Copyright	[2016..2017] Trevor L. McDonell
License	BSD3
Maintainer	Trevor L. McDonell <tmcdonell@cse.unsw.edu.au>
Stability	experimental
Portability	non-portable (GHC extensions)
Safe Haskell	None
Language	Haskell98

Data.Array.Accelerate.Data.Monoid

Contents

Orphan instances

Description

Monoid instances for Accelerate

Since: 1.2.0.0

Synopsis

class Semigroup a => Monoid a where
(<>) :: Semigroup a => a -> a -> a
newtype Sum a = Sum {
- getSum :: a
}
newtype Product a = Product {
- getProduct :: a
}

Documentation

class Semigroup a => Monoid a where #

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

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

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

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

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

Minimal complete definition

mempty

Methods

mempty :: a #

Identity of mappend

mappend :: a -> a -> a #

An associative operation

NOTE: This method is redundant and has the default implementation mappend = '(<>)' since base-4.11.0.0.

mconcat :: [a] -> a #

Fold a list using the monoid.

For most types, the default definition for mconcat 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 Ordering	Since: 2.1
Instance details Methods mempty :: Ordering # mappend :: Ordering -> Ordering -> Ordering # mconcat :: [Ordering] -> Ordering #
Monoid ()	Since: 2.1
Instance details Methods mempty :: () # mappend :: () -> () -> () # mconcat :: [()] -> () #
Monoid Doc
Instance details Methods mempty :: Doc # mappend :: Doc -> Doc -> Doc # mconcat :: [Doc] -> Doc #
Monoid All	Since: 2.1
Instance details Methods mempty :: All # mappend :: All -> All -> All # mconcat :: [All] -> All #
Monoid Any	Since: 2.1
Instance details Methods mempty :: Any # mappend :: Any -> Any -> Any # mconcat :: [Any] -> Any #
Monoid String
Instance details Methods mempty :: String # mappend :: String -> String -> String # mconcat :: [String] -> String #
Monoid ShortByteString
Instance details Methods mempty :: ShortByteString # mappend :: ShortByteString -> ShortByteString -> ShortByteString # mconcat :: [ShortByteString] -> ShortByteString #
Monoid ByteString
Instance details Methods mempty :: ByteString # mappend :: ByteString -> ByteString -> ByteString # mconcat :: [ByteString] -> ByteString #
Monoid ByteString
Instance details Methods mempty :: ByteString # mappend :: ByteString -> ByteString -> ByteString # mconcat :: [ByteString] -> ByteString #
Monoid Builder
Instance details Methods mempty :: Builder # mappend :: Builder -> Builder -> Builder # mconcat :: [Builder] -> Builder #
Monoid IntSet
Instance details Methods mempty :: IntSet # mappend :: IntSet -> IntSet -> IntSet # mconcat :: [IntSet] -> IntSet #
Monoid ParseError
Instance details Methods mempty :: ParseError # mappend :: ParseError -> ParseError -> ParseError # mconcat :: [ParseError] -> ParseError #
Monoid Completer
Instance details Methods mempty :: Completer # mappend :: Completer -> Completer -> Completer # mconcat :: [Completer] -> Completer #
Monoid Doc
Instance details Methods mempty :: Doc # mappend :: Doc -> Doc -> Doc # mconcat :: [Doc] -> Doc #
Monoid OptionSet	Later options override earlier ones
Instance details Methods mempty :: OptionSet # mappend :: OptionSet -> OptionSet -> OptionSet # mconcat :: [OptionSet] -> OptionSet #
Monoid Slot
Instance details Methods mempty :: Slot # mappend :: Slot -> Slot -> Slot # mconcat :: [Slot] -> Slot #
a :=> (Monoid (Dict a))
Instance details Methods ins :: a :- Monoid (Dict a) #
() :=> (Monoid [a])
Instance details Methods ins :: () :- Monoid [a] #
() :=> (Monoid Ordering)
Instance details Methods ins :: () :- Monoid Ordering #
() :=> (Monoid ())
Instance details Methods ins :: () :- Monoid () #
Monoid [a]	Since: 2.1
Instance details Methods mempty :: [a] # mappend :: [a] -> [a] -> [a] # mconcat :: [[a]] -> [a] #
Semigroup a => Monoid (Maybe a)	Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `ee = e` and `es = s = se` for all `s ∈ S`." Since 4.11.0: constraint on inner `a` value generalised from `Monoid` to `Semigroup`. Since: 2.1*
Instance details Methods mempty :: Maybe a # mappend :: Maybe a -> Maybe a -> Maybe a # mconcat :: [Maybe a] -> Maybe a #
Monoid a => Monoid (IO a)	Since: 4.9.0.0
Instance details Methods mempty :: IO a # mappend :: IO a -> IO a -> IO a # mconcat :: [IO a] -> IO a #
