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

Data.Array.Accelerate.Data.Monoid

Contents

Orphan instances

Description

Monoid instances for Accelerate

Synopsis

Documentation

class Monoid a where #

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

```
mappend mempty x = x
```
```
mappend x mempty = x
```

mappend x (mappend y z) = mappend (mappend x y) z

```
mconcat = foldr mappend 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.

Minimal complete definition

mempty, mappend

Methods

mempty :: a #

Identity of mappend

mappend :: a -> a -> a #

An associative operation

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 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 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 Slot
Methods mempty :: Slot # mappend :: Slot -> Slot -> Slot # mconcat :: [Slot] -> Slot #
Monoid Doc
Methods mempty :: Doc # mappend :: Doc -> Doc -> Doc # mconcat :: [Doc] -> Doc #
Monoid [a]	Since: 2.1
Methods mempty :: [a] # mappend :: [a] -> [a] -> [a] # mconcat :: [[a]] -> [a] #
Monoid 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 there used to be no "Semigroup" typeclass providing just `mappend`, we use `Monoid` instead. 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 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 (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 (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 (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 #
(Hashable a, Eq a) => Monoid (HashSet a)
Methods mempty :: HashSet a # mappend :: HashSet a -> HashSet a -> HashSet a # mconcat :: [HashSet a] -> HashSet a #
Prim a => Monoid (Vector a)
Methods mempty :: Vector a # mappend :: Vector a -> Vector a -> Vector a # mconcat :: [Vector a] -> Vector a #
Monoid (Vector a)
Methods mempty :: Vector a # mappend :: Vector a -> Vector a -> Vector a # mconcat :: [Vector a] -> Vector 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 (Proxy k s)	Since: 4.7.0.0
Methods mempty :: Proxy k s # mappend :: Proxy k s -> Proxy k s -> Proxy k s # mconcat :: [Proxy k s] -> Proxy k 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 #
(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 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 k a b)
Methods mempty :: Const k a b # mappend :: Const k a b -> Const k a b -> Const k a b # mconcat :: [Const k a b] -> Const k 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 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) #

(<>) :: Monoid m => m -> m -> m infixr 6 #

An infix synonym for mappend.

Since: 4.5.0.0

newtype Sum a :: * -> * #

Monoid under addition.

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) #
NFData1 Sum	Since: 1.4.3.0
Methods liftRnf :: (a -> ()) -> Sum a -> () #
Bounded a => Bounded (Sum a)
Methods minBound :: Sum a # maxBound :: 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 #
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 => Monoid (Sum a)	Since: 2.1
Methods mempty :: Sum a # mappend :: Sum a -> Sum a -> Sum a # mconcat :: [Sum a] -> Sum a #
NFData a => NFData (Sum a)	Since: 1.4.0.0
Methods rnf :: Sum a -> () #
Generic1 * Sum
Associated Types type Rep1 Sum (f :: Sum -> ) :: k -> # Methods from1 :: f a -> Rep1 Sum f a # to1 :: Rep1 Sum f a -> f a #
type Rep (Sum a)
type Rep (Sum a) = D1 * (MetaData "Sum" "Data.Monoid" "base" True) (C1 * (MetaCons "Sum" PrefixI True) (S1 * (MetaSel (Just Symbol "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Plain (Sum a) Source #
type Plain (Sum a) = Sum (Plain a)
type Rep1 * Sum
type Rep1 * Sum = D1 * (MetaData "Sum" "Data.Monoid" "base" True) (C1 * (MetaCons "Sum" PrefixI True) (S1 * (MetaSel (Just Symbol "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Product a :: * -> * #

Monoid under multiplication.

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) #
NFData1 Product	Since: 1.4.3.0
Methods liftRnf :: (a -> ()) -> Product a -> () #
