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

You can alternatively define mconcat instead of mempty, in which case the laws are:

Unit: mconcat (pure x) = x
Multiplication: mconcat (join xss) = mconcat (fmap mconcat xss)
Subclass: mconcat (toList xs) = sconcat xs

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 | mconcat

Methods

mempty :: a #

Identity of mappend

Examples

Expand

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

>>> mempty <> [1, 2, 3]
[1,2,3]

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 ByteArray	Since: base-4.17.0.0
Instance details Defined in Data.Array.Byte Methods mempty :: ByteArray # mappend :: ByteArray -> ByteArray -> ByteArray # mconcat :: [ByteArray] -> ByteArray #
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 Builder
Instance details Defined in Data.ByteString.Builder.Internal Methods mempty :: Builder # mappend :: Builder -> Builder -> Builder # mconcat :: [Builder] -> Builder #
Monoid ByteString
Instance details Defined in Data.ByteString.Internal.Type Methods mempty :: ByteString # mappend :: ByteString -> ByteString -> ByteString # mconcat :: [ByteString] -> ByteString #
Monoid ByteString
Instance details Defined in Data.ByteString.Lazy.Internal Methods mempty :: ByteString # mappend :: ByteString -> ByteString -> ByteString # mconcat :: [ByteString] -> ByteString #
Monoid ShortByteString
Instance details Defined in Data.ByteString.Short.Internal Methods mempty :: ShortByteString # mappend :: ShortByteString -> ShortByteString -> ShortByteString # mconcat :: [ShortByteString] -> ShortByteString #
Monoid IntSet
Instance details Defined in Data.IntSet.Internal Methods mempty :: IntSet # mappend :: IntSet -> IntSet -> IntSet # mconcat :: [IntSet] -> IntSet #
Monoid Unit
Instance details Defined in Control.DeepSeq Methods mempty :: Unit # mappend :: Unit -> Unit -> Unit # mconcat :: [Unit] -> Unit #
Monoid OsString	"String-Concatenation" for `OsString`. This is not the same as `(</>)`.
Instance details Defined in System.OsString.Internal.Types.Hidden Methods mempty :: OsString # mappend :: OsString -> OsString -> OsString # mconcat :: [OsString] -> OsString #
Monoid PosixString
Instance details Defined in System.OsString.Internal.Types.Hidden Methods mempty :: PosixString # mappend :: PosixString -> PosixString -> PosixString # mconcat :: [PosixString] -> PosixString #
Monoid WindowsString
Instance details Defined in System.OsString.Internal.Types.Hidden Methods mempty :: WindowsString # mappend :: WindowsString -> WindowsString -> WindowsString # mconcat :: [WindowsString] -> WindowsString #
Monoid Ordering	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering # mappend :: Ordering -> Ordering -> Ordering # mconcat :: [Ordering] -> Ordering #
Monoid Slot
Instance details Defined in Data.HashTable.ST.Basic Methods mempty :: Slot # mappend :: Slot -> Slot -> Slot # mconcat :: [Slot] -> Slot #
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 Journal
Instance details Defined in Hedgehog.Internal.Property Methods mempty :: Journal # mappend :: Journal -> Journal -> Journal # mconcat :: [Journal] -> Journal #
Monoid LabelName
Instance details Defined in Hedgehog.Internal.Property Methods mempty :: LabelName # mappend :: LabelName -> LabelName -> LabelName # mconcat :: [LabelName] -> LabelName #
Monoid ColumnWidth
Instance details Defined in Hedgehog.Internal.Report Methods mempty :: ColumnWidth # mappend :: ColumnWidth -> ColumnWidth -> ColumnWidth # mconcat :: [ColumnWidth] -> ColumnWidth #
Monoid Summary
Instance details Defined in Hedgehog.Internal.Report Methods mempty :: Summary # mappend :: Summary -> Summary -> Summary # mconcat :: [Summary] -> Summary #
Monoid Completer
Instance details Defined in Options.Applicative.Types Methods mempty :: Completer # mappend :: Completer -> Completer -> Completer # mconcat :: [Completer] -> Completer #
Monoid ParseError
Instance details Defined in Options.Applicative.Types Methods mempty :: ParseError # mappend :: ParseError -> ParseError -> ParseError # mconcat :: [ParseError] -> ParseError #
Monoid OsString
Instance details Defined in System.OsString.Internal.Types Methods mempty :: OsString # mappend :: OsString -> OsString -> OsString # mconcat :: [OsString] -> OsString #
Monoid PosixString
Instance details Defined in System.OsString.Internal.Types Methods mempty :: PosixString # mappend :: PosixString -> PosixString -> PosixString # mconcat :: [PosixString] -> PosixString #
Monoid WindowsString