(Ord a, Bounded a) => Monoid (Min a)	Since: 4.9.0.0
Instance details Methods mempty :: Min a # mappend :: Min a -> Min a -> Min a # mconcat :: [Min a] -> Min a #
(Ord a, Bounded a) => Monoid (Max a)	Since: 4.9.0.0
Instance details Methods mempty :: Max a # mappend :: Max a -> Max a -> Max a # mconcat :: [Max a] -> Max a #
Monoid m => Monoid (WrappedMonoid m)	Since: 4.9.0.0
Instance details Methods mempty :: WrappedMonoid m # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # mconcat :: [WrappedMonoid m] -> WrappedMonoid m #
Semigroup a => Monoid (Option a)	Since: 4.9.0.0
Instance details Methods mempty :: Option a # mappend :: Option a -> Option a -> Option a # mconcat :: [Option a] -> Option a #
Monoid a => Monoid (Identity a)
Instance details Methods mempty :: Identity a # mappend :: Identity a -> Identity a -> Identity a # mconcat :: [Identity a] -> Identity a #
Monoid (First a)	Since: 2.1
Instance details Methods mempty :: First a # mappend :: First a -> First a -> First a # mconcat :: [First a] -> First a #
Monoid (Last a)	Since: 2.1
Instance details Methods mempty :: Last a # mappend :: Last a -> Last a -> Last a # mconcat :: [Last a] -> Last a #
Monoid a => Monoid (Dual a)	Since: 2.1
Instance details Methods mempty :: Dual a # mappend :: Dual a -> Dual a -> Dual a # mconcat :: [Dual a] -> Dual a #
Monoid (Endo a)	Since: 2.1
Instance details Methods mempty :: Endo a # mappend :: Endo a -> Endo a -> Endo a # mconcat :: [Endo a] -> Endo a #
Num a => Monoid (Sum a)	Since: 2.1
Instance details Methods mempty :: Sum a # mappend :: Sum a -> Sum a -> Sum a # mconcat :: [Sum a] -> Sum a #
Num a => Monoid (Product a)	Since: 2.1
Instance details Methods mempty :: Product a # mappend :: Product a -> Product a -> Product a # mconcat :: [Product a] -> Product a #
Monoid a => Monoid (Down a)	Since: 4.11.0.0
Instance details Methods mempty :: Down a # mappend :: Down a -> Down a -> Down a # mconcat :: [Down a] -> Down a #
PrimType ty => Monoid (UArray ty)
Instance details Methods mempty :: UArray ty # mappend :: UArray ty -> UArray ty -> UArray ty # mconcat :: [UArray ty] -> UArray ty #
PrimType ty => Monoid (Block ty)
Instance details Methods mempty :: Block ty # mappend :: Block ty -> Block ty -> Block ty # mconcat :: [Block ty] -> Block ty #
Monoid (CountOf ty)
Instance details Methods mempty :: CountOf ty # mappend :: CountOf ty -> CountOf ty -> CountOf ty # mconcat :: [CountOf ty] -> CountOf ty #
Num a => Monoid (Colour a)
Instance details Methods mempty :: Colour a # mappend :: Colour a -> Colour a -> Colour a # mconcat :: [Colour a] -> Colour a #
Num a => Monoid (AlphaColour a)
Instance details Methods mempty :: AlphaColour a # mappend :: AlphaColour a -> AlphaColour a -> AlphaColour a # mconcat :: [AlphaColour a] -> AlphaColour a #
a => Monoid (Dict a)
Instance details Methods mempty :: Dict a # mappend :: Dict a -> Dict a -> Dict a # mconcat :: [Dict a] -> Dict a #
Monoid (IntMap a)
Instance details Methods mempty :: IntMap a # mappend :: IntMap a -> IntMap a -> IntMap a # mconcat :: [IntMap a] -> IntMap a #
Monoid (Seq a)
Instance details Methods mempty :: Seq a # mappend :: Seq a -> Seq a -> Seq a # mconcat :: [Seq a] -> Seq a #
Ord a => Monoid (Set a)
Instance details Methods mempty :: Set a # mappend :: Set a -> Set a -> Set a # mconcat :: [Set a] -> Set a #
Monoid (Predicate a)
Instance details Methods mempty :: Predicate a # mappend :: Predicate a -> Predicate a -> Predicate a # mconcat :: [Predicate a] -> Predicate a #
Monoid (Comparison a)
Instance details Methods mempty :: Comparison a # mappend :: Comparison a -> Comparison a -> Comparison a # mconcat :: [Comparison a] -> Comparison a #
Monoid (Equivalence a)
Instance details Methods mempty :: Equivalence a # mappend :: Equivalence a -> Equivalence a -> Equivalence a # mconcat :: [Equivalence a] -> Equivalence a #
Prim a => Monoid (Vector a)
Instance details Methods mempty :: Vector a # mappend :: Vector a -> Vector a -> Vector a # mconcat :: [Vector a] -> Vector a #
Storable a => Monoid (Vector a)
Instance details Methods mempty :: Vector a # mappend :: Vector a -> Vector a -> Vector a # mconcat :: [Vector a] -> Vector a #
(Hashable a, Eq a) => Monoid (HashSet a)
Instance details Methods mempty :: HashSet a # mappend :: HashSet a -> HashSet a -> HashSet a # mconcat :: [HashSet a] -> HashSet a #
Monoid (Vector a)
