First a) ::Type ->Type Source # Methods from ::First a ->Rep (First a) xSource # to ::Rep (First a) x ->First aSource #
Semigroup (First a)Source #	Since: 4.9.0.0
Instance details Defined inData.Monoid Methods (<>) ::First a ->First a ->First aSource # sconcat ::NonEmpty (First a) ->First aSource # stimes ::Integral b => b ->First a ->First aSource #
Monoid (First a)Source #	Since: 2.1
Instance details Defined inData.Monoid Methods mempty ::First aSource # mappend ::First a ->First a ->First aSource # mconcat :: [First a] ->First aSource #
Generic1 FirstSource #
Instance details Defined inData.Monoid Associated Types typeRep1 First :: k ->Type Source # Methods from1 ::First a ->Rep1 First aSource # to1 ::Rep1 First a ->First aSource #
typeRep (First a)Source #	Since: 4.7.0.0
Instance details Defined inData.Monoid typeRep (First a) =D1 (MetaData "First" "Data.Monoid" "base"True) (C1 (MetaCons "First"PrefixI True) (S1 (MetaSel (Just "getFirst")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe a))))
typeRep1 FirstSource #	Since: 4.7.0.0
Instance details Defined inData.Monoid typeRep1 First =D1 (MetaData "First" "Data.Monoid" "base"True) (C1 (MetaCons "First"PrefixI True) (S1 (MetaSel (Just "getFirst")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 Maybe)))

newtypeLast aSource #

Maybe monoid returning the rightmost non-Nothing value.

Last a is isomorphic toDual (First a), and thus toDual (AltMaybe a)

>>>getLast (Last (Just "hello") <> Last Nothing <> Last (Just "world"))Just "world"

Use of this type is discouraged. Note the following equivalence:

Data.Monoid.Last x === Maybe (Data.Semigroup.Last x)