Instance details Defined in System.OsString.Internal.Types Methods mempty :: WindowsString # mappend :: WindowsString -> WindowsString -> WindowsString # mconcat :: [WindowsString] -> WindowsString #
Monoid Doc
Instance details Defined in Text.PrettyPrint.HughesPJ Methods mempty :: Doc # mappend :: Doc -> Doc -> Doc # mconcat :: [Doc] -> Doc #
Monoid AnsiStyle
Instance details Defined in Prettyprinter.Render.Terminal.Internal Methods mempty :: AnsiStyle # mappend :: AnsiStyle -> AnsiStyle -> AnsiStyle # mconcat :: [AnsiStyle] -> AnsiStyle #
Monoid Statistics
Instance details Defined in Test.Tasty.Ingredients.ConsoleReporter Methods mempty :: Statistics # mappend :: Statistics -> Statistics -> Statistics # mconcat :: [Statistics] -> Statistics #
Monoid TestOutput
Instance details Defined in Test.Tasty.Ingredients.ConsoleReporter Methods mempty :: TestOutput # mappend :: TestOutput -> TestOutput -> TestOutput # mconcat :: [TestOutput] -> TestOutput #
Monoid OptionSet
Instance details Defined in Test.Tasty.Options Methods mempty :: OptionSet # mappend :: OptionSet -> OptionSet -> OptionSet # mconcat :: [OptionSet] -> OptionSet #
Monoid Builder
Instance details Defined in Data.Text.Internal.Builder Methods mempty :: Builder # mappend :: Builder -> Builder -> Builder # mconcat :: [Builder] -> Builder #
Monoid StrictBuilder
Instance details Defined in Data.Text.Internal.StrictBuilder Methods mempty :: StrictBuilder # mappend :: StrictBuilder -> StrictBuilder -> StrictBuilder # mconcat :: [StrictBuilder] -> StrictBuilder #
Monoid ()	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: () # mappend :: () -> () -> () # mconcat :: [()] -> () #
(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) #
(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) #
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) #
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) #
(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) #
(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) #
Monoid (Exp ()) Source #
Instance details Defined in Data.Array.Accelerate.Data.Monoid Methods mempty :: Exp () # mappend :: Exp () -> Exp () -> Exp () # mconcat :: [Exp ()] -> Exp () #
FiniteBits a => Monoid (And a)	This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: And a # mappend :: And a -> And a -> And a # mconcat :: [And a] -> And a #
FiniteBits a => Monoid (Iff a)	This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Iff a # mappend :: Iff a -> Iff a -> Iff a # mconcat :: [Iff a] -> Iff a #
Bits a => Monoid (Ior a)	Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Ior a # mappend :: Ior a -> Ior a -> Ior a # mconcat :: [Ior a] -> Ior a #
Bits a => Monoid (Xor a)	Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Xor a # mappend :: Xor a -> Xor a -> Xor a # mconcat :: [Xor a] -> Xor a #
Monoid (Comparison a)	`mempty` on comparisons always returns `EQ`. Without newtypes this equals `pure (pure EQ)`. mempty :: Comparison a mempty = Comparison _ _ -> EQ
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)	`mempty` on equivalences always returns `True`. Without newtypes this equals `pure (pure True)`. mempty :: Equivalence a mempty = Equivalence _ _ -> True
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Equivalence a # mappend :: Equivalence a -> Equivalence a -> Equivalence a # mconcat :: [Equivalence a] -> Equivalence a #
Monoid (Predicate a)	`mempty` on predicates always returns `True`. Without newtypes this equals `pure True`. mempty :: Predicate a mempty = _ -> True
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Predicate a # mappend :: Predicate a -> Predicate a -> Predicate a # mconcat :: [Predicate a] -> Predicate 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 (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 #
(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 #
(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 #
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 #
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 (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 (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 #
Monoid a => Monoid (STM a)	Since: base-4.17.0.0
Instance details Defined in GHC.Conc.Sync Methods mempty :: STM a # mappend :: STM a -> STM a -> STM a # mconcat :: [STM a] -> STM a #
(Generic a, Monoid (Rep a ())) => Monoid (Generically a)	Since: base-4.17.0.0