Instance details Methods mempty :: Vector a # mappend :: Vector a -> Vector a -> Vector a # mconcat :: [Vector a] -> Vector a #
Ord a => Monoid (Min a)
Instance details Methods mempty :: Min a # mappend :: Min a -> Min a -> Min a # mconcat :: [Min a] -> Min a #
Ord a => Monoid (Max a)
Instance details Methods mempty :: Max a # mappend :: Max a -> Max a -> Max a # mconcat :: [Max a] -> Max a #
Monoid (Leftmost a)
Instance details Methods mempty :: Leftmost a # mappend :: Leftmost a -> Leftmost a -> Leftmost a # mconcat :: [Leftmost a] -> Leftmost a #
Monoid (Rightmost a)
Instance details Methods mempty :: Rightmost a # mappend :: Rightmost a -> Rightmost a -> Rightmost a # mconcat :: [Rightmost a] -> Rightmost a #
Monoid (Doc a)
Instance details Methods mempty :: Doc a # mappend :: Doc a -> Doc a -> Doc a # mconcat :: [Doc a] -> Doc a #
Monoid (Array a)
Instance details Methods mempty :: Array a # mappend :: Array a -> Array a -> Array a # mconcat :: [Array a] -> Array a #
Monoid (Doc a)
Instance details Methods mempty :: Doc a # mappend :: Doc a -> Doc a -> Doc a # mconcat :: [Doc a] -> Doc a #
Monoid (MergeSet a)
Instance details Methods mempty :: MergeSet a # mappend :: MergeSet a -> MergeSet a -> MergeSet a # mconcat :: [MergeSet a] -> MergeSet a #
(Monoid (Exp a), Elt a) => Monoid (Exp (Maybe a)) #
Instance details Methods mempty :: Exp (Maybe a) # mappend :: Exp (Maybe a) -> Exp (Maybe a) -> Exp (Maybe a) # mconcat :: [Exp (Maybe a)] -> Exp (Maybe a) #
Monoid (Exp ()) #
Instance details Methods mempty :: Exp () # mappend :: Exp () -> Exp () -> Exp () # mconcat :: [Exp ()] -> Exp () #
(Elt a, Elt b, Monoid (Exp a), Monoid (Exp b)) => Monoid (Exp (a, b)) #
Instance details Methods mempty :: Exp (a, b) # mappend :: Exp (a, b) -> Exp (a, b) -> Exp (a, b) # mconcat :: [Exp (a, b)] -> Exp (a, b) #
(Elt a, Elt b, Elt c, Monoid (Exp a), Monoid (Exp b), Monoid (Exp c)) => Monoid (Exp (a, b, c)) #
Instance details Methods mempty :: Exp (a, b, c) # mappend :: Exp (a, b, c) -> Exp (a, b, c) -> Exp (a, b, c) # mconcat :: [Exp (a, b, c)] -> Exp (a, b, c) #
(Elt a, Elt b, Elt c, Elt d, Monoid (Exp a), Monoid (Exp b), Monoid (Exp c), Monoid (Exp d)) => Monoid (Exp (a, b, c, d)) #
Instance details Methods mempty :: Exp (a, b, c, d) # mappend :: Exp (a, b, c, d) -> Exp (a, b, c, d) -> Exp (a, b, c, d) # mconcat :: [Exp (a, b, c, d)] -> Exp (a, b, c, d) #
(Elt a, Elt b, Elt c, Elt d, Elt e, Monoid (Exp a), Monoid (Exp b), Monoid (Exp c), Monoid (Exp d), Monoid (Exp e)) => Monoid (Exp (a, b, c, d, e)) #
Instance details Methods mempty :: Exp (a, b, c, d, e) # mappend :: Exp (a, b, c, d, e) -> Exp (a, b, c, d, e) -> Exp (a, b, c, d, e) # mconcat :: [Exp (a, b, c, d, e)] -> Exp (a, b, c, d, e) #
(Ord a, Bounded a) => Monoid (Exp (Min a)) #
Instance details Methods mempty :: Exp (Min a) # mappend :: Exp (Min a) -> Exp (Min a) -> Exp (Min a) # mconcat :: [Exp (Min a)] -> Exp (Min a) #
(Ord a, Bounded a) => Monoid (Exp (Max a)) #
Instance details Methods mempty :: Exp (Max a) # mappend :: Exp (Max a) -> Exp (Max a) -> Exp (Max a) # mconcat :: [Exp (Max a)] -> Exp (Max a) #
Num a => Monoid (Exp (Sum a)) #
Instance details Methods mempty :: Exp (Sum a) # mappend :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a) # mconcat :: [Exp (Sum a)] -> Exp (Sum a) #
Num a => Monoid (Exp (Product a)) #
Instance details Methods mempty :: Exp (Product a) # mappend :: Exp (Product a) -> Exp (Product a) -> Exp (Product a) # mconcat :: [Exp (Product a)] -> Exp (Product a) #
Class (Semigroup a) (Monoid a)
Instance details Methods cls :: Monoid a :- Semigroup a #
(Monoid a) :=> (Monoid (Maybe a))
Instance details Methods ins :: Monoid a :- Monoid (Maybe a) #
(Monoid a) :=> (Monoid (Const a b))
Instance details Methods ins :: Monoid a :- Monoid (Const a b) #
(Monoid a) :=> (Monoid (Identity a))
Instance details Methods ins :: Monoid a :- Monoid (Identity a) #
(Monoid a) :=> (Monoid (IO a))
Instance details Methods ins :: Monoid a :- Monoid (IO a) #
(Monoid a) :=> (Applicative ((,) a))
Instance details Methods ins :: Monoid a :- Applicative ((,) a) #
(Monoid a) :=> (Applicative (Const a :: * -> *))
Instance details Methods ins :: Monoid a :- Applicative (Const a) #
Monoid b => Monoid (a -> b)	Since: 2.1
Instance details Methods mempty :: a -> b # mappend :: (a -> b) -> (a -> b) -> a -> b # mconcat :: [a -> b] -> a -> b #
(Monoid a, Monoid b) => Monoid (a, b)	Since: 2.1