Constructors

Last
Fields getLast ::Maybe a

Instances

Monad LastSource #	Since: 4.8.0.0
Instance details Defined inData.Monoid Methods (>>=) ::Last a -> (a ->Last b) ->Last bSource # (>>) ::Last a ->Last b ->Last bSource # return :: a ->Last aSource # fail ::String ->Last aSource #
Functor LastSource #	Since: 4.8.0.0
Instance details Defined inData.Monoid Methods fmap :: (a -> b) ->Last a ->Last bSource # (<$) :: a ->Last b ->Last aSource #
MonadFix LastSource #	Since: 4.8.0.0
Instance details Defined inControl.Monad.Fix Methods mfix :: (a ->Last a) ->Last aSource #
Applicative LastSource #	Since: 4.8.0.0
Instance details Defined inData.Monoid Methods pure :: a ->Last aSource # (<>) ::Last (a -> b) ->Last a ->Last bSource # liftA2 :: (a -> b -> c) ->Last a ->Last b ->Last cSource # (>) ::Last a ->Last b ->Last bSource # (<*) ::Last a ->Last b ->Last aSource #
Foldable LastSource #	Since: 4.8.0.0
Instance details Defined inData.Foldable Methods fold ::Monoid m =>Last m -> mSource # foldMap ::Monoid m => (a -> m) ->Last a -> mSource # foldr :: (a -> b -> b) -> b ->Last a -> bSource # foldr' :: (a -> b -> b) -> b ->Last a -> bSource # foldl :: (b -> a -> b) -> b ->Last a -> bSource # foldl' :: (b -> a -> b) -> b ->Last a -> bSource # foldr1 :: (a -> a -> a) ->Last a -> aSource # foldl1 :: (a -> a -> a) ->Last a -> aSource # toList ::Last a -> [a]Source # null ::Last a ->Bool Source # length ::Last a ->Int Source # elem ::Eq a => a ->Last a ->Bool Source # maximum ::Ord a =>Last a -> aSource # minimum ::Ord a =>Last a -> aSource # sum ::Num a =>Last a -> aSource # product ::Num a =>Last a -> aSource #
Traversable LastSource #	Since: 4.8.0.0
Instance details Defined inData.Traversable Methods traverse ::Applicative f => (a -> f b) ->Last a -> f (Last b)Source # sequenceA ::Applicative f =>Last (f a) -> f (Last a)Source # mapM ::Monad m => (a -> m b) ->Last a -> m (Last b)Source # sequence ::Monad m =>Last (m a) -> m (Last a)Source #
MonadZip LastSource #	Since: 4.8.0.0
Instance details Defined inControl.Monad.Zip Methods mzip ::Last a ->Last b ->Last (a, b)Source # mzipWith :: (a -> b -> c) ->Last a ->Last b ->Last cSource # munzip ::Last (a, b) -> (Last a,Last b)Source #
Eq a =>Eq (Last a)Source #	Since: 2.1
Instance details Defined inData.Monoid Methods (==) ::Last a ->Last a ->Bool # (/=) ::Last a ->Last a ->Bool #
Data a =>Data (Last a)Source #	Since: 4.8.0.0
