Copyright	[2016..2020] The Accelerate Team
License	BSD3
Maintainer	Trevor L. McDonell <trevor.mcdonell@gmail.com>
Stability	experimental
Portability	non-portable (GHC extensions)
Safe Haskell	None
Language	Haskell2010

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
- mempty :: a
- mappend :: a -> a -> a
- mconcat :: [a] -> a
(<>) :: Semigroup a => a -> a -> a
newtype Sum a = Sum {
- getSum :: a
}
pattern Sum_ :: Elt a => Exp a -> Exp (Sum a)
newtype Product a = Product {
- getProduct :: a
}
pattern Product_ :: Elt a => Exp a -> Exp (Product 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:

Right identity: x <> mempty = x
Left identity: mempty <> x = x
Associativity: x <> (y <> z) = (x <> y) <> z (Semigroup law)
Concatenation: 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

>>> "Hello world" <> mempty
"Hello world"

mappend :: a -> a -> a #

An associative operation

NOTE: This method is redundant and has the default implementation mappend = (<>) since base-4.11.0.0. Should it be implemented manually, since mappend is a synonym for (<>), it is expected that the two functions are defined the same way. In a future GHC release mappend will be removed from Monoid.

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.

>>> mconcat ["Hello", " ", "Haskell", "!"]
"Hello Haskell!"