Instance details Methods mempty :: (a, b) # mappend :: (a, b) -> (a, b) -> (a, b) # mconcat :: [(a, b)] -> (a, b) #
Monoid a => Monoid (Op a b)
Instance details Methods mempty :: Op a b # mappend :: Op a b -> Op a b -> Op a b # mconcat :: [Op a b] -> Op a b #
Monoid (Proxy s)	Since: 4.7.0.0
Instance details Methods mempty :: Proxy s # mappend :: Proxy s -> Proxy s -> Proxy s # mconcat :: [Proxy s] -> Proxy s #
Ord k => Monoid (Map k v)
Instance details Methods mempty :: Map k v # mappend :: Map k v -> Map k v -> Map k v # mconcat :: [Map k v] -> Map k v #
(Monad m, Monoid a) => Monoid (GenT m a)
Instance details Methods mempty :: GenT m a # mappend :: GenT m a -> GenT m a -> GenT m a # mconcat :: [GenT m a] -> GenT m a #
(Eq k, Hashable k) => Monoid (HashMap k v)
Instance details Methods mempty :: HashMap k v # mappend :: HashMap k v -> HashMap k v -> HashMap k v # mconcat :: [HashMap k v] -> HashMap k v #
Monoid (ReifiedFold s a)
Instance details Methods mempty :: ReifiedFold s a # mappend :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a # mconcat :: [ReifiedFold s a] -> ReifiedFold s a #
Monoid (Deepening i a)	This is an illegal `Monoid`.
Instance details Methods mempty :: Deepening i a # mappend :: Deepening i a -> Deepening i a -> Deepening i a # mconcat :: [Deepening i a] -> Deepening i a #
Monoid (f a) => Monoid (Indexing f a)	`>>>` `"cat" ^@.. (folded <> folded)`[(0,'c'),(1,'a'),(2,'t'),(0,'c'),(1,'a'),(2,'t')] `>>>` `"cat" ^@.. indexing (folded <> folded)`[(0,'c'),(1,'a'),(2,'t'),(3,'c'),(4,'a'),(5,'t')]
Instance details Methods mempty :: Indexing f a # mappend :: Indexing f a -> Indexing f a -> Indexing f a # mconcat :: [Indexing f a] -> Indexing f a #
(Contravariant f, Applicative f) => Monoid (Folding f a)
Instance details Methods mempty :: Folding f a # mappend :: Folding f a -> Folding f a -> Folding f a # mconcat :: [Folding f a] -> Folding f a #
Applicative f => Monoid (Traversed a f)
Instance details Methods mempty :: Traversed a f # mappend :: Traversed a f -> Traversed a f -> Traversed a f # mconcat :: [Traversed a f] -> Traversed a f #
(Apply f, Applicative f) => Monoid (TraversedF a f)
Instance details Methods mempty :: TraversedF a f # mappend :: TraversedF a f -> TraversedF a f -> TraversedF a f # mconcat :: [TraversedF a f] -> TraversedF a f #
Monad m => Monoid (Sequenced a m)
Instance details Methods mempty :: Sequenced a m # mappend :: Sequenced a m -> Sequenced a m -> Sequenced a m # mconcat :: [Sequenced a m] -> Sequenced a m #
(Monoid a, Monoid b) :=> (Monoid (a, b))
Instance details Methods ins :: (Monoid a, Monoid b) :- Monoid (a, b) #
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)	Since: 2.1
Instance details Methods mempty :: (a, b, c) # mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) # mconcat :: [(a, b, c)] -> (a, b, c) #
Monoid a => Monoid (Const a b)
Instance details Methods mempty :: Const a b # mappend :: Const a b -> Const a b -> Const a b # mconcat :: [Const a b] -> Const a b #
Alternative f => Monoid (Alt f a)	Since: 4.8.0.0
Instance details Methods mempty :: Alt f a # mappend :: Alt f a -> Alt f a -> Alt f a # mconcat :: [Alt f a] -> Alt f a #
Monoid (ReifiedIndexedFold i s a)
Instance details Methods mempty :: ReifiedIndexedFold i s a # mappend :: ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a # mconcat :: [ReifiedIndexedFold i s a] -> ReifiedIndexedFold i s a #
Reifies s (ReifiedMonoid a) => Monoid (ReflectedMonoid a s)
Instance details Methods mempty :: ReflectedMonoid a s # mappend :: ReflectedMonoid a s -> ReflectedMonoid a s -> ReflectedMonoid a s # mconcat :: [ReflectedMonoid a s] -> ReflectedMonoid a s #
(Semigroup a, Monoid a) => Monoid (Tagged s a)
Instance details Methods mempty :: Tagged s a # mappend :: Tagged s a -> Tagged s a -> Tagged s a # mconcat :: [Tagged s a] -> Tagged s a #
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d)	Since: 2.1
Instance details Methods mempty :: (a, b, c, d) # mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # mconcat :: [(a, b, c, d)] -> (a, b, c, d) #
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e)	Since: 2.1
Instance details 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) #
Contravariant g => Monoid (BazaarT p g a b t)
Instance details Methods mempty :: BazaarT p g a b t # mappend :: BazaarT p g a b t -> BazaarT p g a b t -> BazaarT p g a b t # mconcat :: [BazaarT p g a b t] -> BazaarT p g a b t #

