Data.Array.Accelerate.Data.Monoid

Monoid instances for Accelerate

Since: 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: 2.1

Methods

mempty :: Ordering

mappend :: Ordering -> Ordering -> Ordering

mconcat :: [Ordering] -> Ordering

Monoid ()

Since: 2.1

Methods

mempty :: ()

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

mconcat :: [()] -> ()

Monoid Doc

Methods

mempty :: Doc

mappend :: Doc -> Doc -> Doc

mconcat :: [Doc] -> Doc

Monoid All

Since: 2.1

Methods

mempty :: All

mappend :: All -> All -> All

mconcat :: [All] -> All

Monoid Any

Since: 2.1

Methods

mempty :: Any

mappend :: Any -> Any -> Any

mconcat :: [Any] -> Any

Monoid String

Methods

mempty :: String

mappend :: String -> String -> String

mconcat :: [String] -> String

Monoid ShortByteString

Methods

mempty :: ShortByteString

mappend :: ShortByteString -> ShortByteString -> ShortByteString

mconcat :: [ShortByteString] -> ShortByteString

Monoid ByteString

Methods

mempty :: ByteString

mappend :: ByteString -> ByteString -> ByteString

mconcat :: [ByteString] -> ByteString

Monoid ByteString

Methods

mempty :: ByteString

mappend :: ByteString -> ByteString -> ByteString

mconcat :: [ByteString] -> ByteString

Monoid Builder

Methods

mempty :: Builder

mappend :: Builder -> Builder -> Builder

mconcat :: [Builder] -> Builder

Monoid IntSet

Methods

mempty :: IntSet

mappend :: IntSet -> IntSet -> IntSet

mconcat :: [IntSet] -> IntSet

Monoid ParseError

Methods

mempty :: ParseError

mappend :: ParseError -> ParseError -> ParseError

mconcat :: [ParseError] -> ParseError

Monoid Completer

Methods

mempty :: Completer

mappend :: Completer -> Completer -> Completer

mconcat :: [Completer] -> Completer

Monoid Doc

Methods

mempty :: Doc

mappend :: Doc -> Doc -> Doc

mconcat :: [Doc] -> Doc

Monoid OptionSet

Later options override earlier ones

Methods

mempty :: OptionSet

mappend :: OptionSet -> OptionSet -> OptionSet

mconcat :: [OptionSet] -> OptionSet

Monoid Slot

Methods

mempty :: Slot

mappend :: Slot -> Slot -> Slot

mconcat :: [Slot] -> Slot

a :=> (Monoid (Dict a))

Methods

ins :: a :- Monoid (Dict a)

() :=> (Monoid [a])

Methods

ins :: () :- Monoid [a]

() :=> (Monoid Ordering)

Methods

ins :: () :- Monoid Ordering

() :=> (Monoid ())

Methods

ins :: () :- Monoid ()

Monoid [a]

Since: 2.1

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: 2.1

Methods

mempty :: Maybe a

mappend :: Maybe a -> Maybe a -> Maybe a

mconcat :: [Maybe a] -> Maybe a

Monoid a => Monoid (IO a)

Since: 4.9.0.0

Methods

mempty :: IO a

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

mconcat :: [IO a] -> IO a

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

Since: 4.9.0.0

Methods

mempty :: Min a

mappend :: Min a -> Min a -> Min a

mconcat :: [Min a] -> Min a

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

Since: 4.9.0.0

Methods

mempty :: Max a

mappend :: Max a -> Max a -> Max a

mconcat :: [Max a] -> Max a

Monoid m => Monoid (WrappedMonoid m)

Since: 4.9.0.0

Methods

mempty :: WrappedMonoid m

mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

mconcat :: [WrappedMonoid m] -> WrappedMonoid m

Semigroup a => Monoid (Option a)

Since: 4.9.0.0

Methods

mempty :: Option a

mappend :: Option a -> Option a -> Option a

mconcat :: [Option a] -> Option a

Monoid a => Monoid (Identity a)

Methods

mempty :: Identity a

mappend :: Identity a -> Identity a -> Identity a

mconcat :: [Identity a] -> Identity a

Monoid (First a)

Since: 2.1

Methods

mempty :: First a

mappend :: First a -> First a -> First a

mconcat :: [First a] -> First a

Monoid (Last a)