Instances

Instances details

Monoid Ordering	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering # mappend :: Ordering -> Ordering -> Ordering # mconcat :: [Ordering] -> Ordering #
Monoid ()	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: () # mappend :: () -> () -> () # mconcat :: [()] -> () #
Monoid All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All # mappend :: All -> All -> All # mconcat :: [All] -> All #
Monoid Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any # mappend :: Any -> Any -> Any # mconcat :: [Any] -> Any #
Monoid String
Instance details Defined in Basement.UTF8.Base Methods mempty :: String # mappend :: String -> String -> String # mconcat :: [String] -> String #
Monoid ShortByteString
Instance details Defined in Data.ByteString.Short.Internal Methods mempty :: ShortByteString # mappend :: ShortByteString -> ShortByteString -> ShortByteString # mconcat :: [ShortByteString] -> ShortByteString #
Monoid ByteString
Instance details Defined in Data.ByteString.Lazy.Internal Methods mempty :: ByteString # mappend :: ByteString -> ByteString -> ByteString # mconcat :: [ByteString] -> ByteString #
Monoid ByteString
Instance details Defined in Data.ByteString.Internal Methods mempty :: ByteString # mappend :: ByteString -> ByteString -> ByteString # mconcat :: [ByteString] -> ByteString #
Monoid Builder
Instance details Defined in Data.ByteString.Builder.Internal Methods mempty :: Builder # mappend :: Builder -> Builder -> Builder # mconcat :: [Builder] -> Builder #
Monoid IntSet
Instance details Defined in Data.IntSet.Internal Methods mempty :: IntSet # mappend :: IntSet -> IntSet -> IntSet # mconcat :: [IntSet] -> IntSet #
Monoid Journal
Instance details Defined in Hedgehog.Internal.Property Methods mempty :: Journal # mappend :: Journal -> Journal -> Journal # mconcat :: [Journal] -> Journal #
Monoid Cover
Instance details Defined in Hedgehog.Internal.Property Methods mempty :: Cover # mappend :: Cover -> Cover -> Cover # mconcat :: [Cover] -> Cover #
Monoid CoverCount
Instance details Defined in Hedgehog.Internal.Property Methods mempty :: CoverCount # mappend :: CoverCount -> CoverCount -> CoverCount # mconcat :: [CoverCount] -> CoverCount #
Monoid LabelName
Instance details Defined in Hedgehog.Internal.Property Methods mempty :: LabelName # mappend :: LabelName -> LabelName -> LabelName # mconcat :: [LabelName] -> LabelName #
Monoid ParseError
Instance details Defined in Options.Applicative.Types Methods mempty :: ParseError # mappend :: ParseError -> ParseError -> ParseError # mconcat :: [ParseError] -> ParseError #
Monoid Completer
Instance details Defined in Options.Applicative.Types Methods mempty :: Completer # mappend :: Completer -> Completer -> Completer # mconcat :: [Completer] -> Completer #
Monoid Doc
Instance details Defined in Text.PrettyPrint.HughesPJ Methods mempty :: Doc # mappend :: Doc -> Doc -> Doc # mconcat :: [Doc] -> Doc #
Monoid AnsiStyle	`mempty` does nothing, which is equivalent to inheriting the style of the surrounding doc, or the terminal’s default if no style has been set yet.
Instance details Defined in Prettyprinter.Render.Terminal.Internal Methods mempty :: AnsiStyle # mappend :: AnsiStyle -> AnsiStyle -> AnsiStyle # mconcat :: [AnsiStyle] -> AnsiStyle #
Monoid ByteArray
Instance details Defined in Data.Primitive.ByteArray Methods mempty :: ByteArray # mappend :: ByteArray -> ByteArray -> ByteArray # mconcat :: [ByteArray] -> ByteArray #
Monoid OptionSet	Later options override earlier ones
Instance details Defined in Test.Tasty.Options Methods mempty :: OptionSet # mappend :: OptionSet -> OptionSet -> OptionSet # mconcat :: [OptionSet] -> OptionSet #
Monoid Slot
Instance details Defined in Data.HashTable.ST.Basic Methods mempty :: Slot # mappend :: Slot -> Slot -> Slot # mconcat :: [Slot] -> Slot #
Monoid [a]	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: [a] # mappend :: [a] -> [a] -> [a] # mconcat :: [[a]] -> [a] #
Semigroup a => Monoid (Maybe a)	Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `ee = e` and `es = s = se` for all `s ∈ S`." Since 4.11.0: constraint on inner `a` value generalised from `Monoid` to `Semigroup`. Since: base-2.1*
Instance details Defined in GHC.Base Methods mempty :: Maybe a # mappend :: Maybe a -> Maybe a -> Maybe a # mconcat :: [Maybe a] -> Maybe a #
Monoid a => Monoid (IO a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mempty :: IO a # mappend :: IO a -> IO a -> IO a # mconcat :: [IO a] -> IO a #
Monoid p => Monoid (Par1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: Par1 p # mappend :: Par1 p -> Par1 p -> Par1 p # mconcat :: [Par1 p] -> Par1 p #
Monoid (Predicate a)
