Data.Array.Accelerate.Data.Monoid

Monoid instances for Accelerate

Since: accelerate-1.2.0.0

Documentation

class Semigroup a => Monoid a where

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

• x <> mempty = x

• mempty <> x = x

• x <> (y <> z) = (x <> y) <> z (Semigroup law)

• mconcat = foldr '(<>)' mempty

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

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

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

Minimal complete definition

mempty

Methods

mempty :: a

Identity of mappend

mappend :: a -> a -> a

An associative operation

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

mconcat :: [a] -> a

Fold a list using the monoid.

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

Instances

Monoid Ordering

Since: base-2.1

Defined in GHC.Base

Methods

mempty :: Ordering

mappend :: Ordering -> Ordering -> Ordering

mconcat :: [Ordering] -> Ordering

Monoid ()

Since: base-2.1

Defined in GHC.Base

Methods

mempty :: ()

mappend :: () -> () -> ()

mconcat :: [()] -> ()

Monoid Doc

Defined in Text.PrettyPrint.ANSI.Leijen.Internal

Methods

mempty :: Doc

mappend :: Doc -> Doc -> Doc

mconcat :: [Doc] -> Doc

Monoid All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: All

mappend :: All -> All -> All

mconcat :: [All] -> All

Monoid Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Any

mappend :: Any -> Any -> Any

mconcat :: [Any] -> Any

Monoid String

Defined in Basement.UTF8.Base

Methods

mempty :: String

mappend :: String -> String -> String

mconcat :: [String] -> String

Monoid ShortByteString

Defined in Data.ByteString.Short.Internal

Methods

mempty :: ShortByteString

mappend :: ShortByteString -> ShortByteString -> ShortByteString

mconcat :: [ShortByteString] -> ShortByteString

Monoid ByteString

Defined in Data.ByteString.Lazy.Internal

Methods

mempty :: ByteString

mappend :: ByteString -> ByteString -> ByteString

mconcat :: [ByteString] -> ByteString

Monoid ByteString

Defined in Data.ByteString.Internal

Methods

mempty :: ByteString

mappend :: ByteString -> ByteString -> ByteString

mconcat :: [ByteString] -> ByteString

Monoid Builder

Defined in Data.ByteString.Builder.Internal

Methods

mempty :: Builder

mappend :: Builder -> Builder -> Builder

mconcat :: [Builder] -> Builder

Monoid IntSet

Defined in Data.IntSet.Internal

Methods

mempty :: IntSet

mappend :: IntSet -> IntSet -> IntSet

mconcat :: [IntSet] -> IntSet

Monoid ParseError

Defined in Options.Applicative.Types

Methods

mempty :: ParseError

mappend :: ParseError -> ParseError -> ParseError

mconcat :: [ParseError] -> ParseError

Monoid Completer

Defined in Options.Applicative.Types

Methods

mempty :: Completer

mappend :: Completer -> Completer -> Completer

mconcat :: [Completer] -> Completer

Monoid Doc

Defined in Text.PrettyPrint.HughesPJ

Methods

mempty :: Doc

mappend :: Doc -> Doc -> Doc

mconcat :: [Doc] -> Doc

Monoid ByteArray

Defined in Data.Primitive.ByteArray

Methods

mempty :: ByteArray

mappend :: ByteArray -> ByteArray -> ByteArray

mconcat :: [ByteArray] -> ByteArray

Monoid OptionSet

Later options override earlier ones

Defined in Test.Tasty.Options

Methods

mempty :: OptionSet

mappend :: OptionSet -> OptionSet -> OptionSet

mconcat :: [OptionSet] -> OptionSet

Monoid Slot

Defined in Data.HashTable.ST.Basic

Methods

mempty :: Slot

mappend :: Slot -> Slot -> Slot

mconcat :: [Slot] -> Slot

a :=> (Monoid (Dict a))

Defined in Data.Constraint

Methods

ins :: a :- Monoid (Dict a)

() :=> (Monoid [a])

Defined in Data.Constraint

Methods

ins :: () :- Monoid [a]

() :=> (Monoid Ordering)

Defined in Data.Constraint

Methods

ins :: () :- Monoid Ordering

() :=> (Monoid ())

Defined in Data.Constraint

Methods

ins :: () :- Monoid ()

Monoid [a]

Since: base-2.1

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 e*e = e and e*s = s = s*e for all s ∈ S."

Since 4.11.0: constraint on inner a value generalised from Monoid to Semigroup.