(<>) :: Semigroup a => a -> a -> a infixr 6 #

An associative operation.

newtype Sum a #

Monoid under addition.

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

Constructors

Sum
Fields getSum :: a

Instances

Monad Sum	Since: 4.8.0.0
Instance details Methods (>>=) :: Sum a -> (a -> Sum b) -> Sum b # (>>) :: Sum a -> Sum b -> Sum b # return :: a -> Sum a # fail :: String -> Sum a #
Functor Sum	Since: 4.8.0.0
Instance details Methods fmap :: (a -> b) -> Sum a -> Sum b # (<$) :: a -> Sum b -> Sum a #
MonadFix Sum	Since: 4.8.0.0
Instance details Methods mfix :: (a -> Sum a) -> Sum a #
Applicative Sum	Since: 4.8.0.0
Instance details Methods pure :: a -> Sum a # (<>) :: Sum (a -> b) -> Sum a -> Sum b # liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c # (>) :: Sum a -> Sum b -> Sum b # (<*) :: Sum a -> Sum b -> Sum a #
Foldable Sum	Since: 4.8.0.0
Instance details Methods fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> m # foldr :: (a -> b -> b) -> b -> Sum a -> b # foldr' :: (a -> b -> b) -> b -> Sum a -> b # foldl :: (b -> a -> b) -> b -> Sum a -> b # foldl' :: (b -> a -> b) -> b -> Sum a -> b # foldr1 :: (a -> a -> a) -> Sum a -> a # foldl1 :: (a -> a -> a) -> Sum a -> a # toList :: Sum a -> [a] # null :: Sum a -> Bool # length :: Sum a -> Int # elem :: Eq a => a -> Sum a -> Bool # maximum :: Ord a => Sum a -> a # minimum :: Ord a => Sum a -> a # sum :: Num a => Sum a -> a # product :: Num a => Sum a -> a #
Traversable Sum	Since: 4.8.0.0
Instance details Methods traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) # sequenceA :: Applicative f => Sum (f a) -> f (Sum a) # mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) # sequence :: Monad m => Sum (m a) -> m (Sum a) #
Representable Sum
Instance details Associated Types type Rep Sum :: * # Methods tabulate :: (Rep Sum -> a) -> Sum a # index :: Sum a -> Rep Sum -> a #
NFData1 Sum	Since: 1.4.3.0
Instance details Methods liftRnf :: (a -> ()) -> Sum a -> () #
Functor Sum Source #
Instance details Methods fmap :: (Elt a, Elt b, Elt (Sum a), Elt (Sum b)) => (Exp a -> Exp b) -> Exp (Sum a) -> Exp (Sum b) Source # (<$) :: (Elt a, Elt b, Elt (Sum a), Elt (Sum b)) => Exp a -> Exp (Sum b) -> Exp (Sum a) Source #
Elt a => Unlift Exp (Sum (Exp a)) Source #
Instance details Methods unlift :: Exp (Plain (Sum (Exp a))) -> Sum (Exp a) Source #
(Lift Exp a, Elt (Plain a)) => Lift Exp (Sum a) Source #
Instance details Associated Types type Plain (Sum a) :: * Source # Methods lift :: Sum a -> Exp (Plain (Sum a)) Source #
Bounded a => Bounded (Sum a)
Instance details Methods minBound :: Sum a # maxBound :: Sum a #
Bounded a => Bounded (Exp (Sum a)) #
Instance details Methods minBound :: Exp (Sum a) # maxBound :: Exp (Sum a) #
Eq a => Eq (Sum a)
Instance details Methods (==) :: Sum a -> Sum a -> Bool # (/=) :: Sum a -> Sum a -> Bool #
Num a => Num (Sum a)
Instance details Methods (+) :: Sum a -> Sum a -> Sum a # (-) :: Sum a -> Sum a -> Sum a # (*) :: Sum a -> Sum a -> Sum a # negate :: Sum a -> Sum a # abs :: Sum a -> Sum a # signum :: Sum a -> Sum a # fromInteger :: Integer -> Sum a #
Num a => Num (Exp (Sum a)) #
Instance details Methods (+) :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a) # (-) :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a) # (*) :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a) # negate :: Exp (Sum a) -> Exp (Sum a) # abs :: Exp (Sum a) -> Exp (Sum a) # signum :: Exp (Sum a) -> Exp (Sum a) # fromInteger :: Integer -> Exp (Sum a) #