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Predicate a # mappend :: Predicate a -> Predicate a -> Predicate a # mconcat :: [Predicate a] -> Predicate a #
Monoid (Comparison a)
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Comparison a # mappend :: Comparison a -> Comparison a -> Comparison a # mconcat :: [Comparison a] -> Comparison a #
Monoid (Equivalence a)
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Equivalence a # mappend :: Equivalence a -> Equivalence a -> Equivalence a # mconcat :: [Equivalence a] -> Equivalence a #
(Ord a, Bounded a) => Monoid (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Min a # mappend :: Min a -> Min a -> Min a # mconcat :: [Min a] -> Min a #
(Ord a, Bounded a) => Monoid (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Max a # mappend :: Max a -> Max a -> Max a # mconcat :: [Max a] -> Max a #
Monoid m => Monoid (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: WrappedMonoid m # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # mconcat :: [WrappedMonoid m] -> WrappedMonoid m #
Semigroup a => Monoid (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Option a # mappend :: Option a -> Option a -> Option a # mconcat :: [Option a] -> Option a #
Monoid a => Monoid (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods mempty :: Identity a # mappend :: Identity a -> Identity a -> Identity a # mconcat :: [Identity a] -> Identity a #
Monoid (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: First a # mappend :: First a -> First a -> First a # mconcat :: [First a] -> First a #
Monoid (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: Last a # mappend :: Last a -> Last a -> Last a # mconcat :: [Last a] -> Last a #
Monoid a => Monoid (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a # mappend :: Dual a -> Dual a -> Dual a # mconcat :: [Dual a] -> Dual a #
Monoid (Endo a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a # mappend :: Endo a -> Endo a -> Endo a # mconcat :: [Endo a] -> Endo a #
Num a => Monoid (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a # mappend :: Sum a -> Sum a -> Sum a # mconcat :: [Sum a] -> Sum a #
Num a => Monoid (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a # mappend :: Product a -> Product a -> Product a # mconcat :: [Product a] -> Product a #
Monoid a => Monoid (Down a)	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods mempty :: Down a # mappend :: Down a -> Down a -> Down a # mconcat :: [Down a] -> Down a #
PrimType ty => Monoid (UArray ty)
Instance details Defined in Basement.UArray.Base Methods mempty :: UArray ty # mappend :: UArray ty -> UArray ty -> UArray ty # mconcat :: [UArray ty] -> UArray ty #
PrimType ty => Monoid (Block ty)
Instance details Defined in Basement.Block.Base Methods mempty :: Block ty # mappend :: Block ty -> Block ty -> Block ty # mconcat :: [Block ty] -> Block ty #
Monoid (CountOf ty)
Instance details Defined in Basement.Types.OffsetSize Methods mempty :: CountOf ty # mappend :: CountOf ty -> CountOf ty -> CountOf ty # mconcat :: [CountOf ty] -> CountOf ty #
Num a => Monoid (Colour a)
Instance details Defined in Data.Colour.Internal Methods mempty :: Colour a # mappend :: Colour a -> Colour a -> Colour a # mconcat :: [Colour a] -> Colour a #
Num a => Monoid (AlphaColour a)
Instance details Defined in Data.Colour.Internal Methods mempty :: AlphaColour a # mappend :: AlphaColour a -> AlphaColour a -> AlphaColour a # mconcat :: [AlphaColour a] -> AlphaColour a #
Monoid (IntMap a)
Instance details Defined in Data.IntMap.Internal Methods mempty :: IntMap a # mappend :: IntMap a -> IntMap a -> IntMap a # mconcat :: [IntMap a] -> IntMap a #
Monoid (Seq a)
Instance details Defined in Data.Sequence.Internal Methods mempty :: Seq a # mappend :: Seq a -> Seq a -> Seq a # mconcat :: [Seq a] -> Seq a #
Ord a => Monoid (Set a)
Instance details Defined in Data.Set.Internal Methods mempty :: Set a # mappend :: Set a -> Set a -> Set a # mconcat :: [Set a] -> Set a #
(Semigroup a, Monoid a) => Monoid (Coverage a)
Instance details Defined in Hedgehog.Internal.Property Methods mempty :: Coverage a # mappend :: Coverage a -> Coverage a -> Coverage a # mconcat :: [Coverage a] -> Coverage a #
Prim a => Monoid (Vector a)
Instance details Defined in Data.Vector.Primitive Methods mempty :: Vector a # mappend :: Vector a -> Vector a -> Vector a # mconcat :: [Vector a] -> Vector a #
Storable a => Monoid (Vector a)
Instance details Defined in Data.Vector.Storable Methods mempty :: Vector a # mappend :: Vector a -> Vector a -> Vector a # mconcat :: [Vector a] -> Vector a #
