Data.Array.Accelerate.Data.Monoid

Monoid instances for Accelerate

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 e*e = e and e*s = s = s*e 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)

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)

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))

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))

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)

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)

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)