Instance details Defined inData.Data Methods gfoldl :: (forall d b.Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) ->Last a -> c (Last a)Source # gunfold :: (forall b r.Data b => c (b -> r) -> c r) -> (forall r. r -> c r) ->Constr -> c (Last a)Source # toConstr ::Last a ->Constr Source # dataTypeOf ::Last a ->DataType Source # dataCast1 ::Typeable t => (forall d.Data d => c (t d)) ->Maybe (c (Last a))Source # dataCast2 ::Typeable t => (forall d e. (Data d,Data e) => c (t d e)) ->Maybe (c (Last a))Source # gmapT :: (forall b.Data b => b -> b) ->Last a ->Last aSource # gmapQl :: (r -> r' -> r) -> r -> (forall d.Data d => d -> r') ->Last a -> rSource # gmapQr :: (r' -> r -> r) -> r -> (forall d.Data d => d -> r') ->Last a -> rSource # gmapQ :: (forall d.Data d => d -> u) ->Last a -> [u]Source # gmapQi ::Int -> (forall d.Data d => d -> u) ->Last a -> uSource # gmapM ::Monad m => (forall d.Data d => d -> m d) ->Last a -> m (Last a)Source # gmapMp ::MonadPlus m => (forall d.Data d => d -> m d) ->Last a -> m (Last a)Source # gmapMo ::MonadPlus m => (forall d.Data d => d -> m d) ->Last a -> m (Last a)Source #
Ord a =>Ord (Last a)Source #	Since: 2.1
Instance details Defined inData.Monoid Methods compare ::Last a ->Last a ->Ordering # (<) ::Last a ->Last a ->Bool # (<=) ::Last a ->Last a ->Bool # (>) ::Last a ->Last a ->Bool # (>=) ::Last a ->Last a ->Bool # max ::Last a ->Last a ->Last a# min ::Last a ->Last a ->Last a#
Read a =>Read (Last a)Source #	Since: 2.1
Instance details Defined inData.Monoid Methods readsPrec ::Int ->ReadS (Last a)Source # readList ::ReadS [Last a]Source # readPrec ::ReadPrec (Last a)Source # readListPrec ::ReadPrec [Last a]Source #
Show a =>Show (Last a)Source #	Since: 2.1
Instance details Defined inData.Monoid Methods showsPrec ::Int ->Last a ->ShowS Source # show ::Last a ->String Source # showList :: [Last a] ->ShowS Source #
Generic (Last a)Source #
Instance details Defined inData.Monoid Associated Types typeRep (Last a) ::Type ->Type Source # Methods from ::Last a ->Rep (Last a) xSource # to ::Rep (Last a) x ->Last aSource #
Semigroup (Last a)Source #	Since: 4.9.0.0
Instance details Defined inData.Monoid Methods (<>) ::Last a ->Last a ->Last aSource # sconcat ::NonEmpty (Last a) ->Last aSource # stimes ::Integral b => b ->Last a ->Last aSource #
Monoid (Last a)Source #	Since: 2.1
Instance details Defined inData.Monoid Methods mempty ::Last aSource # mappend ::Last a ->Last a ->Last aSource # mconcat :: [Last a] ->Last aSource #
Generic1 LastSource #
Instance details Defined inData.Monoid Associated Types typeRep1 Last :: k ->Type Source # Methods from1 ::Last a ->Rep1 Last aSource # to1 ::Rep1 Last a ->Last aSource #
typeRep (Last a)Source #	Since: 4.7.0.0
Instance details Defined inData.Monoid typeRep (Last a) =D1 (MetaData "Last" "Data.Monoid" "base"True) (C1 (MetaCons "Last"PrefixI True) (S1 (MetaSel (Just "getLast")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe a))))
typeRep1 LastSource #	Since: 4.7.0.0
Instance details Defined inData.Monoid typeRep1 Last =D1 (MetaData "Last" "Data.Monoid" "base"True) (C1 (MetaCons "Last"PrefixI True) (S1 (MetaSel (Just "getLast")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 Maybe)))