(Hashable a, Eq a) => Monoid (HashSet a)	`mempty` = `empty` `mappend` = `union` O(n+m) To obtain good performance, the smaller set must be presented as the first argument. Examples Expand `>>>` `mappend (fromList [1,2]) (fromList [2,3])`fromList [1,2,3]
Instance details Defined in Data.HashSet.Internal Methods mempty :: HashSet a # mappend :: HashSet a -> HashSet a -> HashSet a # mconcat :: [HashSet a] -> HashSet a #
Monoid (Vector a)
Instance details Defined in Data.Vector Methods mempty :: Vector a # mappend :: Vector a -> Vector a -> Vector a # mconcat :: [Vector a] -> Vector a #
Ord a => Monoid (Min a)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Min a # mappend :: Min a -> Min a -> Min a # mconcat :: [Min a] -> Min a #
Ord a => Monoid (Max a)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Max a # mappend :: Max a -> Max a -> Max a # mconcat :: [Max a] -> Max a #
Monoid (Leftmost a)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Leftmost a # mappend :: Leftmost a -> Leftmost a -> Leftmost a # mconcat :: [Leftmost a] -> Leftmost a #
Monoid (Rightmost a)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Rightmost a # mappend :: Rightmost a -> Rightmost a -> Rightmost a # mconcat :: [Rightmost a] -> Rightmost a #
Monoid (Doc a)
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods mempty :: Doc a # mappend :: Doc a -> Doc a -> Doc a # mconcat :: [Doc a] -> Doc a #
Monoid (Doc ann)	`mempty` = `emptyDoc` `mconcat` = `hcat` `>>>` `mappend "hello" "world" :: Doc ann`helloworld
Instance details Defined in Data.Text.Prettyprint.Doc.Internal Methods mempty :: Doc ann # mappend :: Doc ann -> Doc ann -> Doc ann # mconcat :: [Doc ann] -> Doc ann #
Monoid (PrimArray a)	Since: primitive-0.6.4.0
Instance details Defined in Data.Primitive.PrimArray Methods mempty :: PrimArray a # mappend :: PrimArray a -> PrimArray a -> PrimArray a # mconcat :: [PrimArray a] -> PrimArray a #
Monoid (SmallArray a)
Instance details Defined in Data.Primitive.SmallArray Methods mempty :: SmallArray a # mappend :: SmallArray a -> SmallArray a -> SmallArray a # mconcat :: [SmallArray a] -> SmallArray a #
Monoid (Array a)
Instance details Defined in Data.Primitive.Array Methods mempty :: Array a # mappend :: Array a -> Array a -> Array a # mconcat :: [Array a] -> Array a #
Monoid (Doc a)
Instance details Defined in Text.PrettyPrint.Annotated.WL Methods mempty :: Doc a # mappend :: Doc a -> Doc a -> Doc a # mconcat :: [Doc a] -> Doc a #
Monoid (MergeSet a)
Instance details Defined in Data.Set.Internal Methods mempty :: MergeSet a # mappend :: MergeSet a -> MergeSet a -> MergeSet a # mconcat :: [MergeSet a] -> MergeSet a #
(Monoid (Exp a), Elt a) => Monoid (Exp (Maybe a)) Source #
Instance details Defined in Data.Array.Accelerate.Data.Maybe Methods mempty :: Exp (Maybe a) # mappend :: Exp (Maybe a) -> Exp (Maybe a) -> Exp (Maybe a) # mconcat :: [Exp (Maybe a)] -> Exp (Maybe a) #
Monoid (Exp ()) Source #
Instance details Defined in Data.Array.Accelerate.Data.Monoid 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 Defined in Data.Array.Accelerate.Data.Monoid 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 Defined in Data.Array.Accelerate.Data.Monoid 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 Defined in Data.Array.Accelerate.Data.Monoid 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 Defined in Data.Array.Accelerate.Data.Monoid 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)) Source #
Instance details Defined in Data.Array.Accelerate.Data.Semigroup 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)) Source #
Instance details Defined in Data.Array.Accelerate.Data.Semigroup 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)) Source #
Instance details Defined in Data.Array.Accelerate.Data.Monoid 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 Defined in Data.Array.Accelerate.Data.Monoid Methods mempty :: Exp (Product a) # mappend :: Exp (Product a) -> Exp (Product a) -> Exp (Product a) # mconcat :: [Exp (Product a)] -> Exp (Product a) #
Monoid b => Monoid (a -> b)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: a -> b # mappend :: (a -> b) -> (a -> b) -> a -> b # mconcat :: [a -> b] -> a -> b #
Monoid (U1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: U1 p # mappend :: U1 p -> U1 p -> U1 p # mconcat :: [U1 p] -> U1 p #
(Monoid a, Monoid b) => Monoid (a, b)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b) # mappend :: (a, b) -> (a, b) -> (a, b) # mconcat :: [(a, b)] -> (a, b) #
Monoid a => Monoid (Op a b)
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Op a b # mappend :: Op a b -> Op a b -> Op a b # mconcat :: [Op a b] -> Op a b #
Monoid a => Monoid (ST s a)	Since: base-4.11.0.0
Instance details Defined in GHC.ST Methods mempty :: ST s a # mappend :: ST s a -> ST s a -> ST s a # mconcat :: [ST s a] -> ST s a #