Since: base-2.1

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

Defined in GHC.Base

Methods

mempty :: IO a

mappend :: IO a -> IO a -> IO a

mconcat :: [IO a] -> IO a

(Ord a, Bounded a) => Monoid (Min a)

Since: base-4.9.0.0

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

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

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

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)

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

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

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

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

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

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

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

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)

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)

Defined in Basement.Block.Base

Methods

mempty :: Block ty

mappend :: Block ty -> Block ty -> Block ty

mconcat :: [Block ty] -> Block ty

Monoid (CountOf ty)

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)

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)

Defined in Data.Colour.Internal

Methods

mempty :: AlphaColour a

mappend :: AlphaColour a -> AlphaColour a -> AlphaColour a

mconcat :: [AlphaColour a] -> AlphaColour a

a => Monoid (Dict a)

Defined in Data.Constraint

Methods

mempty :: Dict a

mappend :: Dict a -> Dict a -> Dict a

mconcat :: [Dict a] -> Dict a

Monoid (IntMap a)

Defined in Data.IntMap.Internal

Methods

mempty :: IntMap a

mappend :: IntMap a -> IntMap a -> IntMap a

mconcat :: [IntMap a] -> IntMap a

Monoid (Seq a)

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)

Defined in Data.Set.Internal

Methods

mempty :: Set a

mappend :: Set a -> Set a -> Set a

mconcat :: [Set a] -> Set a

Monoid (Predicate a)

Defined in Data.Functor.Contravariant

Methods

mempty :: Predicate a

mappend :: Predicate a -> Predicate a -> Predicate a

mconcat :: [Predicate a] -> Predicate a

Monoid (Comparison a)

Defined in Data.Functor.Contravariant

Methods

mempty :: Comparison a

mappend :: Comparison a -> Comparison a -> Comparison a

mconcat :: [Comparison a] -> Comparison a

Monoid (Equivalence a)

Defined in Data.Functor.Contravariant

Methods

mempty :: Equivalence a

mappend :: Equivalence a -> Equivalence a -> Equivalence a

mconcat :: [Equivalence a] -> Equivalence a

Prim a => Monoid (Vector a)

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)

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)

Defined in Data.HashSet

Methods

mempty :: HashSet a

mappend :: HashSet a -> HashSet a -> HashSet a

mconcat :: [HashSet a] -> HashSet a

Monoid (Vector a)

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)

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)

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)

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)

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)

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

mempty :: Doc a

mappend :: Doc a -> Doc a -> Doc a

mconcat :: [Doc a] -> Doc a

PrimUnlifted a => Monoid (UnliftedArray a)

Since: primitive-0.6.4.0

Defined in Data.Primitive.UnliftedArray

Methods

mempty :: UnliftedArray a

mappend :: UnliftedArray a -> UnliftedArray a -> UnliftedArray a

mconcat :: [UnliftedArray a] -> UnliftedArray a

Monoid (PrimArray a)

Since: primitive-0.6.4.0

Defined in Data.Primitive.PrimArray

Methods

mempty :: PrimArray a

mappend :: PrimArray a -> PrimArray a -> PrimArray a

mconcat :: [PrimArray a] -> PrimArray a

Monoid (SmallArray a)

Defined in Data.Primitive.SmallArray

Methods

mempty :: SmallArray a

mappend :: SmallArray a -> SmallArray a -> SmallArray a

mconcat :: [SmallArray a] -> SmallArray a

Monoid (Array a)

Defined in Data.Primitive.Array

Methods

mempty :: Array a

mappend :: Array a -> Array a -> Array a

mconcat :: [Array a] -> Array a

Monoid (Doc a)

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)

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))

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 ())

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))

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))

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))

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))

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))

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))

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))

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))

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)

Class (Semigroup a) (Monoid a)

Defined in Data.Constraint

Methods

cls :: Monoid a :- Semigroup a

(Monoid a) :=> (Monoid (Maybe a))

Defined in Data.Constraint

Methods

ins :: Monoid a :- Monoid (Maybe a)

(Monoid a) :=> (Monoid (Const a b))

Defined in Data.Constraint

Methods

ins :: Monoid a :- Monoid (Const a b)

(Monoid a) :=> (Monoid (Identity a))

Defined in Data.Constraint

Methods

ins :: Monoid a :- Monoid (Identity a)

(Monoid a) :=> (Monoid (IO a))

Defined in Data.Constraint

Methods

ins :: Monoid a :- Monoid (IO a)