`Alternative` wrapper

newtypeAlt f aSource #

Monoid under<|>.

Since: 4.8.0.0

Constructors

Alt
Fields getAlt :: f a

Instances

Generic1 (Alt f :: k ->Type)Source #
Instance details Defined inData.Semigroup.Internal Associated Types typeRep1 (Alt f) :: k ->Type Source # Methods from1 ::Alt f a ->Rep1 (Alt f) aSource # to1 ::Rep1 (Alt f) a ->Alt f aSource #
Monad f =>Monad (Alt f)Source #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods (>>=) ::Alt f a -> (a ->Alt f b) ->Alt f bSource # (>>) ::Alt f a ->Alt f b ->Alt f bSource # return :: a ->Alt f aSource # fail ::String ->Alt f aSource #
Functor f =>Functor (Alt f)Source #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods fmap :: (a -> b) ->Alt f a ->Alt f bSource # (<$) :: a ->Alt f b ->Alt f aSource #
MonadFix f =>MonadFix (Alt f)Source #	Since: 4.8.0.0
Instance details Defined inControl.Monad.Fix Methods mfix :: (a ->Alt f a) ->Alt f aSource #
Applicative f =>Applicative (Alt f)Source #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods pure :: a ->Alt f aSource # (<>) ::Alt f (a -> b) ->Alt f a ->Alt f bSource # liftA2 :: (a -> b -> c) ->Alt f a ->Alt f b ->Alt f cSource # (>) ::Alt f a ->Alt f b ->Alt f bSource # (<*) ::Alt f a ->Alt f b ->Alt f aSource #
Foldable f =>Foldable (Alt f)Source #	Since: 4.12.0.0
Instance details Defined inData.Foldable Methods fold ::Monoid m =>Alt f m -> mSource # foldMap ::Monoid m => (a -> m) ->Alt f a -> mSource # foldr :: (a -> b -> b) -> b ->Alt f a -> bSource # foldr' :: (a -> b -> b) -> b ->Alt f a -> bSource # foldl :: (b -> a -> b) -> b ->Alt f a -> bSource # foldl' :: (b -> a -> b) -> b ->Alt f a -> bSource # foldr1 :: (a -> a -> a) ->Alt f a -> aSource # foldl1 :: (a -> a -> a) ->Alt f a -> aSource # toList ::Alt f a -> [a]Source # null ::Alt f a ->Bool Source # length ::Alt f a ->Int Source # elem ::Eq a => a ->Alt f a ->Bool Source # maximum ::Ord a =>Alt f a -> aSource # minimum ::Ord a =>Alt f a -> aSource # sum ::Num a =>Alt f a -> aSource # product ::Num a =>Alt f a -> aSource #
Traversable f =>Traversable (Alt f)Source #	Since: 4.12.0.0
Instance details Defined inData.Traversable Methods traverse ::Applicative f0 => (a -> f0 b) ->Alt f a -> f0 (Alt f b)Source # sequenceA ::Applicative f0 =>Alt f (f0 a) -> f0 (Alt f a)Source # mapM ::Monad m => (a -> m b) ->Alt f a -> m (Alt f b)Source # sequence ::Monad m =>Alt f (m a) -> m (Alt f a)Source #
MonadPlus f =>MonadPlus (Alt f)Source #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods mzero ::Alt f aSource # mplus ::Alt f a ->Alt f a ->Alt f aSource #
Alternative f =>Alternative (Alt f)Source #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods empty ::Alt f aSource # (<\|>) ::Alt f a ->Alt f a ->Alt f aSource # some ::Alt f a ->Alt f [a]Source # many ::Alt f a ->Alt f [a]Source #
MonadZip f =>MonadZip (Alt f)Source #	Since: 4.8.0.0
Instance details Defined inControl.Monad.Zip Methods mzip ::Alt f a ->Alt f b ->Alt f (a, b)Source # mzipWith :: (a -> b -> c) ->Alt f a ->Alt f b ->Alt f cSource # munzip ::Alt f (a, b) -> (Alt f a,Alt f b)Source #
Contravariant f =>Contravariant (Alt f)Source #
Instance details Defined inData.Functor.Contravariant Methods contramap :: (a -> b) ->Alt f b ->Alt f aSource # (>$) :: b ->Alt f b ->Alt f aSource #
Enum (f a) =>Enum (Alt f a)Source #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods succ ::Alt f a ->Alt f aSource # pred ::Alt f a ->Alt f aSource # toEnum ::Int ->Alt f aSource # fromEnum ::Alt f a ->Int Source # enumFrom ::Alt f a -> [Alt f a]Source # enumFromThen ::Alt f a ->Alt f a -> [Alt f a]Source # enumFromTo ::Alt f a ->Alt f a -> [Alt f a]Source # enumFromThenTo ::Alt f a ->Alt f a ->Alt f a -> [Alt f a]Source #
