Data.Semigroup.Join

Documentation

(∨) :: (Join - Semigroup) a => a -> a -> a infixr 5

Join operation on a semilattice.

>>> (> (0::Int)) ∧ ((< 10) ∨ (== 15)) $ 10
False

>>> IntSet.fromList [1..5] ∧ IntSet.fromList [2..5]
fromList [2,3,4,5]

bottom :: (Join - Monoid) a => a

type JoinSemilattice a = (Prd a, (Join - Semigroup) a)

joinLeq :: Eq a => (Join - Semigroup) a => a -> a -> Bool

The partial ordering induced by the join-semilattice structure.

Normally when a implements Prd we should have: joinLeq x y ≡ x Prd y

joinGeq :: Eq a => (Join - Semigroup) a => a -> a -> Bool

The partial ordering induced by the join-semilattice structure.

Normally when a implements Prd we should have: joinGeq x y ≡ x Prd y

pcompareJoin :: Eq a => (Join - Semigroup) a => a -> a -> Maybe Ordering

Partial version of compare.

Normally when a implements Prd we should have: pcompareJoin x y ≡ pcompare x y

newtype Join a

A commutative Semigroup under ∨.

Constructors

Join

Fields

• unJoin :: a

Instances

Functor Join

Defined in Data.Semigroup.Join

Methods

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

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

Applicative Join

Defined in Data.Semigroup.Join

Methods

pure :: a -> Join a

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

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

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

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

Eq a => Eq (Join a)

Defined in Data.Semigroup.Join

Methods

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

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

Ord a => Ord (Join a)

Defined in Data.Semigroup.Join

Methods

compare :: Join a -> Join a -> Ordering

(<) :: Join a -> Join a -> Bool

(<=) :: Join a -> Join a -> Bool

(>) :: Join a -> Join a -> Bool

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

max :: Join a -> Join a -> Join a

min :: Join a -> Join a -> Join a

Show a => Show (Join a)

Defined in Data.Semigroup.Join

Methods

showsPrec :: Int -> Join a -> ShowS

show :: Join a -> String

showList :: [Join a] -> ShowS

Generic (Join a)

Defined in Data.Semigroup.Join

Associated Types

type Rep (Join a) :: Type -> Type

Methods

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

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

Semigroup (Join Bool)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Bool -> Join Bool -> Join Bool

sconcat :: NonEmpty (Join Bool) -> Join Bool

stimes :: Integral b => b -> Join Bool -> Join Bool

Semigroup (Join Int)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Int -> Join Int -> Join Int

sconcat :: NonEmpty (Join Int) -> Join Int

stimes :: Integral b => b -> Join Int -> Join Int

Semigroup (Join Int8)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Int8 -> Join Int8 -> Join Int8

sconcat :: NonEmpty (Join Int8) -> Join Int8

stimes :: Integral b => b -> Join Int8 -> Join Int8

Semigroup (Join Int16)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Int16 -> Join Int16 -> Join Int16

sconcat :: NonEmpty (Join Int16) -> Join Int16

stimes :: Integral b => b -> Join Int16 -> Join Int16

Semigroup (Join Int32)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Int32 -> Join Int32 -> Join Int32

sconcat :: NonEmpty (Join Int32) -> Join Int32

stimes :: Integral b => b -> Join Int32 -> Join Int32

Semigroup (Join Int64)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Int64 -> Join Int64 -> Join Int64

sconcat :: NonEmpty (Join Int64) -> Join Int64

stimes :: Integral b => b -> Join Int64 -> Join Int64

Semigroup (Join Integer)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Integer -> Join Integer -> Join Integer

sconcat :: NonEmpty (Join Integer) -> Join Integer

stimes :: Integral b => b -> Join Integer -> Join Integer

Semigroup (Join Natural)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Natural -> Join Natural -> Join Natural

sconcat :: NonEmpty (Join Natural) -> Join Natural

stimes :: Integral b => b -> Join Natural -> Join Natural

(Join - Semigroup) a => Semigroup (Join (Maybe a))

Defined in Data.Semigroup.Join

Methods

(<>) :: Join (Maybe a) -> Join (Maybe a) -> Join (Maybe a)

sconcat :: NonEmpty (Join (Maybe a)) -> Join (Maybe a)

stimes :: Integral b => b -> Join (Maybe a) -> Join (Maybe a)

Semigroup (Join Word)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Word -> Join Word -> Join Word

sconcat :: NonEmpty (Join Word) -> Join Word

stimes :: Integral b => b -> Join Word -> Join Word

Semigroup (Join Word8)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Word8 -> Join Word8 -> Join Word8

sconcat :: NonEmpty (Join Word8) -> Join Word8

stimes :: Integral b => b -> Join Word8 -> Join Word8

Semigroup (Join Word16)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Word16 -> Join Word16 -> Join Word16

sconcat :: NonEmpty (Join Word16) -> Join Word16

stimes :: Integral b => b -> Join Word16 -> Join Word16

Semigroup (Join Word32)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Word32 -> Join Word32 -> Join Word32

sconcat :: NonEmpty (Join Word32) -> Join Word32

stimes :: Integral b => b -> Join Word32 -> Join Word32

Semigroup (Join Word64)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Word64 -> Join Word64 -> Join Word64

sconcat :: NonEmpty (Join Word64) -> Join Word64

stimes :: Integral b => b -> Join Word64 -> Join Word64

((Join - Semigroup) a, (Join - Semigroup) b) => Semigroup (Join (Either a b))