Ord a => Ord (Sum a)
Instance details 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)
Instance details Methods readsPrec :: Int -> ReadS (Sum a) # readList :: ReadS [Sum a] # readPrec :: ReadPrec (Sum a) # readListPrec :: ReadPrec [Sum a] #
Show a => Show (Sum a)
Instance details Methods showsPrec :: Int -> Sum a -> ShowS # show :: Sum a -> String # showList :: [Sum a] -> ShowS #
Generic (Sum a)
Instance details Associated Types type Rep (Sum a) :: * -> * # Methods from :: Sum a -> Rep (Sum a) x # to :: Rep (Sum a) x -> Sum a #
Num a => Semigroup (Sum a)	Since: 4.9.0.0
Instance details Methods (<>) :: Sum a -> Sum a -> Sum a # sconcat :: NonEmpty (Sum a) -> Sum a # stimes :: Integral b => b -> Sum a -> Sum a #
Num a => Semigroup (Exp (Sum a)) #	Since: 1.2.0.0
Instance details Methods (<>) :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a) # sconcat :: NonEmpty (Exp (Sum a)) -> Exp (Sum a) # stimes :: Integral b => b -> Exp (Sum a) -> Exp (Sum a) #
Num a => Monoid (Sum a)	Since: 2.1
Instance details Methods mempty :: Sum a # mappend :: Sum a -> Sum a -> Sum a # mconcat :: [Sum a] -> Sum a #
Num a => Monoid (Exp (Sum a)) #
Instance details Methods mempty :: Exp (Sum a) # mappend :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a) # mconcat :: [Exp (Sum a)] -> Exp (Sum a) #
NFData a => NFData (Sum a)	Since: 1.4.0.0
Instance details Methods rnf :: Sum a -> () #
Wrapped (Sum a)
Instance details Associated Types type Unwrapped (Sum a) :: * # Methods _Wrapped' :: Iso' (Sum a) (Unwrapped (Sum a)) #
(Eq a, Num a) => AsEmpty (Sum a)
Instance details Methods _Empty :: Prism' (Sum a) () #
Elt a => Elt (Sum a) Source #
Instance details Methods eltType :: Sum a -> TupleType (EltRepr (Sum a)) fromElt :: Sum a -> EltRepr (Sum a) toElt :: EltRepr (Sum a) -> Sum a
Eq a => Eq (Sum a) Source #
Instance details Methods (==) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool Source # (/=) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool Source #
Ord a => Ord (Sum a) Source #
Instance details Methods (<) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool Source # (>) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool Source # (<=) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool Source # (>=) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool Source # min :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a) Source # max :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a) Source # compare :: Exp (Sum a) -> Exp (Sum a) -> Exp Ordering Source #
Generic1 Sum
Instance details Associated Types type Rep1 Sum :: k -> * # Methods from1 :: Sum a -> Rep1 Sum a # to1 :: Rep1 Sum a -> Sum a #
t ~ Sum b => Rewrapped (Sum a) t
Instance details
type Rep Sum
Instance details type Rep Sum = ()
type Rep (Sum a)
Instance details type Rep (Sum a) = D1 (MetaData "Sum" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Sum" PrefixI True) (S1 (MetaSel (Just "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Unwrapped (Sum a)
Instance details type Unwrapped (Sum a) = a
type Plain (Sum a) Source #
Instance details type Plain (Sum a) = Sum (Plain a)
type Rep1 Sum
Instance details type Rep1 Sum = D1 (MetaData "Sum" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Sum" PrefixI True) (S1 (MetaSel (Just "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Product a #