Monoid (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods mempty :: Proxy s # mappend :: Proxy s -> Proxy s -> Proxy s # mconcat :: [Proxy s] -> Proxy s #
Ord k => Monoid (Map k v)
Instance details Defined in Data.Map.Internal Methods mempty :: Map k v # mappend :: Map k v -> Map k v -> Map k v # mconcat :: [Map k v] -> Map k v #
(Monad m, Monoid a) => Monoid (GenT m a)
Instance details Defined in Hedgehog.Internal.Gen 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)	`mempty` = `empty` `mappend` = `union` If a key occurs in both maps, the mapping from the first will be the mapping in the result. Examples Expand `>>>` `mappend (fromList [(1,'a'),(2,'b')]) (fromList [(2,'c'),(3,'d')])`fromList [(1,'a'),(2,'b'),(3,'d')]
Instance details Defined in Data.HashMap.Internal 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 Defined in Control.Lens.Reified Methods mempty :: ReifiedFold s a # mappend :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a # mconcat :: [ReifiedFold s a] -> ReifiedFold s a #
(Contravariant f, Applicative f) => Monoid (Folding f a)
Instance details Defined in Control.Lens.Internal.Fold 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 Defined in Control.Lens.Internal.Fold 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 Defined in Control.Lens.Internal.Fold 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 Defined in Control.Lens.Internal.Fold Methods mempty :: Sequenced a m # mappend :: Sequenced a m -> Sequenced a m -> Sequenced a m # mconcat :: [Sequenced a m] -> Sequenced a m #
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 Defined in Control.Lens.Internal.Indexed Methods mempty :: Indexing f a # mappend :: Indexing f a -> Indexing f a -> Indexing f a # mconcat :: [Indexing f a] -> Indexing f a #
Monoid (Deepening i a)	This is an illegal `Monoid`.
Instance details Defined in Control.Lens.Internal.Level Methods mempty :: Deepening i a # mappend :: Deepening i a -> Deepening i a -> Deepening i a # mconcat :: [Deepening i a] -> Deepening i a #
Monoid (f p) => Monoid (Rec1 f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: Rec1 f p # mappend :: Rec1 f p -> Rec1 f p -> Rec1 f p # mconcat :: [Rec1 f p] -> Rec1 f p #
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c) # mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) # mconcat :: [(a, b, c)] -> (a, b, c) #
Monoid a => Monoid (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods mempty :: Const a b # mappend :: Const a b -> Const a b -> Const a b # mconcat :: [Const a b] -> Const a b #
(Applicative f, Monoid a) => Monoid (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mempty :: Ap f a # mappend :: Ap f a -> Ap f a -> Ap f a # mconcat :: [Ap f a] -> Ap f a #
Alternative f => Monoid (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Alt f a # mappend :: Alt f a -> Alt f a -> Alt f a # mconcat :: [Alt f a] -> Alt f a #
(Semigroup a, Monoid a) => Monoid (Tagged s a)
Instance details Defined in Data.Tagged Methods mempty :: Tagged s a # mappend :: Tagged s a -> Tagged s a -> Tagged s a # mconcat :: [Tagged s a] -> Tagged s a #
Monoid (ReifiedIndexedFold i s a)
Instance details Defined in Control.Lens.Reified 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 Defined in Data.Reflection Methods mempty :: ReflectedMonoid a s # mappend :: ReflectedMonoid a s -> ReflectedMonoid a s -> ReflectedMonoid a s # mconcat :: [ReflectedMonoid a s] -> ReflectedMonoid a s #
Monoid c => Monoid (K1 i c p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: K1 i c p # mappend :: K1 i c p -> K1 i c p -> K1 i c p # mconcat :: [K1 i c p] -> K1 i c p #
(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: (f :: g) p # mappend :: (f :: g) p -> (f :: g) p -> (f :: g) p # mconcat :: [(f :: g) p] -> (f :: g) p #
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d) # mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # mconcat :: [(a, b, c, d)] -> (a, b, c, d) #
Monoid (f p) => Monoid (M1 i c f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: M1 i c f p # mappend :: M1 i c f p -> M1 i c f p -> M1 i c f p # mconcat :: [M1 i c f p] -> M1 i c f p #
Monoid (f (g p)) => Monoid ((f :.: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: (f :.: g) p # mappend :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p # mconcat :: [(f :.: g) p] -> (f :.: g) p #
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d, e) # mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) #
Contravariant g => Monoid (BazaarT p g a b t)
Instance details Defined in Control.Lens.Internal.Bazaar 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.