Instance details Defined in GHC.Generics Methods mempty :: Generically a # mappend :: Generically a -> Generically a -> Generically a # mconcat :: [Generically a] -> Generically 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 (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 #
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 #
Ord a => Monoid (Set a)
Instance details Defined in Data.Set.Internal Methods mempty :: Set a # mappend :: Set a -> Set a -> Set a # mconcat :: [Set a] -> Set a #
Monoid 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 #
(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 #
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)
Instance details Defined in Prettyprinter.Internal Methods mempty :: Doc ann # mappend :: Doc ann -> Doc ann -> Doc ann # mconcat :: [Doc ann] -> Doc ann #
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 (PrimArray a)
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 a => Monoid (Q a)	Since: template-haskell-2.17.0.0
Instance details Defined in Language.Haskell.TH.Syntax Methods mempty :: Q a # mappend :: Q a -> Q a -> Q a # mconcat :: [Q a] -> Q a #
Monoid (Validity k)
Instance details Defined in Data.HashMap.Internal.Debug Methods mempty :: Validity k # mappend :: Validity k -> Validity k -> Validity k # mconcat :: [Validity k] -> Validity k #
Hashable a => Monoid (HashSet a)
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 #
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 #
Monoid (Vector a)
Instance details Defined in Data.Vector.Strict Methods mempty :: Vector a # mappend :: Vector a -> Vector a -> Vector a # mconcat :: [Vector a] -> Vector 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 #
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 (Solo a)	Since: base-4.15
Instance details Defined in GHC.Base Methods mempty :: Solo a # mappend :: Solo a -> Solo a -> Solo a # mconcat :: [Solo a] -> Solo a #
Monoid [a]	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: [a] # mappend :: [a] -> [a] -> [a] # mconcat :: [[a]] -> [a] #
Monoid a => Monoid (Op a b)	`mempty @(Op a b)` without newtypes is `mempty @(b->a)` = `_ -> mempty`. mempty :: Op a b mempty = Op _ -> mempty
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 (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 #
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 (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 #
Ord k => Monoid (Map k v)
Instance details Defined in Data.Map.Internal Methods mempty :: Map k v # mappend :: Map k v -> Map k v -> Map k v # mconcat :: [Map k v] -> Map k v #
Monoid (Format r (a -> r))
Instance details Defined in Formatting.Internal Methods mempty :: Format r (a -> r) # mappend :: Format r (a -> r) -> Format r (a -> r) -> Format r (a -> r) # mconcat :: [Format r (a -> r)] -> Format r (a -> r) #
(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 #
Applicative f => Monoid (Traversed a f)
Instance details Defined in Lens.Micro Methods mempty :: Traversed a f # mappend :: Traversed a f -> Traversed a f -> Traversed a f # mconcat :: [Traversed a f] -> Traversed a f #
Hashable k => Monoid (HashMap k v)
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 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 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 (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 #
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 #
(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 a => Monoid (Constant a b)
Instance details Defined in Data.Functor.Constant Methods mempty :: Constant a b # mappend :: Constant a b -> Constant a b -> Constant a b # mconcat :: [Constant a b] -> Constant a b #
(Monoid a, Monoid b, Monoid c) => Monoid (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 (f a), Monoid (g a)) => Monoid (Product f g a)	Since: base-4.16.0.0
Instance details Defined in Data.Functor.Product Methods mempty :: Product f g a # mappend :: Product f g a -> Product f g a -> Product f g a # mconcat :: [Product f g a] -> Product f g a #
(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 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 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 (g a)) => Monoid (Compose f g a)	Since: base-4.16.0.0
Instance details Defined in Data.Functor.Compose Methods mempty :: Compose f g a # mappend :: Compose f g a -> Compose f g a -> Compose f g a # mconcat :: [Compose f g a] -> Compose f g a #
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 (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 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) #