Since: 2.1

Methods

mempty :: Last a

mappend :: Last a -> Last a -> Last a

mconcat :: [Last a] -> Last a

Monoid a => Monoid (Dual a)

Since: 2.1

Methods

mempty :: Dual a

mappend :: Dual a -> Dual a -> Dual a

mconcat :: [Dual a] -> Dual a

Monoid (Endo a)

Since: 2.1

Methods

mempty :: Endo a

mappend :: Endo a -> Endo a -> Endo a

mconcat :: [Endo a] -> Endo a

Num a => Monoid (Sum a)

Since: 2.1

Methods

mempty :: Sum a

mappend :: Sum a -> Sum a -> Sum a

mconcat :: [Sum a] -> Sum a

Num a => Monoid (Product a)

Since: 2.1

Methods

mempty :: Product a

mappend :: Product a -> Product a -> Product a

mconcat :: [Product a] -> Product a

Monoid a => Monoid (Down a)

Since: 4.11.0.0

Methods

mempty :: Down a

mappend :: Down a -> Down a -> Down a

mconcat :: [Down a] -> Down a

PrimType ty => Monoid (UArray ty)

Methods

mempty :: UArray ty

mappend :: UArray ty -> UArray ty -> UArray ty

mconcat :: [UArray ty] -> UArray ty

PrimType ty => Monoid (Block ty)

Methods

mempty :: Block ty

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

mconcat :: [Block ty] -> Block ty

Monoid (CountOf ty)

Methods

mempty :: CountOf ty

mappend :: CountOf ty -> CountOf ty -> CountOf ty

mconcat :: [CountOf ty] -> CountOf ty

Num a => Monoid (Colour a)

Methods

mempty :: Colour a

mappend :: Colour a -> Colour a -> Colour a

mconcat :: [Colour a] -> Colour a

Num a => Monoid (AlphaColour a)

Methods

mempty :: AlphaColour a

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

mconcat :: [AlphaColour a] -> AlphaColour a

a => Monoid (Dict a)

Methods

mempty :: Dict a

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

mconcat :: [Dict a] -> Dict a

Monoid (IntMap a)

Methods

mempty :: IntMap a

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

mconcat :: [IntMap a] -> IntMap a

Monoid (Seq a)

Methods

mempty :: Seq a

mappend :: Seq a -> Seq a -> Seq a

mconcat :: [Seq a] -> Seq a

Ord a => Monoid (Set a)

Methods

mempty :: Set a

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

mconcat :: [Set a] -> Set a

Monoid (Predicate a)

Methods

mempty :: Predicate a

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

mconcat :: [Predicate a] -> Predicate a

Monoid (Comparison a)

Methods

mempty :: Comparison a

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

mconcat :: [Comparison a] -> Comparison a

Monoid (Equivalence a)

Methods

mempty :: Equivalence a

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

mconcat :: [Equivalence a] -> Equivalence a

Prim a => Monoid (Vector a)

Methods

mempty :: Vector a

mappend :: Vector a -> Vector a -> Vector a

mconcat :: [Vector a] -> Vector a

Storable a => Monoid (Vector a)

Methods

mempty :: Vector a

mappend :: Vector a -> Vector a -> Vector a

mconcat :: [Vector a] -> Vector a

(Hashable a, Eq a) => Monoid (HashSet a)

Methods

mempty :: HashSet a

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

mconcat :: [HashSet a] -> HashSet a

Monoid (Vector a)

Methods

mempty :: Vector a

mappend :: Vector a -> Vector a -> Vector a

mconcat :: [Vector a] -> Vector a

Ord a => Monoid (Min a)

Methods

mempty :: Min a

mappend :: Min a -> Min a -> Min a

mconcat :: [Min a] -> Min a

Ord a => Monoid (Max a)

Methods

mempty :: Max a

mappend :: Max a -> Max a -> Max a

mconcat :: [Max a] -> Max a

Monoid (Leftmost a)

Methods

mempty :: Leftmost a

mappend :: Leftmost a -> Leftmost a -> Leftmost a

mconcat :: [Leftmost a] -> Leftmost a

Monoid (Rightmost a)

Methods

mempty :: Rightmost a

mappend :: Rightmost a -> Rightmost a -> Rightmost a

mconcat :: [Rightmost a] -> Rightmost a

Monoid (Doc a)