(Monoid a) :=> (Applicative ((,) a))

Defined in Data.Constraint

Methods

ins :: Monoid a :- Applicative ((,) a)

(Monoid a) :=> (Applicative (Const a :: * -> *))

Defined in Data.Constraint

Methods

ins :: Monoid a :- Applicative (Const a)

Monoid b => Monoid (a -> b)

Since: base-2.1

Defined in GHC.Base

Methods

mempty :: a -> b

mappend :: (a -> b) -> (a -> b) -> a -> b

mconcat :: [a -> b] -> a -> b

(Monoid a, Monoid b) => Monoid (a, b)

Since: base-2.1

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)

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

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)

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)

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)

Defined in Data.HashMap.Base

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)

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

Monoid (Deepening i a)

This is an illegal Monoid.

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 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')]

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

(Contravariant f, Applicative f) => Monoid (Folding f a)

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)

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)

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)

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 a, Monoid b) :=> (Monoid (a, b))

Defined in Data.Constraint

Methods

ins :: (Monoid a, Monoid b) :- Monoid (a, b)

(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)

Since: base-2.1

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)

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

Alternative f => Monoid (Alt f a)

Since: base-4.8.0.0

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 (ReifiedIndexedFold i s a)

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)

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

(Semigroup a, Monoid a) => Monoid (Tagged s a)

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 b, Monoid c, Monoid d) => Monoid (a, b, c, d)

Since: base-2.1

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 a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e)

Since: base-2.1

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)

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.

newtype Sum a

Monoid under addition.

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

Constructors

Sum

Fields

• getSum :: a

Instances

Monad Sum

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

(>>=) :: Sum a -> (a -> Sum b) -> Sum b

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

return :: a -> Sum a

fail :: String -> Sum a

Functor Sum

Since: base-4.8.0.0

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

Defined in Control.Monad.Fix

Methods

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

Applicative Sum

Since: base-4.8.0.0

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

Defined in Data.Foldable

Methods

fold :: Monoid m => Sum m -> m

foldMap :: Monoid m => (a -> m) -> Sum a -> m

foldr :: (a -> b -> b) -> b -> Sum a -> b

foldr' :: (a -> b -> b) -> b -> Sum a -> b

foldl :: (b -> a -> b) -> b -> Sum a -> b

foldl' :: (b -> a -> b) -> b -> Sum a -> b

foldr1 :: (a -> a -> a) -> Sum a -> a

foldl1 :: (a -> a -> a) -> Sum a -> a

toList :: Sum a -> [a]

null :: Sum a -> Bool

length :: Sum a -> Int

elem :: Eq a => a -> Sum a -> Bool

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

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

sum :: Num a => Sum a -> a

product :: Num a => Sum a -> a

Traversable Sum

Since: base-4.8.0.0

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

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

Defined in Control.DeepSeq

Methods

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

Traversable1 Sum

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

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)

(<$) :: (Elt a, Elt b, Elt (Sum a), Elt (Sum b)) => Exp a -> Exp (Sum b) -> Exp (Sum a)

Elt a => Unlift Exp (Sum (Exp a))

Defined in Data.Array.Accelerate.Data.Monoid

Methods

unlift :: Exp (Plain (Sum (Exp a))) -> Sum (Exp a)

(Lift Exp a, Elt (Plain a)) => Lift Exp (Sum a)

Defined in Data.Array.Accelerate.Data.Monoid

Associated Types

type Plain (Sum a) :: *

Methods

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

Bounded a => Bounded (Sum a)

Defined in Data.Semigroup.Internal

Methods

minBound :: Sum a

maxBound :: Sum a

Bounded a => Bounded (Exp (Sum a))

Defined in Data.Array.Accelerate.Data.Monoid

Methods

minBound :: Exp (Sum a)

maxBound :: Exp (Sum a)

Eq a => Eq (Sum a)

Defined in Data.Semigroup.Internal

Methods

(==) :: Sum a -> Sum a -> Bool

(/=) :: Sum a -> Sum a -> Bool

Num a => Num (Sum a)

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))

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)

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)

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)

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Sum a -> ShowS

show :: Sum a -> String

showList :: [Sum a] -> ShowS

Generic (Sum a)

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Sum a) :: * -> *

Methods

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

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

Num a => Semigroup (Sum a)

Since: base-4.9.0.0

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))

Since: accelerate-1.2.0.0

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

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))

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

Defined in Control.DeepSeq

Methods

rnf :: Sum a -> ()