Defined in Data.Semigroup.Join

Methods

(<>) :: Join (Either a b) -> Join (Either a b) -> Join (Either a b)

sconcat :: NonEmpty (Join (Either a b)) -> Join (Either a b)

stimes :: Integral b0 => b0 -> Join (Either a b) -> Join (Either a b)

Semigroup (Join ())

Defined in Data.Semigroup.Join

Methods

(<>) :: Join () -> Join () -> Join ()

sconcat :: NonEmpty (Join ()) -> Join ()

stimes :: Integral b => b -> Join () -> Join ()

((Join - Semigroup) a, (Join - Semigroup) b) => Semigroup (Join (a, b))

Defined in Data.Semigroup.Join

Methods

(<>) :: Join (a, b) -> Join (a, b) -> Join (a, b)

sconcat :: NonEmpty (Join (a, b)) -> Join (a, b)

stimes :: Integral b0 => b0 -> Join (a, b) -> Join (a, b)

Semigroup (Join Uni)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Uni -> Join Uni -> Join Uni

sconcat :: NonEmpty (Join Uni) -> Join Uni

stimes :: Integral b => b -> Join Uni -> Join Uni

Semigroup (Join Deci)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Deci -> Join Deci -> Join Deci

sconcat :: NonEmpty (Join Deci) -> Join Deci

stimes :: Integral b => b -> Join Deci -> Join Deci

Semigroup (Join Centi)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Centi -> Join Centi -> Join Centi

sconcat :: NonEmpty (Join Centi) -> Join Centi

stimes :: Integral b => b -> Join Centi -> Join Centi

Semigroup (Join Milli)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Milli -> Join Milli -> Join Milli

sconcat :: NonEmpty (Join Milli) -> Join Milli

stimes :: Integral b => b -> Join Milli -> Join Milli

Semigroup (Join Micro)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Micro -> Join Micro -> Join Micro

sconcat :: NonEmpty (Join Micro) -> Join Micro

stimes :: Integral b => b -> Join Micro -> Join Micro

Semigroup (Join Nano)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Nano -> Join Nano -> Join Nano

sconcat :: NonEmpty (Join Nano) -> Join Nano

stimes :: Integral b => b -> Join Nano -> Join Nano

Semigroup (Join Pico)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join Pico -> Join Pico -> Join Pico

sconcat :: NonEmpty (Join Pico) -> Join Pico

stimes :: Integral b => b -> Join Pico -> Join Pico

Semigroup (Max a) => Semigroup (Join (Max a))

Defined in Data.Semigroup.Join

Methods

(<>) :: Join (Max a) -> Join (Max a) -> Join (Max a)

sconcat :: NonEmpty (Join (Max a)) -> Join (Max a)

stimes :: Integral b => b -> Join (Max a) -> Join (Max a)

(Meet - Semigroup) a => Semigroup (Join (Down a))

Defined in Data.Semigroup.Join

Methods

(<>) :: Join (Down a) -> Join (Down a) -> Join (Down a)

sconcat :: NonEmpty (Join (Down a)) -> Join (Down a)

stimes :: Integral b => b -> Join (Down a) -> Join (Down a)

(Join - Semigroup) a => Semigroup (Join (IntMap a))

Defined in Data.Semigroup.Join

Methods

(<>) :: Join (IntMap a) -> Join (IntMap a) -> Join (IntMap a)

sconcat :: NonEmpty (Join (IntMap a)) -> Join (IntMap a)

stimes :: Integral b => b -> Join (IntMap a) -> Join (IntMap a)

Semigroup (Join IntSet)

Defined in Data.Semigroup.Join

Methods

(<>) :: Join IntSet -> Join IntSet -> Join IntSet

sconcat :: NonEmpty (Join IntSet) -> Join IntSet

stimes :: Integral b => b -> Join IntSet -> Join IntSet

(Ord k, (Join - Semigroup) a) => Semigroup (Join (Map k a))

Defined in Data.Semigroup.Join

Methods

(<>) :: Join (Map k a) -> Join (Map k a) -> Join (Map k a)

sconcat :: NonEmpty (Join (Map k a)) -> Join (Map k a)

stimes :: Integral b => b -> Join (Map k a) -> Join (Map k a)

Ord a => Semigroup (Join (Set a))

Defined in Data.Semigroup.Join

Methods

(<>) :: Join (Set a) -> Join (Set a) -> Join (Set a)

sconcat :: NonEmpty (Join (Set a)) -> Join (Set a)

stimes :: Integral b => b -> Join (Set a) -> Join (Set a)

Semigroup (Join Ulp32)