Methods

mempty :: Doc a

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

mconcat :: [Doc a] -> Doc a

Monoid (Array a)

Methods

mempty :: Array a

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

mconcat :: [Array a] -> Array a

Monoid (Doc a)

Methods

mempty :: Doc a

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

mconcat :: [Doc a] -> Doc a

Monoid (MergeSet a)

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))

Methods

mempty :: Exp (Maybe a)

mappend :: Exp (Maybe a) -> Exp (Maybe a) -> Exp (Maybe a)

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

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

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))

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))

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)

Class (Semigroup a) (Monoid a)

Methods

cls :: Monoid a :- Semigroup a

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

Methods

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

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

Methods

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

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

Methods

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

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

Methods

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

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

Methods

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

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

Methods

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

Monoid b => Monoid (a -> b)

Since: 2.1

Methods

mempty :: a -> b

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

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

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

Since: 2.1

Methods

mempty :: (a, b)

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

mconcat :: [(a, b)] -> (a, b)

Monoid a => Monoid (Op a b)

Methods

mempty :: Op a b

mappend :: Op a b -> Op a b -> Op a b

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

Monoid (Proxy s)

Since: 4.7.0.0

Methods

mempty :: Proxy s

mappend :: Proxy s -> Proxy s -> Proxy s

mconcat :: [Proxy s] -> Proxy s

Ord k => Monoid (Map k v)

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)

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)

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)

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.

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')]

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)

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)

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)

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)

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))

Methods

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

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

Since: 2.1

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)

Methods

mempty :: Const a b

mappend :: Const a b -> Const a b -> Const a b

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

Alternative f => Monoid (Alt f a)

Since: 4.8.0.0

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)

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)

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)

Methods

mempty :: Tagged s a

mappend :: Tagged s a -> Tagged s a -> Tagged s a

mconcat :: [Tagged s a] -> Tagged s a

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

Since: 2.1

Methods

mempty :: (a, b, c, d)

mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d)

mconcat :: [(a, b, c, d)] -> (a, b, c, d)

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

Since: 2.1

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)

Methods

mempty :: BazaarT p g a b t

mappend :: BazaarT p g a b t -> BazaarT p g a b t -> BazaarT p g a b t

mconcat :: [BazaarT p g a b t] -> BazaarT p g a b t

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

An associative operation.

newtype Sum a

Monoid under addition.

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

Constructors

Sum

Fields

• getSum :: a

Instances

Monad Sum

Since: 4.8.0.0

Methods

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

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

return :: a -> Sum a

fail :: String -> Sum a

Functor Sum

Since: 4.8.0.0

Methods

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

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

MonadFix Sum

Since: 4.8.0.0

Methods

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

Applicative Sum

Since: 4.8.0.0

Methods

pure :: a -> Sum a

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

liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c

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

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

Foldable Sum

Since: 4.8.0.0

Methods

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

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

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

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

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

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

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

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

toList :: Sum a -> [a]

null :: Sum a -> Bool

length :: Sum a -> Int

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

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

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

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

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

Traversable Sum

Since: 4.8.0.0

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

Associated Types

type Rep Sum :: *

Methods

tabulate :: (Rep Sum -> a) -> Sum a

index :: Sum a -> Rep Sum -> a

NFData1 Sum

Since: 1.4.3.0

Methods

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

Functor Sum

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))

Methods

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

Bounded a => Bounded (Sum a)

Methods

minBound :: Sum a

maxBound :: Sum a

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

Methods

minBound :: Exp (Sum a)

maxBound :: Exp (Sum a)

Eq a => Eq (Sum a)

Methods

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

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

Num a => Num (Sum a)

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))

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)

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)

Methods

readsPrec :: Int -> ReadS (Sum a)

readList :: ReadS [Sum a]

readPrec :: ReadPrec (Sum a)

readListPrec :: ReadPrec [Sum a]

Show a => Show (Sum a)

Methods

showsPrec :: Int -> Sum a -> ShowS

show :: Sum a -> String

showList :: [Sum a] -> ShowS

Generic (Sum a)

Associated Types

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

Methods

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

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

Num a => Semigroup (Sum a)