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

An associative operation.

Examples

Expand

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

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

>>> putStr "Hello, " <> putStrLn "World!"
Hello, World!

newtype Sum a #

Monoid under addition.

Sum a <> Sum b = Sum (a + b)

Examples

Expand

>>> Sum 1 <> Sum 2 <> mempty
Sum {getSum = 3}

>>> mconcat [ Sum n | n <- [3 .. 9]]
Sum {getSum = 42}

Constructors

Sum
Fields getSum :: a

Instances

Instances details

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 #

MonadFix Sum

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

mfix :: (a -> Sum a) -> Sum a #

MonadZip Sum

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Zip

Methods

mzip :: Sum a -> Sum b -> Sum (a, b) #

mzipWith :: (a -> b -> c) -> Sum a -> Sum b -> Sum c #

munzip :: Sum (a, b) -> (Sum a, Sum b) #

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 #

Foldable1 Sum

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Sum m -> m #

foldMap1 :: Semigroup m => (a -> m) -> Sum a -> m #

foldMap1' :: Semigroup m => (a -> m) -> Sum a -> m #

toNonEmpty :: Sum a -> NonEmpty a #

maximum :: Ord a => Sum a -> a #

minimum :: Ord a => Sum a -> a #

head :: Sum a -> a #

last :: Sum a -> a #

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Sum a -> b #

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Sum a -> b #

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Sum a -> b #

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Sum a -> b #

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) #

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 #

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 #

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 #

NFData1 Sum

Since: deepseq-1.4.3.0

Instance details

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> Sum a -> () #

Generic1 Sum

Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Sum	Since: base-4.7.0.0
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))

Methods

from1 :: Sum a -> Rep1 Sum a #

to1 :: Rep1 Sum a -> Sum a #

(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)
Instance details Defined in Data.Array.Accelerate.Data.Monoid type Plain (Sum a) = Sum (Plain a)

Methods

lift :: Sum a -> Exp (Plain (Sum a)) Source #

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 #

Unbox a => Vector Vector (Sum a)

Instance details

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: Mutable Vector s (Sum a) -> ST s (Vector (Sum a))

basicUnsafeThaw :: Vector (Sum a) -> ST s (Mutable Vector s (Sum a))

basicLength :: Vector (Sum a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Sum a) -> Vector (Sum a)

basicUnsafeIndexM :: Vector (Sum a) -> Int -> Box (Sum a)

basicUnsafeCopy :: Mutable Vector s (Sum a) -> Vector (Sum a) -> ST s ()

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 :: Int -> ST s (MVector s (Sum a))

basicInitialize :: MVector s (Sum a) -> ST s ()

basicUnsafeReplicate :: Int -> Sum a -> ST s (MVector s (Sum a))

basicUnsafeRead :: MVector s (Sum a) -> Int -> ST s (Sum a)

basicUnsafeWrite :: MVector s (Sum a) -> Int -> Sum a -> ST s ()

basicClear :: MVector s (Sum a) -> ST s ()

basicSet :: MVector s (Sum a) -> Sum a -> ST s ()

basicUnsafeCopy :: MVector s (Sum a) -> MVector s (Sum a) -> ST s ()

basicUnsafeMove :: MVector s (Sum a) -> MVector s (Sum a) -> ST s ()

basicUnsafeGrow :: MVector s (Sum a) -> Int -> ST s (MVector s (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 #

Elt a => Elt (Sum a) Source #

Instance details

Defined in Data.Array.Accelerate.Data.Monoid

Methods

eltR :: TypeR (EltR (Sum a))

tagsR :: [TagR (EltR (Sum a))]

fromElt :: Sum a -> EltR (Sum a)

toElt :: EltR (Sum a) -> Sum a

Data a => Data (Sum a)

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Sum a -> c (Sum a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum a) #

toConstr :: Sum a -> Constr #

dataTypeOf :: Sum a -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Sum a)) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum a)) #

gmapT :: (forall b. Data b => b -> b) -> Sum a -> Sum a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Sum a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (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) #

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 => 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 => 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 #

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) #

Bounded a => Bounded (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: Sum a #

maxBound :: Sum a #

Generic (Sum a)

Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Sum a)	Since: base-4.7.0.0
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)))

Methods

from :: Sum a -> Rep (Sum a) x #

to :: Rep (Sum a) x -> 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) #

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 #

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 #

NFData a => NFData (Sum a)

Since: deepseq-1.4.0.0

Instance details

Defined in Control.DeepSeq

Methods

rnf :: 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 #

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 #

Prim a => Prim (Sum a)

Instance details

Defined in Data.Primitive.Types

Methods

sizeOfType# :: Proxy (Sum a) -> Int#

sizeOf# :: Sum a -> Int#

alignmentOfType# :: Proxy (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

type Rep1 Sum

Since: base-4.7.0.0

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))

newtype MVector s (Sum a)

Instance details

Defined in Data.Vector.Unboxed.Base

newtype MVector s (Sum a) = MV_Sum (MVector s a)

type Plain (Sum a) Source #

Instance details

Defined in Data.Array.Accelerate.Data.Monoid

type Plain (Sum a) = Sum (Plain a)

type Rep (Sum a)

Since: base-4.7.0.0

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)

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

newtype Product a #

Monoid under multiplication.