Monoid under multiplication.

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

Constructors

Product
Fields getProduct :: a

Instances

Monad Product	Since: 4.8.0.0
Instance details Methods (>>=) :: Product a -> (a -> Product b) -> Product b # (>>) :: Product a -> Product b -> Product b # return :: a -> Product a # fail :: String -> Product a #
Functor Product	Since: 4.8.0.0
Instance details Methods fmap :: (a -> b) -> Product a -> Product b # (<$) :: a -> Product b -> Product a #
MonadFix Product	Since: 4.8.0.0
Instance details Methods mfix :: (a -> Product a) -> Product a #
Applicative Product	Since: 4.8.0.0
Instance details Methods pure :: a -> Product a # (<>) :: Product (a -> b) -> Product a -> Product b # liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c # (>) :: Product a -> Product b -> Product b # (<*) :: Product a -> Product b -> Product a #
Foldable Product	Since: 4.8.0.0
Instance details Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # toList :: Product a -> [a] # null :: Product a -> Bool # length :: Product a -> Int # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # sum :: Num a => Product a -> a # product :: Num a => Product a -> a #
Traversable Product	Since: 4.8.0.0
Instance details Methods traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) # sequenceA :: Applicative f => Product (f a) -> f (Product a) # mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) # sequence :: Monad m => Product (m a) -> m (Product a) #
Representable Product
Instance details Associated Types type Rep Product :: * # Methods tabulate :: (Rep Product -> a) -> Product a # index :: Product a -> Rep Product -> a #
NFData1 Product	Since: 1.4.3.0
Instance details Methods liftRnf :: (a -> ()) -> Product a -> () #
Functor Product Source #
Instance details Methods fmap :: (Elt a, Elt b, Elt (Product a), Elt (Product b)) => (Exp a -> Exp b) -> Exp (Product a) -> Exp (Product b) Source # (<$) :: (Elt a, Elt b, Elt (Product a), Elt (Product b)) => Exp a -> Exp (Product b) -> Exp (Product a) Source #
Elt a => Unlift Exp (Product (Exp a)) Source #
Instance details Methods unlift :: Exp (Plain (Product (Exp a))) -> Product (Exp a) Source #
(Lift Exp a, Elt (Plain a)) => Lift Exp (Product a) Source #
Instance details Associated Types type Plain (Product a) :: * Source # Methods lift :: Product a -> Exp (Plain (Product a)) Source #
Bounded a => Bounded (Product a)
Instance details Methods minBound :: Product a # maxBound :: Product a #
Bounded a => Bounded (Exp (Product a)) #
Instance details Methods minBound :: Exp (Product a) # maxBound :: Exp (Product a) #
Eq a => Eq (Product a)
Instance details Methods (==) :: Product a -> Product a -> Bool # (/=) :: Product a -> Product a -> Bool #
Num a => Num (Product a)
Instance details Methods (+) :: Product a -> Product a -> Product a # (-) :: Product a -> Product a -> Product a # (*) :: Product a -> Product a -> Product a # negate :: Product a -> Product a # abs :: Product a -> Product a # signum :: Product a -> Product a # fromInteger :: Integer -> Product a #
Num a => Num (Exp (Product a)) #
Instance details Methods (+) :: Exp (Product a) -> Exp (Product a) -> Exp (Product a) # (-) :: Exp (Product a) -> Exp (Product a) -> Exp (Product a) # (*) :: Exp (Product a) -> Exp (Product a) -> Exp (Product a) # negate :: Exp (Product a) -> Exp (Product a) # abs :: Exp (Product a) -> Exp (Product a) # signum :: Exp (Product a) -> Exp (Product a) # fromInteger :: Integer -> Exp (Product a) #
Ord a => Ord (Product a)
Instance details 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)
Instance details Methods readsPrec :: Int -> ReadS (Product a) # readList :: ReadS [Product a] # readPrec :: ReadPrec (Product a) # readListPrec :: ReadPrec [Product a] #
Show a => Show (Product a)
Instance details Methods showsPrec :: Int -> Product a -> ShowS # show :: Product a -> String # showList :: [Product a] -> ShowS #
Generic (Product a)
Instance details Associated Types type Rep (Product a) :: * -> * # Methods from :: Product a -> Rep (Product a) x # to :: Rep (Product a) x -> Product a #
Num a => Semigroup (Product a)	Since: 4.9.0.0
Instance details Methods (<>) :: Product a -> Product a -> Product a # sconcat :: NonEmpty (Product a) -> Product a # stimes :: Integral b => b -> Product a -> Product a #
Num a => Semigroup (Exp (Product a)) #	Since: 1.2.0.0
Instance details Methods (<>) :: Exp (Product a) -> Exp (Product a) -> Exp (Product a) # sconcat :: NonEmpty (Exp (Product a)) -> Exp (Product a) # stimes :: Integral b => b -> Exp (Product a) -> Exp (Product a) #
Num a => Monoid (Product a)	Since: 2.1
Instance details Methods mempty :: Product a # mappend :: Product a -> Product a -> Product a # mconcat :: [Product a] -> Product a #
Num a => Monoid (Exp (Product a)) #
Instance details Methods mempty :: Exp (Product a) # mappend :: Exp (Product a) -> Exp (Product a) -> Exp (Product a) # mconcat :: [Exp (Product a)] -> Exp (Product a) #
NFData a => NFData (Product a)	Since: 1.4.0.0
Instance details Methods rnf :: Product a -> () #
Wrapped (Product a)
Instance details Associated Types type Unwrapped (Product a) :: * # Methods _Wrapped' :: Iso' (Product a) (Unwrapped (Product a)) #
(Eq a, Num a) => AsEmpty (Product a)
Instance details Methods _Empty :: Prism' (Product a) () #
Elt a => Elt (Product a) Source #
Instance details Methods eltType :: Product a -> TupleType (EltRepr (Product a)) fromElt :: Product a -> EltRepr (Product a) toElt :: EltRepr (Product a) -> Product a
Eq a => Eq (Product a) Source #
Instance details Methods (==) :: Exp (Product a) -> Exp (Product a) -> Exp Bool Source # (/=) :: Exp (Product a) -> Exp (Product a) -> Exp Bool Source #
Ord a => Ord (Product a) Source #
Instance details Methods (<) :: Exp (Product a) -> Exp (Product a) -> Exp Bool Source # (>) :: Exp (Product a) -> Exp (Product a) -> Exp Bool Source # (<=) :: Exp (Product a) -> Exp (Product a) -> Exp Bool Source # (>=) :: Exp (Product a) -> Exp (Product a) -> Exp Bool Source # min :: Exp (Product a) -> Exp (Product a) -> Exp (Product a) Source # max :: Exp (Product a) -> Exp (Product a) -> Exp (Product a) Source # compare :: Exp (Product a) -> Exp (Product a) -> Exp Ordering Source #
Generic1 Product
Instance details Associated Types type Rep1 Product :: k -> * # Methods from1 :: Product a -> Rep1 Product a # to1 :: Rep1 Product a -> Product a #
t ~ Product b => Rewrapped (Product a) t
Instance details
type Rep Product
Instance details type Rep Product = ()
type Rep (Product a)
Instance details type Rep (Product a) = D1 (MetaData "Product" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Product" PrefixI True) (S1 (MetaSel (Just "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Unwrapped (Product a)
Instance details type Unwrapped (Product a) = a
type Plain (Product a) Source #
Instance details type Plain (Product a) = Product (Plain a)
type Rep1 Product
Instance details type Rep1 Product = D1 (MetaData "Product" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Product" PrefixI True) (S1 (MetaSel (Just "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