Since: 4.9.0.0

Methods

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

sconcat :: NonEmpty (Sum a) -> Sum a

stimes :: Integral b => b -> Sum a -> Sum a

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

Since: 1.2.0.0

Methods

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

sconcat :: NonEmpty (Exp (Sum a)) -> Exp (Sum a)

stimes :: Integral b => b -> Exp (Sum a) -> Exp (Sum a)

Num a => Monoid (Sum a)

Since: 2.1

Methods

mempty :: Sum a

mappend :: Sum a -> Sum a -> Sum a

mconcat :: [Sum a] -> Sum a

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)

NFData a => NFData (Sum a)

Since: 1.4.0.0

Methods

rnf :: Sum a -> ()

Wrapped (Sum a)

Associated Types

type Unwrapped (Sum a) :: *

Methods

_Wrapped' :: Iso' (Sum a) (Unwrapped (Sum a))

(Eq a, Num a) => AsEmpty (Sum a)

Methods

_Empty :: Prism' (Sum 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

Eq a => Eq (Sum a)

Methods

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

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

Generic1 Sum

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

type Rep Sum

type Rep Sum = ()

type Rep (Sum a)

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)

type Unwrapped (Sum a) = a

type Plain (Sum a)

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

type Rep1 Sum

type Rep1 Sum = D1 (MetaData "Sum" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Sum" PrefixI True) (S1 (MetaSel (Just "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Product a

Monoid under multiplication.

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

Constructors

Product

Fields

• getProduct :: a

Instances

Monad Product

Since: 4.8.0.0

Methods

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

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

return :: a -> Product a

fail :: String -> Product a

Functor Product

Since: 4.8.0.0

Methods

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

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

MonadFix Product

Since: 4.8.0.0

Methods

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

Applicative Product

Since: 4.8.0.0

Methods

pure :: a -> Product a

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

liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c

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

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

Foldable Product

Since: 4.8.0.0

Methods

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

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

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

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

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

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

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

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

toList :: Product a -> [a]

null :: Product a -> Bool

length :: Product a -> Int

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

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

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

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

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

Traversable Product

Since: 4.8.0.0

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

Associated Types

type Rep Product :: *

Methods

tabulate :: (Rep Product -> a) -> Product a

index :: Product a -> Rep Product -> a

NFData1 Product

Since: 1.4.3.0

Methods

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

Functor Product

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))

Methods

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

Methods

minBound :: Product a

maxBound :: Product a

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

Methods

minBound :: Exp (Product a)

maxBound :: Exp (Product a)

Eq a => Eq (Product a)

Methods

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

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

Num a => Num (Product a)

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))

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)

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)

Methods

readsPrec :: Int -> ReadS (Product a)

readList :: ReadS [Product a]

readPrec :: ReadPrec (Product a)

readListPrec :: ReadPrec [Product a]

Show a => Show (Product a)

Methods

showsPrec :: Int -> Product a -> ShowS

show :: Product a -> String

showList :: [Product a] -> ShowS

Generic (Product a)

Associated Types

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

Methods

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

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

Num a => Semigroup (Product a)

Since: 4.9.0.0

Methods

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

sconcat :: NonEmpty (Product a) -> Product a

stimes :: Integral b => b -> Product a -> Product a

Num a => Semigroup (Exp (Product a))

Since: 1.2.0.0

Methods

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

sconcat :: NonEmpty (Exp (Product a)) -> Exp (Product a)

stimes :: Integral b => b -> Exp (Product a) -> Exp (Product a)

Num a => Monoid (Product a)

Since: 2.1

Methods

mempty :: Product a

mappend :: Product a -> Product a -> Product a

mconcat :: [Product a] -> Product 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)

NFData a => NFData (Product a)

Since: 1.4.0.0

Methods

rnf :: Product a -> ()

Wrapped (Product a)

Associated Types

type Unwrapped (Product a) :: *

Methods

_Wrapped' :: Iso' (Product a) (Unwrapped (Product a))

(Eq a, Num a) => AsEmpty (Product a)

Methods

_Empty :: Prism' (Product 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 (Product a)

Methods

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

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

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

Generic1 Product

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

type Rep Product

type Rep Product = ()

type Rep (Product a)

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)

type Unwrapped (Product a) = a

type Plain (Product a)

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

type Rep1 Product

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: 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: 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