>>> [1,2,3] <> [4,5,6]
[1,2,3,4,5,6]

newtype Sum a #

Monoid under addition.

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

Constructors

Sum
Fields getSum :: a

Instances

Instances details

Monad Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Sum a -> (a -> Sum b) -> Sum b # (>>) :: Sum a -> Sum b -> Sum b # return :: a -> Sum a #
Functor Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Sum a -> Sum b # (<$) :: a -> Sum b -> Sum a #
MonadFix Sum	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Sum a) -> Sum a #
Applicative Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal 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: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> 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: base-4.8.0.0
Instance details Defined in Data.Traversable 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 Defined in Data.Functor.Rep Associated Types type Rep Sum # Methods tabulate :: (Rep Sum -> a) -> Sum a # index :: Sum a -> Rep Sum -> a #
NFData1 Sum	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a -> ()) -> Sum a -> () #
Traversable1 Sum
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Sum a -> f (Sum b) # sequence1 :: Apply f => Sum (f b) -> f (Sum b) #
Functor Sum Source #
Instance details Defined in Data.Array.Accelerate.Data.Functor 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 #
Unbox a => Vector Vector (Sum a)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Sum a) -> m (Vector (Sum a)) # basicUnsafeThaw :: PrimMonad m => Vector (Sum a) -> m (Mutable Vector (PrimState m) (Sum a)) # basicLength :: Vector (Sum a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Sum a) -> Vector (Sum a) # basicUnsafeIndexM :: Monad m => Vector (Sum a) -> Int -> m (Sum a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Sum a) -> Vector (Sum a) -> m () # elemseq :: Vector (Sum a) -> Sum a -> b -> b #
Unbox a => MVector MVector (Sum a)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s (Sum a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Sum a) -> MVector s (Sum a) # basicOverlaps :: MVector s (Sum a) -> MVector s (Sum a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Sum a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (Sum a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Sum a -> m (MVector (PrimState m) (Sum a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Sum a) -> Int -> m (Sum a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Sum a) -> Int -> Sum a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (Sum a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (Sum a) -> Sum a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Sum a) -> MVector (PrimState m) (Sum a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Sum a) -> MVector (PrimState m) (Sum a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Sum a) -> Int -> m (MVector (PrimState m) (Sum a)) #
Elt a => Unlift Exp (Sum (Exp a)) Source #
Instance details Defined in Data.Array.Accelerate.Data.Monoid Methods unlift :: Exp (Plain (Sum (Exp a))) -> Sum (Exp a) Source #
(Lift Exp a, Elt (Plain a)) => Lift Exp (Sum a) Source #
Instance details Defined in Data.Array.Accelerate.Data.Monoid Associated Types type Plain (Sum a) Source # Methods lift :: Sum a -> Exp (Plain (Sum a)) Source #
Bounded a => Bounded (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Sum a # maxBound :: Sum a #
Bounded a => Bounded (Exp (Sum a)) Source #
Instance details Defined in Data.Array.Accelerate.Data.Monoid Methods minBound :: Exp (Sum a) # maxBound :: Exp (Sum a) #
Eq a => Eq (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Sum a -> Sum a -> Bool # (/=) :: Sum a -> Sum a -> Bool #
Num a => Num (Sum a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal 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)) Source #
Instance details Defined in Data.Array.Accelerate.Data.Monoid 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)	Since: base-2.1
Instance details Defined in Data.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)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Sum a) # readList :: ReadS [Sum a] # readPrec :: ReadPrec (Sum a) # readListPrec :: ReadPrec [Sum a] #
Show a => Show (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Sum a -> ShowS # show :: Sum a -> String # showList :: [Sum a] -> ShowS #
Generic (Sum a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Sum a) :: Type -> Type # Methods from :: Sum a -> Rep (Sum a) x # to :: Rep (Sum a) x -> Sum a #
Num a => Semigroup (Sum a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal 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)) Source #	Since: 1.2.0.0
Instance details Defined in Data.Array.Accelerate.Data.Monoid 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: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a # mappend :: Sum a -> Sum a -> Sum a # mconcat :: [Sum a] -> Sum a #
Num a => Monoid (Exp (Sum a)) Source #
Instance details Defined in Data.Array.Accelerate.Data.Monoid 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: deepseq-1.4.0.0
Instance details Defined in Control.DeepSeq Methods rnf :: Sum a -> () #
Prim a => Prim (Sum a)	Since: primitive-0.6.5.0
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Sum a -> Int# # alignment# :: Sum a -> Int# # indexByteArray# :: ByteArray# -> Int# -> Sum a # readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Sum a #) # writeByteArray# :: MutableByteArray# s -> Int# -> Sum a -> State# s -> State# s # setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Sum a -> State# s -> State# s # indexOffAddr# :: Addr# -> Int# -> Sum a # readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Sum a #) # writeOffAddr# :: Addr# -> Int# -> Sum a -> State# s -> State# s # setOffAddr# :: Addr# -> Int# -> Int# -> Sum a -> State# s -> State# s #
Unbox a => Unbox (Sum a)
Instance details Defined in Data.Vector.Unboxed.Base
Wrapped (Sum a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Sum a) # Methods _Wrapped' :: Iso' (Sum a) (Unwrapped (Sum a)) #
(Eq a, Num a) => AsEmpty (Sum a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Sum a) () #
Elt a => Elt (Sum a) Source #
Instance details Defined in Data.Array.Accelerate.Data.Monoid Associated Types type EltR (Sum a) Methods eltR :: TypeR (EltR (Sum a)) tagsR :: [TagR (EltR (Sum a))] fromElt :: Sum a -> EltR (Sum a) toElt :: EltR (Sum a) -> Sum a
Eq a => Eq (Sum a) Source #
Instance details Defined in Data.Array.Accelerate.Data.Monoid 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 Defined in Data.Array.Accelerate.Data.Monoid 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	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Sum :: k -> Type # Methods from1 :: forall (a :: k). Sum a -> Rep1 Sum a # to1 :: forall (a :: k). Rep1 Sum a -> Sum a #
t ~ Sum b => Rewrapped (Sum a) t
Instance details Defined in Control.Lens.Wrapped
type Rep Sum
Instance details Defined in Data.Functor.Rep type Rep Sum = ()
newtype MVector s (Sum a)
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s (Sum a) = MV_Sum (MVector s a)
type Rep (Sum a)
Instance details Defined in Data.Semigroup.Internal 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)))
newtype Vector (Sum a)
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector (Sum a) = V_Sum (Vector a)
type Unwrapped (Sum a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Sum a) = a
type Plain (Sum a) Source #
Instance details Defined in Data.Array.Accelerate.Data.Monoid type Plain (Sum a) = Sum (Plain a)
type Rep1 Sum
Instance details Defined in Data.Semigroup.Internal type Rep1 Sum = D1 ('MetaData "Sum" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