Bounded a => Bounded (Product a)
Methods minBound :: Product a # maxBound :: 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 #
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 => Monoid (Product a)	Since: 2.1
Methods mempty :: Product a # mappend :: Product a -> Product a -> Product a # mconcat :: [Product a] -> Product a #
NFData a => NFData (Product a)	Since: 1.4.0.0
Methods rnf :: Product a -> () #
Generic1 * Product
Associated Types type Rep1 Product (f :: Product -> ) :: k -> # Methods from1 :: f a -> Rep1 Product f a # to1 :: Rep1 Product f a -> f a #
type Rep (Product a)
type Rep (Product a) = D1 * (MetaData "Product" "Data.Monoid" "base" True) (C1 * (MetaCons "Product" PrefixI True) (S1 * (MetaSel (Just Symbol "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Plain (Product a) Source #
type Plain (Product a) = Product (Plain a)
type Rep1 * Product
type Rep1 * Product = D1 * (MetaData "Product" "Data.Monoid" "base" True) (C1 * (MetaCons "Product" PrefixI True) (S1 * (MetaSel (Just Symbol "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

Orphan instances

Elt a => Unlift Exp (Sum (Exp a)) Source #
Methods unlift :: Exp (Plain (Sum (Exp a))) -> Sum (Exp a) Source #
Elt a => Unlift Exp (Product (Exp a)) Source #
Methods unlift :: Exp (Plain (Product (Exp a))) -> Product (Exp a) Source #
(Lift Exp a, Elt (Plain a)) => Lift Exp (Sum a) Source #
Associated Types type Plain (Sum a) :: * Source # Methods lift :: Sum a -> Exp (Plain (Sum a)) Source #
(Lift Exp a, Elt (Plain a)) => Lift Exp (Product a) Source #
Associated Types type Plain (Product a) :: * Source # Methods lift :: Product a -> Exp (Plain (Product a)) Source #
Num a => Num (Exp (Sum a)) Source #
Methods (+) :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a) # (-) :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a) # (*) :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a) # negate :: Exp (Sum a) -> Exp (Sum a) # abs :: Exp (Sum a) -> Exp (Sum a) # signum :: Exp (Sum a) -> Exp (Sum a) # fromInteger :: Integer -> Exp (Sum a) #
Num a => Num (Exp (Product a)) Source #
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) #
Monoid (Exp ()) Source #
Methods mempty :: Exp () # mappend :: Exp () -> Exp () -> Exp () # mconcat :: [Exp ()] -> Exp () #
(Elt a, Elt b, Monoid (Exp a), Monoid (Exp b)) => Monoid (Exp (a, b)) Source #
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 #
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 #
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 #
Methods mempty :: Exp (a, b, c, d, e) # mappend :: Exp (a, b, c, d, e) -> Exp (a, b, c, d, e) -> Exp (a, b, c, d, e) # mconcat :: [Exp (a, b, c, d, e)] -> Exp (a, b, c, d, e) #
Num a => Monoid (Exp (Sum a)) Source #
Methods mempty :: Exp (Sum a) # mappend :: Exp (Sum a) -> Exp (Sum a) -> Exp (Sum a) # mconcat :: [Exp (Sum a)] -> Exp (Sum a) #
Num a => Monoid (Exp (Product a)) Source #
Methods mempty :: Exp (Product a) # mappend :: Exp (Product a) -> Exp (Product a) -> Exp (Product a) # mconcat :: [Exp (Product a)] -> Exp (Product a) #
Elt a => Elt (Sum a) Source #
Methods eltType :: Sum a -> TupleType (EltRepr (Sum a)) fromElt :: Sum a -> EltRepr (Sum a) toElt :: EltRepr (Sum a) -> Sum a
Elt a => Elt (Product a) Source #
Methods eltType :: Product a -> TupleType (EltRepr (Product a)) fromElt :: Product a -> EltRepr (Product a) toElt :: EltRepr (Product a) -> Product a
Eq a => Eq (Sum a) Source #
Methods (==) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool Source # (/=) :: Exp (Sum a) -> Exp (Sum a) -> Exp Bool Source #
Eq a => Eq (Product a) Source #
Methods (==) :: Exp (Product a) -> Exp (Product a) -> Exp Bool Source # (/=) :: Exp (Product a) -> Exp (Product a) -> Exp Bool Source #
Ord a => Ord (Sum a) Source #
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 #
Ord a => Ord (Product a) Source #
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 #