Wrapped (Sum a)

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)

Defined in Control.Lens.Empty

Methods

_Empty :: Prism' (Sum a) ()

Elt a => Elt (Sum a)

Defined in Data.Array.Accelerate.Data.Monoid

Methods

eltType :: Sum a -> TupleType (EltRepr (Sum a))

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

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

Eq a => Eq (Sum a)

Defined in Data.Array.Accelerate.Data.Monoid

Methods

(==) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool

(/=) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool

Ord a => Ord (Sum a)

Defined in Data.Array.Accelerate.Data.Monoid

Methods

(<) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool

(>) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool

(<=) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool

(>=) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool

min :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a)

max :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a)

compare :: Exp (Sum a) -> Exp (Sum a) -> Exp Ordering

Generic1 Sum

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Sum :: k -> *

Methods

from1 :: Sum a -> Rep1 Sum a

to1 :: Rep1 Sum a -> Sum a

t ~ Sum b => Rewrapped (Sum a) t

Defined in Control.Lens.Wrapped

type Rep Sum

Defined in Data.Functor.Rep

type Rep Sum = ()

type Rep (Sum a)

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)))

type Unwrapped (Sum a)

Defined in Control.Lens.Wrapped

type Unwrapped (Sum a) = a

type Plain (Sum a)

Defined in Data.Array.Accelerate.Data.Monoid

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

type Rep1 Sum

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 Product a

Monoid under multiplication.

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

Constructors

Product

Fields

• getProduct :: a

Instances

Monad Product

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

(>>=) :: Product a -> (a -> Product b) -> Product b

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

return :: a -> Product a

fail :: String -> Product a

Functor Product

Since: base-4.8.0.0

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

Defined in Control.Monad.Fix

Methods

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

Applicative Product

Since: base-4.8.0.0

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

Defined in Data.Foldable

Methods

fold :: Monoid m => Product m -> m

foldMap :: Monoid m => (a -> m) -> Product a -> m

foldr :: (a -> b -> b) -> b -> Product a -> b

foldr' :: (a -> b -> b) -> b -> Product a -> b

foldl :: (b -> a -> b) -> b -> Product a -> b

foldl' :: (b -> a -> b) -> b -> Product a -> b

foldr1 :: (a -> a -> a) -> Product a -> a

foldl1 :: (a -> a -> a) -> Product a -> a

toList :: Product a -> [a]

null :: Product a -> Bool

length :: Product a -> Int

elem :: Eq a => a -> Product a -> Bool

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

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

sum :: Num a => Product a -> a

product :: Num a => Product a -> a

Traversable Product

Since: base-4.8.0.0

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

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

Defined in Control.DeepSeq

Methods

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

Traversable1 Product

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

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)

(<$) :: (Elt a, Elt b, Elt (Product a), Elt (Product b)) => Exp a -> Exp (Product b) -> Exp (Product a)

Elt a => Unlift Exp (Product (Exp a))

Defined in Data.Array.Accelerate.Data.Monoid

Methods

unlift :: Exp (Plain (Product (Exp a))) -> Product (Exp a)

(Lift Exp a, Elt (Plain a)) => Lift Exp (Product a)

Defined in Data.Array.Accelerate.Data.Monoid

Associated Types

type Plain (Product a) :: *

Methods

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

Bounded a => Bounded (Product a)

Defined in Data.Semigroup.Internal

Methods

minBound :: Product a

maxBound :: Product a

Bounded a => Bounded (Exp (Product a))

Defined in Data.Array.Accelerate.Data.Monoid

Methods

minBound :: Exp (Product a)

maxBound :: Exp (Product a)

Eq a => Eq (Product a)

Defined in Data.Semigroup.Internal

Methods

(==) :: Product a -> Product a -> Bool

(/=) :: Product a -> Product a -> Bool

Num a => Num (Product a)

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))

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)

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)

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)

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Product a -> ShowS

show :: Product a -> String

showList :: [Product a] -> ShowS

Generic (Product a)

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Product a) :: * -> *

Methods

from :: Product a -> Rep (Product a) x

to :: Rep (Product a) x -> Product a

Num a => Semigroup (Product a)

Since: base-4.9.0.0

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))

Since: accelerate-1.2.0.0

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

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))

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

Defined in Control.DeepSeq

Methods

rnf :: Product a -> ()

Wrapped (Product a)

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)

Defined in Control.Lens.Empty

Methods

_Empty :: Prism' (Product a) ()