pattern Sum_ :: Elt a => Exp a -> Exp (Sum a) Source #

newtype Product a #

Monoid under multiplication.

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

Constructors

Product
Fields getProduct :: a

Instances

Instances details

Monad Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Product a -> (a -> Product b) -> Product b # (>>) :: Product a -> Product b -> Product b # return :: a -> Product a #
Functor Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Product a -> Product b # (<$) :: a -> Product b -> Product a #
MonadFix Product	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Product a) -> Product a #
Applicative Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal 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: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> 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: base-4.8.0.0
Instance details Defined in Data.Traversable 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 Defined in Data.Functor.Rep Associated Types type Rep Product # Methods tabulate :: (Rep Product -> a) -> Product a # index :: Product a -> Rep Product -> a #
NFData1 Product	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a -> ()) -> Product a -> () #
Traversable1 Product
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Product a -> f (Product b) # sequence1 :: Apply f => Product (f b) -> f (Product b) #
Functor Product Source #
Instance details Defined in Data.Array.Accelerate.Data.Functor 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 #
Unbox a => Vector Vector (Product a)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Product a) -> m (Vector (Product a)) # basicUnsafeThaw :: PrimMonad m => Vector (Product a) -> m (Mutable Vector (PrimState m) (Product a)) # basicLength :: Vector (Product a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Product a) -> Vector (Product a) # basicUnsafeIndexM :: Monad m => Vector (Product a) -> Int -> m (Product a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Product a) -> Vector (Product a) -> m () # elemseq :: Vector (Product a) -> Product a -> b -> b #
Unbox a => MVector MVector (Product a)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s (Product a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Product a) -> MVector s (Product a) # basicOverlaps :: MVector s (Product a) -> MVector s (Product a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Product a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (Product a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Product a -> m (MVector (PrimState m) (Product a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Product a) -> Int -> m (Product a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Product a) -> Int -> Product a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (Product a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (Product a) -> Product a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Product a) -> MVector (PrimState m) (Product a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Product a) -> MVector (PrimState m) (Product a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Product a) -> Int -> m (MVector (PrimState m) (Product a)) #
Elt a => Unlift Exp (Product (Exp a)) Source #
Instance details Defined in Data.Array.Accelerate.Data.Monoid Methods unlift :: Exp (Plain (Product (Exp a))) -> Product (Exp a) Source #
(Lift Exp a, Elt (Plain a)) => Lift Exp (Product a) Source #
Instance details Defined in Data.Array.Accelerate.Data.Monoid Associated Types type Plain (Product a) Source # Methods lift :: Product a -> Exp (Plain (Product a)) Source #
Bounded a => Bounded (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Product a # maxBound :: Product a #
Bounded a => Bounded (Exp (Product a)) Source #
Instance details Defined in Data.Array.Accelerate.Data.Monoid Methods minBound :: Exp (Product a) # maxBound :: Exp (Product a) #
Eq a => Eq (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Product a -> Product a -> Bool # (/=) :: Product a -> Product a -> Bool #
Num a => Num (Product a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal 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)) Source #
Instance details Defined in Data.Array.Accelerate.Data.Monoid 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)	Since: base-2.1
Instance details Defined in Data.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)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Product a) # readList :: ReadS [Product a] # readPrec :: ReadPrec (Product a) # readListPrec :: ReadPrec [Product a] #