Eq (f a) =>Eq (Alt f a)Source #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods (==) ::Alt f a ->Alt f a ->Bool # (/=) ::Alt f a ->Alt f a ->Bool #
(Data (f a),Data a,Typeable f) =>Data (Alt f a)Source #	Since: 4.8.0.0
Instance details Defined inData.Data Methods gfoldl :: (forall d b.Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) ->Alt f a -> c (Alt f a)Source # gunfold :: (forall b r.Data b => c (b -> r) -> c r) -> (forall r. r -> c r) ->Constr -> c (Alt f a)Source # toConstr ::Alt f a ->Constr Source # dataTypeOf ::Alt f a ->DataType Source # dataCast1 ::Typeable t => (forall d.Data d => c (t d)) ->Maybe (c (Alt f a))Source # dataCast2 ::Typeable t => (forall d e. (Data d,Data e) => c (t d e)) ->Maybe (c (Alt f a))Source # gmapT :: (forall b.Data b => b -> b) ->Alt f a ->Alt f aSource # gmapQl :: (r -> r' -> r) -> r -> (forall d.Data d => d -> r') ->Alt f a -> rSource # gmapQr :: (r' -> r -> r) -> r -> (forall d.Data d => d -> r') ->Alt f a -> rSource # gmapQ :: (forall d.Data d => d -> u) ->Alt f a -> [u]Source # gmapQi ::Int -> (forall d.Data d => d -> u) ->Alt f a -> uSource # gmapM ::Monad m => (forall d.Data d => d -> m d) ->Alt f a -> m (Alt f a)Source # gmapMp ::MonadPlus m => (forall d.Data d => d -> m d) ->Alt f a -> m (Alt f a)Source # gmapMo ::MonadPlus m => (forall d.Data d => d -> m d) ->Alt f a -> m (Alt f a)Source #
Num (f a) =>Num (Alt f a)Source #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods (+) ::Alt f a ->Alt f a ->Alt f aSource # (-) ::Alt f a ->Alt f a ->Alt f aSource # (*) ::Alt f a ->Alt f a ->Alt f aSource # negate ::Alt f a ->Alt f aSource # abs ::Alt f a ->Alt f aSource # signum ::Alt f a ->Alt f aSource # fromInteger ::Integer ->Alt f aSource #
Ord (f a) =>Ord (Alt f a)Source #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods compare ::Alt f a ->Alt f a ->Ordering # (<) ::Alt f a ->Alt f a ->Bool # (<=) ::Alt f a ->Alt f a ->Bool # (>) ::Alt f a ->Alt f a ->Bool # (>=) ::Alt f a ->Alt f a ->Bool # max ::Alt f a ->Alt f a ->Alt f a# min ::Alt f a ->Alt f a ->Alt f a#
Read (f a) =>Read (Alt f a)Source #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods readsPrec ::Int ->ReadS (Alt f a)Source # readList ::ReadS [Alt f a]Source # readPrec ::ReadPrec (Alt f a)Source # readListPrec ::ReadPrec [Alt f a]Source #
Show (f a) =>Show (Alt f a)Source #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods showsPrec ::Int ->Alt f a ->ShowS Source # show ::Alt f a ->String Source # showList :: [Alt f a] ->ShowS Source #
Generic (Alt f a)Source #
Instance details Defined inData.Semigroup.Internal Associated Types typeRep (Alt f a) ::Type ->Type Source # Methods from ::Alt f a ->Rep (Alt f a) xSource # to ::Rep (Alt f a) x ->Alt f aSource #
Alternative f =>Semigroup (Alt f a)Source #	Since: 4.9.0.0
Instance details Defined inData.Semigroup.Internal Methods (<>) ::Alt f a ->Alt f a ->Alt f aSource # sconcat ::NonEmpty (Alt f a) ->Alt f aSource # stimes ::Integral b => b ->Alt f a ->Alt f aSource #
Alternative f =>Monoid (Alt f a)Source #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods mempty ::Alt f aSource # mappend ::Alt f a ->Alt f a ->Alt f aSource # mconcat :: [Alt f a] ->Alt f aSource #
typeRep1 (Alt f :: k ->Type)Source #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal typeRep1 (Alt f :: k ->Type) =D1 (MetaData "Alt" "Data.Semigroup.Internal" "base"True) (C1 (MetaCons "Alt"PrefixI True) (S1 (MetaSel (Just "getAlt")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 f)))
typeRep (Alt f a)Source #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal typeRep (Alt f a) =D1 (MetaData "Alt" "Data.Semigroup.Internal" "base"True) (C1 (MetaCons "Alt"PrefixI True) (S1 (MetaSel (Just "getAlt")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f a))))