Elt a => Elt (Product a)

Defined in Data.Array.Accelerate.Data.Monoid

Methods

eltType :: Product a -> TupleType (EltRepr (Product a))

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

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

Eq a => Eq (Product a)

Defined in Data.Array.Accelerate.Data.Monoid

Methods

(==) :: Exp (Product a) -> Exp (Product a) -> Exp Bool

(/=) :: Exp (Product a) -> Exp (Product a) -> Exp Bool

Ord a => Ord (Product a)

Defined in Data.Array.Accelerate.Data.Monoid

Methods

(<) :: Exp (Product a) -> Exp (Product a) -> Exp Bool

(>) :: Exp (Product a) -> Exp (Product a) -> Exp Bool

(<=) :: Exp (Product a) -> Exp (Product a) -> Exp Bool

(>=) :: Exp (Product a) -> Exp (Product a) -> Exp Bool

min :: Exp (Product a) -> Exp (Product a) -> Exp (Product a)

max :: Exp (Product a) -> Exp (Product a) -> Exp (Product a)

compare :: Exp (Product a) -> Exp (Product a) -> Exp Ordering

Generic1 Product

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Product :: k -> *

Methods

from1 :: Product a -> Rep1 Product a

to1 :: Rep1 Product a -> Product a

t ~ Product b => Rewrapped (Product a) t

Defined in Control.Lens.Wrapped

type Rep Product

Defined in Data.Functor.Rep

type Rep Product = ()

type Rep (Product a)

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)))

type Unwrapped (Product a)

Defined in Control.Lens.Wrapped

type Unwrapped (Product a) = a

type Plain (Product a)

Defined in Data.Array.Accelerate.Data.Monoid

type Plain (Product a) = Product (Plain a)

type Rep1 Product

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))

Orphan instances

Elt a => Unlift Exp (Sum (Exp a))

Methods

unlift :: Exp (Plain (Sum (Exp a))) -> Sum (Exp a)

Elt a => Unlift Exp (Product (Exp a))

Methods

unlift :: Exp (Plain (Product (Exp a))) -> Product (Exp a)

(Lift Exp a, Elt (Plain a)) => Lift Exp (Sum a)

Associated Types

type Plain (Sum a) :: *

Methods

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

(Lift Exp a, Elt (Plain a)) => Lift Exp (Product a)

Associated Types

type Plain (Product a) :: *

Methods

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

Bounded a => Bounded (Exp (Sum a))

Methods

minBound :: Exp (Sum a)

maxBound :: Exp (Sum a)

Bounded a => Bounded (Exp (Product a))

Methods

minBound :: Exp (Product a)

maxBound :: Exp (Product a)

Num a => Num (Exp (Sum a))

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))

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))

Since: accelerate-1.2.0.0

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))

Since: accelerate-1.2.0.0

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 ())

Methods

mempty :: Exp ()

mappend :: Exp () -> Exp () -> Exp ()

mconcat :: [Exp ()] -> Exp ()

(Elt a, Elt b, Monoid (Exp a), Monoid (Exp b)) => Monoid (Exp (a, b))

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))

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))

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))

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))

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))

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)

Methods

eltType :: Sum a -> TupleType (EltRepr (Sum a))

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

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

Elt a => Elt (Product a)

Methods

eltType :: Product a -> TupleType (EltRepr (Product a))

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

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

Eq a => Eq (Sum a)

Methods

(==) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool

(/=) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool

Eq a => Eq (Product a)

Methods

(==) :: Exp (Product a) -> Exp (Product a) -> Exp Bool

(/=) :: Exp (Product a) -> Exp (Product a) -> Exp Bool

Ord a => Ord (Sum a)

Methods

(<) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool

(>) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool

(<=) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool

(>=) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool

min :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a)

max :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a)

compare :: Exp (Sum a) -> Exp (Sum a) -> Exp Ordering

Ord a => Ord (Product a)

Methods

(<) :: Exp (Product a) -> Exp (Product a) -> Exp Bool

(>) :: Exp (Product a) -> Exp (Product a) -> Exp Bool

(<=) :: Exp (Product a) -> Exp (Product a) -> Exp Bool

(>=) :: Exp (Product a) -> Exp (Product a) -> Exp Bool

min :: Exp (Product a) -> Exp (Product a) -> Exp (Product a)

max :: Exp (Product a) -> Exp (Product a) -> Exp (Product a)

compare :: Exp (Product a) -> Exp (Product a) -> Exp Ordering