Orphan instances

Elt a => Unlift Exp (Sum (Exp a)) Source #
Instance details Methods unlift :: Exp (Plain (Sum (Exp a))) -> Sum (Exp a) Source #
Elt a => Unlift Exp (Product (Exp a)) Source #
Instance details Methods unlift :: Exp (Plain (Product (Exp a))) -> Product (Exp a) Source #
(Lift Exp a, Elt (Plain a)) => Lift Exp (Sum a) Source #
Instance details Associated Types type Plain (Sum a) :: * Source # Methods lift :: Sum a -> Exp (Plain (Sum a)) Source #
(Lift Exp a, Elt (Plain a)) => Lift Exp (Product a) Source #
Instance details Associated Types type Plain (Product a) :: * Source # Methods lift :: Product a -> Exp (Plain (Product a)) Source #
Bounded a => Bounded (Exp (Sum a)) Source #
Instance details Methods minBound :: Exp (Sum a) # maxBound :: Exp (Sum a) #
Bounded a => Bounded (Exp (Product a)) Source #
Instance details Methods minBound :: Exp (Product a) # maxBound :: Exp (Product a) #
Num a => Num (Exp (Sum a)) Source #
Instance details Methods (+) :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a) # (-) :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a) # (*) :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a) # negate :: Exp (Sum a) -> Exp (Sum a) # abs :: Exp (Sum a) -> Exp (Sum a) # signum :: Exp (Sum a) -> Exp (Sum a) # fromInteger :: Integer -> Exp (Sum a) #
Num a => Num (Exp (Product a)) Source #
Instance details Methods (+) :: Exp (Product a) -> Exp (Product a) -> Exp (Product a) # (-) :: Exp (Product a) -> Exp (Product a) -> Exp (Product a) # (*) :: Exp (Product a) -> Exp (Product a) -> Exp (Product a) # negate :: Exp (Product a) -> Exp (Product a) # abs :: Exp (Product a) -> Exp (Product a) # signum :: Exp (Product a) -> Exp (Product a) # fromInteger :: Integer -> Exp (Product a) #
Num a => Semigroup (Exp (Sum a)) Source #	Since: 1.2.0.0
Instance details Methods (<>) :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a) # sconcat :: NonEmpty (Exp (Sum a)) -> Exp (Sum a) # stimes :: Integral b => b -> Exp (Sum a) -> Exp (Sum a) #
Num a => Semigroup (Exp (Product a)) Source #	Since: 1.2.0.0
Instance details Methods (<>) :: Exp (Product a) -> Exp (Product a) -> Exp (Product a) # sconcat :: NonEmpty (Exp (Product a)) -> Exp (Product a) # stimes :: Integral b => b -> Exp (Product a) -> Exp (Product a) #
Monoid (Exp ()) Source #
Instance details Methods mempty :: Exp () # mappend :: Exp () -> Exp () -> Exp () # mconcat :: [Exp ()] -> Exp () #
(Elt a, Elt b, Monoid (Exp a), Monoid (Exp b)) => Monoid (Exp (a, b)) Source #
Instance details Methods mempty :: Exp (a, b) # mappend :: Exp (a, b) -> Exp (a, b) -> Exp (a, b) # mconcat :: [Exp (a, b)] -> Exp (a, b) #
(Elt a, Elt b, Elt c, Monoid (Exp a), Monoid (Exp b), Monoid (Exp c)) => Monoid (Exp (a, b, c)) Source #
Instance details Methods mempty :: Exp (a, b, c) # mappend :: Exp (a, b, c) -> Exp (a, b, c) -> Exp (a, b, c) # mconcat :: [Exp (a, b, c)] -> Exp (a, b, c) #
(Elt a, Elt b, Elt c, Elt d, Monoid (Exp a), Monoid (Exp b), Monoid (Exp c), Monoid (Exp d)) => Monoid (Exp (a, b, c, d)) Source #
Instance details Methods mempty :: Exp (a, b, c, d) # mappend :: Exp (a, b, c, d) -> Exp (a, b, c, d) -> Exp (a, b, c, d) # mconcat :: [Exp (a, b, c, d)] -> Exp (a, b, c, d) #
(Elt a, Elt b, Elt c, Elt d, Elt e, Monoid (Exp a), Monoid (Exp b), Monoid (Exp c), Monoid (Exp d), Monoid (Exp e)) => Monoid (Exp (a, b, c, d, e)) Source #
Instance details Methods mempty :: Exp (a, b, c, d, e) # mappend :: Exp (a, b, c, d, e) -> Exp (a, b, c, d, e) -> Exp (a, b, c, d, e) # mconcat :: [Exp (a, b, c, d, e)] -> Exp (a, b, c, d, e) #
Num a => Monoid (Exp (Sum a)) Source #
Instance details Methods mempty :: Exp (Sum a) # mappend :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a) # mconcat :: [Exp (Sum a)] -> Exp (Sum a) #
Num a => Monoid (Exp (Product a)) Source #
Instance details Methods mempty :: Exp (Product a) # mappend :: Exp (Product a) -> Exp (Product a) -> Exp (Product a) # mconcat :: [Exp (Product a)] -> Exp (Product a) #
Elt a => Elt (Sum a) Source #
Instance details Methods eltType :: Sum a -> TupleType (EltRepr (Sum a)) fromElt :: Sum a -> EltRepr (Sum a) toElt :: EltRepr (Sum a) -> Sum a
Elt a => Elt (Product a) Source #
Instance details Methods eltType :: Product a -> TupleType (EltRepr (Product a)) fromElt :: Product a -> EltRepr (Product a) toElt :: EltRepr (Product a) -> Product a
Eq a => Eq (Sum a) Source #
Instance details Methods (==) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool Source # (/=) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool Source #
Eq a => Eq (Product a) Source #
Instance details Methods (==) :: Exp (Product a) -> Exp (Product a) -> Exp Bool Source # (/=) :: Exp (Product a) -> Exp (Product a) -> Exp Bool Source #
Ord a => Ord (Sum a) Source #
Instance details Methods (<) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool Source # (>) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool Source # (<=) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool Source # (>=) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool Source # min :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a) Source # max :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a) Source # compare :: Exp (Sum a) -> Exp (Sum a) -> Exp Ordering Source #
Ord a => Ord (Product a) Source #
Instance details Methods (<) :: Exp (Product a) -> Exp (Product a) -> Exp Bool Source # (>) :: Exp (Product a) -> Exp (Product a) -> Exp Bool Source # (<=) :: Exp (Product a) -> Exp (Product a) -> Exp Bool Source # (>=) :: Exp (Product a) -> Exp (Product a) -> Exp Bool Source # min :: Exp (Product a) -> Exp (Product a) -> Exp (Product a) Source # max :: Exp (Product a) -> Exp (Product a) -> Exp (Product a) Source # compare :: Exp (Product a) -> Exp (Product a) -> Exp Ordering Source #