`Applicative` wrapper

newtypeAp f aSource #

This data type witnesses the lifting of aMonoid into anApplicative pointwise.

Since: 4.12.0.0

Constructors

Ap
Fields getAp :: f a

Instances

Generic1 (Ap f :: k ->Type)Source #
Instance details Defined inData.Monoid Associated Types typeRep1 (Ap f) :: k ->Type Source # Methods from1 ::Ap f a ->Rep1 (Ap f) aSource # to1 ::Rep1 (Ap f) a ->Ap f aSource #
Monad f =>Monad (Ap f)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid Methods (>>=) ::Ap f a -> (a ->Ap f b) ->Ap f bSource # (>>) ::Ap f a ->Ap f b ->Ap f bSource # return :: a ->Ap f aSource # fail ::String ->Ap f aSource #
Functor f =>Functor (Ap f)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid Methods fmap :: (a -> b) ->Ap f a ->Ap f bSource # (<$) :: a ->Ap f b ->Ap f aSource #
MonadFix f =>MonadFix (Ap f)Source #	Since: 4.12.0.0
Instance details Defined inControl.Monad.Fix Methods mfix :: (a ->Ap f a) ->Ap f aSource #
MonadFail f =>MonadFail (Ap f)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid Methods fail ::String ->Ap f aSource #
Applicative f =>Applicative (Ap f)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid Methods pure :: a ->Ap f aSource # (<>) ::Ap f (a -> b) ->Ap f a ->Ap f bSource # liftA2 :: (a -> b -> c) ->Ap f a ->Ap f b ->Ap f cSource # (>) ::Ap f a ->Ap f b ->Ap f bSource # (<*) ::Ap f a ->Ap f b ->Ap f aSource #
Foldable f =>Foldable (Ap f)Source #	Since: 4.12.0.0
Instance details Defined inData.Foldable Methods fold ::Monoid m =>Ap f m -> mSource # foldMap ::Monoid m => (a -> m) ->Ap f a -> mSource # foldr :: (a -> b -> b) -> b ->Ap f a -> bSource # foldr' :: (a -> b -> b) -> b ->Ap f a -> bSource # foldl :: (b -> a -> b) -> b ->Ap f a -> bSource # foldl' :: (b -> a -> b) -> b ->Ap f a -> bSource # foldr1 :: (a -> a -> a) ->Ap f a -> aSource # foldl1 :: (a -> a -> a) ->Ap f a -> aSource # toList ::Ap f a -> [a]Source # null ::Ap f a ->Bool Source # length ::Ap f a ->Int Source # elem ::Eq a => a ->Ap f a ->Bool Source # maximum ::Ord a =>Ap f a -> aSource # minimum ::Ord a =>Ap f a -> aSource # sum ::Num a =>Ap f a -> aSource # product ::Num a =>Ap f a -> aSource #
Traversable f =>Traversable (Ap f)Source #	Since: 4.12.0.0
Instance details Defined inData.Traversable Methods traverse ::Applicative f0 => (a -> f0 b) ->Ap f a -> f0 (Ap f b)Source # sequenceA ::Applicative f0 =>Ap f (f0 a) -> f0 (Ap f a)Source # mapM ::Monad m => (a -> m b) ->Ap f a -> m (Ap f b)Source # sequence ::Monad m =>Ap f (m a) -> m (Ap f a)Source #
MonadPlus f =>MonadPlus (Ap f)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid Methods mzero ::Ap f aSource # mplus ::Ap f a ->Ap f a ->Ap f aSource #
Alternative f =>Alternative (Ap f)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid Methods empty ::Ap f aSource # (<\|>) ::Ap f a ->Ap f a ->Ap f aSource # some ::Ap f a ->Ap f [a]Source # many ::Ap f a ->Ap f [a]Source #
(Applicative f,Bounded a) =>Bounded (Ap f a)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid Methods minBound ::Ap f aSource # maxBound ::Ap f aSource #
Enum (f a) =>Enum (Ap f a)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid Methods succ ::Ap f a ->Ap f aSource # pred ::Ap f a ->Ap f aSource # toEnum ::Int ->Ap f aSource # fromEnum ::Ap f a ->Int Source # enumFrom ::Ap f a -> [Ap f a]Source # enumFromThen ::Ap f a ->Ap f a -> [Ap f a]Source # enumFromTo ::Ap f a ->Ap f a -> [Ap f a]Source # enumFromThenTo ::Ap f a ->Ap f a ->Ap f a -> [Ap f a]Source #
Eq (f a) =>Eq (Ap f a)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid Methods (==) ::Ap f a ->Ap f a ->Bool # (/=) ::Ap f a ->Ap f a ->Bool #
(Data (f a),Data a,Typeable f) =>Data (Ap f a)Source #	Since: 4.12.0.0