Show a => Show (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Product a -> ShowS # show :: Product a -> String # showList :: [Product a] -> ShowS #
Generic (Product a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Product a) :: Type -> Type # Methods from :: Product a -> Rep (Product a) x # to :: Rep (Product a) x -> Product a #
Num a => Semigroup (Product a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal 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)) Source #	Since: 1.2.0.0
Instance details Defined in Data.Array.Accelerate.Data.Monoid 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: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a # mappend :: Product a -> Product a -> Product a # mconcat :: [Product a] -> Product a #
Num a => Monoid (Exp (Product a)) Source #
Instance details Defined in Data.Array.Accelerate.Data.Monoid 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: deepseq-1.4.0.0
Instance details Defined in Control.DeepSeq Methods rnf :: Product a -> () #
Prim a => Prim (Product a)	Since: primitive-0.6.5.0
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Product a -> Int# # alignment# :: Product a -> Int# # indexByteArray# :: ByteArray# -> Int# -> Product a # readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Product a #) # writeByteArray# :: MutableByteArray# s -> Int# -> Product a -> State# s -> State# s # setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Product a -> State# s -> State# s # indexOffAddr# :: Addr# -> Int# -> Product a # readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Product a #) # writeOffAddr# :: Addr# -> Int# -> Product a -> State# s -> State# s # setOffAddr# :: Addr# -> Int# -> Int# -> Product a -> State# s -> State# s #
Unbox a => Unbox (Product a)
Instance details Defined in Data.Vector.Unboxed.Base
Wrapped (Product a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Product a) # Methods _Wrapped' :: Iso' (Product a) (Unwrapped (Product a)) #
(Eq a, Num a) => AsEmpty (Product a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Product a) () #
Elt a => Elt (Product a) Source #
Instance details Defined in Data.Array.Accelerate.Data.Monoid Associated Types type EltR (Product a) Methods eltR :: TypeR (EltR (Product a)) tagsR :: [TagR (EltR (Product a))] fromElt :: Product a -> EltR (Product a) toElt :: EltR (Product a) -> Product a
Eq a => Eq (Product a) Source #
Instance details Defined in Data.Array.Accelerate.Data.Monoid 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 Defined in Data.Array.Accelerate.Data.Monoid 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	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Product :: k -> Type # Methods from1 :: forall (a :: k). Product a -> Rep1 Product a # to1 :: forall (a :: k). Rep1 Product a -> Product a #
t ~ Product b => Rewrapped (Product a) t
Instance details Defined in Control.Lens.Wrapped
type Rep Product
Instance details Defined in Data.Functor.Rep type Rep Product = ()
newtype MVector s (Product a)
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s (Product a) = MV_Product (MVector s a)
type Rep (Product a)
Instance details Defined in Data.Semigroup.Internal 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)))
newtype Vector (Product a)
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector (Product a) = V_Product (Vector a)
type Unwrapped (Product a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Product a) = a
type Plain (Product a) Source #
Instance details Defined in Data.Array.Accelerate.Data.Monoid type Plain (Product a) = Product (Plain a)
type Rep1 Product
Instance details Defined in Data.Semigroup.Internal type Rep1 Product = D1 ('MetaData "Product" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

pattern Product_ :: Elt a => Exp a -> Exp (Product a) Source #

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 Associated Types type EltR (Sum a) Methods eltR :: TypeR (EltR (Sum a)) tagsR :: [TagR (EltR (Sum a))] fromElt :: Sum a -> EltR (Sum a) toElt :: EltR (Sum a) -> Sum a
Elt a => Elt (Product a) Source #
Instance details Associated Types type EltR (Product a) Methods eltR :: TypeR (EltR (Product a)) tagsR :: [TagR (EltR (Product a))] fromElt :: Product a -> EltR (Product a) toElt :: EltR (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 #

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