Product x <> Product y == Product (x * y)

Examples

Expand

>>> Product 3 <> Product 4 <> mempty
Product {getProduct = 12}

>>> mconcat [ Product n | n <- [2 .. 10]]
Product {getProduct = 3628800}

Constructors

Product
Fields getProduct :: a

Instances

Instances details

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 #

MonadFix Product

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

mfix :: (a -> Product a) -> Product a #

MonadZip Product

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Zip

Methods

mzip :: Product a -> Product b -> Product (a, b) #

mzipWith :: (a -> b -> c) -> Product a -> Product b -> Product c #

munzip :: Product (a, b) -> (Product a, Product b) #

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 #

Foldable1 Product

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Product m -> m #

foldMap1 :: Semigroup m => (a -> m) -> Product a -> m #

foldMap1' :: Semigroup m => (a -> m) -> Product a -> m #

toNonEmpty :: Product a -> NonEmpty a #

maximum :: Ord a => Product a -> a #

minimum :: Ord a => Product a -> a #

head :: Product a -> a #

last :: Product a -> a #

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Product a -> b #

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Product a -> b #

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Product a -> b #

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Product a -> b #

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) #

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 #

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 #

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 #

NFData1 Product

Since: deepseq-1.4.3.0

Instance details

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> Product a -> () #

Generic1 Product

Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Product	Since: base-4.7.0.0
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))

Methods

from1 :: Product a -> Rep1 Product a #

to1 :: Rep1 Product a -> Product a #

(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)
Instance details Defined in Data.Array.Accelerate.Data.Monoid type Plain (Product a) = Product (Plain a)

Methods

lift :: Product a -> Exp (Plain (Product a)) Source #

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 #

Unbox a => Vector Vector (Product a)

Instance details

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: Mutable Vector s (Product a) -> ST s (Vector (Product a))

basicUnsafeThaw :: Vector (Product a) -> ST s (Mutable Vector s (Product a))

basicLength :: Vector (Product a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Product a) -> Vector (Product a)

basicUnsafeIndexM :: Vector (Product a) -> Int -> Box (Product a)

basicUnsafeCopy :: Mutable Vector s (Product a) -> Vector (Product a) -> ST s ()

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 :: Int -> ST s (MVector s (Product a))

basicInitialize :: MVector s (Product a) -> ST s ()

basicUnsafeReplicate :: Int -> Product a -> ST s (MVector s (Product a))

basicUnsafeRead :: MVector s (Product a) -> Int -> ST s (Product a)

basicUnsafeWrite :: MVector s (Product a) -> Int -> Product a -> ST s ()

basicClear :: MVector s (Product a) -> ST s ()

basicSet :: MVector s (Product a) -> Product a -> ST s ()

basicUnsafeCopy :: MVector s (Product a) -> MVector s (Product a) -> ST s ()

basicUnsafeMove :: MVector s (Product a) -> MVector s (Product a) -> ST s ()

basicUnsafeGrow :: MVector s (Product a) -> Int -> ST s (MVector s (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 #

Elt a => Elt (Product a) Source #

Instance details

Defined in Data.Array.Accelerate.Data.Monoid

Methods

eltR :: TypeR (EltR (Product a))

tagsR :: [TagR (EltR (Product a))]

fromElt :: Product a -> EltR (Product a)

toElt :: EltR (Product a) -> Product a

Data a => Data (Product a)

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Product a -> c (Product a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product a) #

toConstr :: Product a -> Constr #

dataTypeOf :: Product a -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Product a)) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product a)) #

gmapT :: (forall b. Data b => b -> b) -> Product a -> Product a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Product a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Product a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (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) #

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 => 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 => 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 #

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) #

Bounded a => Bounded (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: Product a #

maxBound :: Product a #

Generic (Product a)

Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Product a)	Since: base-4.7.0.0
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)))