Instance details Defined inData.Data Methods gfoldl :: (forall d b.Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) ->Ap f a -> c (Ap f a)Source # gunfold :: (forall b r.Data b => c (b -> r) -> c r) -> (forall r. r -> c r) ->Constr -> c (Ap f a)Source # toConstr ::Ap f a ->Constr Source # dataTypeOf ::Ap f a ->DataType Source # dataCast1 ::Typeable t => (forall d.Data d => c (t d)) ->Maybe (c (Ap f a))Source # dataCast2 ::Typeable t => (forall d e. (Data d,Data e) => c (t d e)) ->Maybe (c (Ap f a))Source # gmapT :: (forall b.Data b => b -> b) ->Ap f a ->Ap f aSource # gmapQl :: (r -> r' -> r) -> r -> (forall d.Data d => d -> r') ->Ap f a -> rSource # gmapQr :: (r' -> r -> r) -> r -> (forall d.Data d => d -> r') ->Ap f a -> rSource # gmapQ :: (forall d.Data d => d -> u) ->Ap f a -> [u]Source # gmapQi ::Int -> (forall d.Data d => d -> u) ->Ap f a -> uSource # gmapM ::Monad m => (forall d.Data d => d -> m d) ->Ap f a -> m (Ap f a)Source # gmapMp ::MonadPlus m => (forall d.Data d => d -> m d) ->Ap f a -> m (Ap f a)Source # gmapMo ::MonadPlus m => (forall d.Data d => d -> m d) ->Ap f a -> m (Ap f a)Source #
(Applicative f,Num a) =>Num (Ap f a)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid Methods (+) ::Ap f a ->Ap f a ->Ap f aSource # (-) ::Ap f a ->Ap f a ->Ap f aSource # (*) ::Ap f a ->Ap f a ->Ap f aSource # negate ::Ap f a ->Ap f aSource # abs ::Ap f a ->Ap f aSource # signum ::Ap f a ->Ap f aSource # fromInteger ::Integer ->Ap f aSource #
Ord (f a) =>Ord (Ap f a)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid Methods compare ::Ap f a ->Ap f a ->Ordering # (<) ::Ap f a ->Ap f a ->Bool # (<=) ::Ap f a ->Ap f a ->Bool # (>) ::Ap f a ->Ap f a ->Bool # (>=) ::Ap f a ->Ap f a ->Bool # max ::Ap f a ->Ap f a ->Ap f a# min ::Ap f a ->Ap f a ->Ap f a#
Read (f a) =>Read (Ap f a)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid Methods readsPrec ::Int ->ReadS (Ap f a)Source # readList ::ReadS [Ap f a]Source # readPrec ::ReadPrec (Ap f a)Source # readListPrec ::ReadPrec [Ap f a]Source #
Show (f a) =>Show (Ap f a)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid Methods showsPrec ::Int ->Ap f a ->ShowS Source # show ::Ap f a ->String Source # showList :: [Ap f a] ->ShowS Source #
Generic (Ap f a)Source #
Instance details Defined inData.Monoid Associated Types typeRep (Ap f a) ::Type ->Type Source # Methods from ::Ap f a ->Rep (Ap f a) xSource # to ::Rep (Ap f a) x ->Ap f aSource #
(Applicative f,Semigroup a) =>Semigroup (Ap f a)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid Methods (<>) ::Ap f a ->Ap f a ->Ap f aSource # sconcat ::NonEmpty (Ap f a) ->Ap f aSource # stimes ::Integral b => b ->Ap f a ->Ap f aSource #
(Applicative f,Monoid a) =>Monoid (Ap f a)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid Methods mempty ::Ap f aSource # mappend ::Ap f a ->Ap f a ->Ap f aSource # mconcat :: [Ap f a] ->Ap f aSource #
typeRep1 (Ap f :: k ->Type)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid typeRep1 (Ap f :: k ->Type) =D1 (MetaData "Ap" "Data.Monoid" "base"True) (C1 (MetaCons "Ap"PrefixI True) (S1 (MetaSel (Just "getAp")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 f)))
typeRep (Ap f a)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid typeRep (Ap f a) =D1 (MetaData "Ap" "Data.Monoid" "base"True) (C1 (MetaCons "Ap"PrefixI True) (S1 (MetaSel (Just "getAp")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f a))))

Movatterモバイル変換

Monoid typeclass

Bool wrappers

Num wrappers

Maybe wrappers

Alternative wrapper

Applicative wrapper

`Monoid` typeclass

`Bool` wrappers

`Num` wrappers

`Maybe` wrappers

`Alternative` wrapper

`Applicative` wrapper