Defined in Data.Float

Methods

(<>) :: Join Ulp32 -> Join Ulp32 -> Join Ulp32

sconcat :: NonEmpty (Join Ulp32) -> Join Ulp32

stimes :: Integral b => b -> Join Ulp32 -> Join Ulp32

Ord a => Semigroup (Join (MaxMin a))

Defined in Data.Semilattice.MaxMin

Methods

(<>) :: Join (MaxMin a) -> Join (MaxMin a) -> Join (MaxMin a)

sconcat :: NonEmpty (Join (MaxMin a)) -> Join (MaxMin a)

stimes :: Integral b => b -> Join (MaxMin a) -> Join (MaxMin a)

(Minimal a, Semifield a) => Semigroup (Join (N5 a))

Defined in Data.Semilattice.N5

Methods

(<>) :: Join (N5 a) -> Join (N5 a) -> Join (N5 a)

sconcat :: NonEmpty (Join (N5 a)) -> Join (N5 a)

stimes :: Integral b => b -> Join (N5 a) -> Join (N5 a)

(Join - Semigroup) a => Semigroup (Join (Top a))

Defined in Data.Semilattice.Top

Methods

(<>) :: Join (Top a) -> Join (Top a) -> Join (Top a)

sconcat :: NonEmpty (Join (Top a)) -> Join (Top a)

stimes :: Integral b => b -> Join (Top a) -> Join (Top a)

Monoid (Join Bool)

Defined in Data.Semigroup.Join

Methods

mempty :: Join Bool

mappend :: Join Bool -> Join Bool -> Join Bool

mconcat :: [Join Bool] -> Join Bool

Monoid (Join Int)

Defined in Data.Semigroup.Join

Methods

mempty :: Join Int

mappend :: Join Int -> Join Int -> Join Int

mconcat :: [Join Int] -> Join Int

Monoid (Join Int8)

Defined in Data.Semigroup.Join

Methods

mempty :: Join Int8

mappend :: Join Int8 -> Join Int8 -> Join Int8

mconcat :: [Join Int8] -> Join Int8

Monoid (Join Int16)

Defined in Data.Semigroup.Join

Methods

mempty :: Join Int16

mappend :: Join Int16 -> Join Int16 -> Join Int16

mconcat :: [Join Int16] -> Join Int16

Monoid (Join Int32)

Defined in Data.Semigroup.Join

Methods

mempty :: Join Int32

mappend :: Join Int32 -> Join Int32 -> Join Int32

mconcat :: [Join Int32] -> Join Int32

Monoid (Join Int64)

Defined in Data.Semigroup.Join

Methods

mempty :: Join Int64

mappend :: Join Int64 -> Join Int64 -> Join Int64

mconcat :: [Join Int64] -> Join Int64

Monoid (Join Natural)

Defined in Data.Semigroup.Join

Methods

mempty :: Join Natural

mappend :: Join Natural -> Join Natural -> Join Natural

mconcat :: [Join Natural] -> Join Natural

(Join - Semigroup) a => Monoid (Join (Maybe a))

Defined in Data.Semigroup.Join

Methods

mempty :: Join (Maybe a)

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

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

Monoid (Join Word)

Defined in Data.Semigroup.Join

Methods

mempty :: Join Word

mappend :: Join Word -> Join Word -> Join Word

mconcat :: [Join Word] -> Join Word

Monoid (Join Word8)

Defined in Data.Semigroup.Join

Methods

mempty :: Join Word8

mappend :: Join Word8 -> Join Word8 -> Join Word8

mconcat :: [Join Word8] -> Join Word8

Monoid (Join Word16)

Defined in Data.Semigroup.Join

Methods

mempty :: Join Word16

mappend :: Join Word16 -> Join Word16 -> Join Word16

mconcat :: [Join Word16] -> Join Word16

Monoid (Join Word32)

Defined in Data.Semigroup.Join

Methods

mempty :: Join Word32

mappend :: Join Word32 -> Join Word32 -> Join Word32

mconcat :: [Join Word32] -> Join Word32

Monoid (Join Word64)

Defined in Data.Semigroup.Join

Methods

mempty :: Join Word64

mappend :: Join Word64 -> Join Word64 -> Join Word64

mconcat :: [Join Word64] -> Join Word64

Monoid (Join ())

Defined in Data.Semigroup.Join

Methods

mempty :: Join ()

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

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

(Minimal a, Semigroup (Max a)) => Monoid (Join (Max a))

Defined in Data.Semigroup.Join

Methods

mempty :: Join (Max a)

mappend :: Join (Max a) -> Join (Max a) -> Join (Max a)

mconcat :: [Join (Max a)] -> Join (Max a)

(Meet - Monoid) a => Monoid (Join (Down a))

Defined in Data.Semigroup.Join

Methods

mempty :: Join (Down a)

mappend :: Join (Down a) -> Join (Down a) -> Join (Down a)

mconcat :: [Join (Down a)] -> Join (Down a)

(Join - Semigroup) a => Monoid (Join (IntMap a))

Defined in Data.Semigroup.Join

Methods

mempty :: Join (IntMap a)

mappend :: Join (IntMap a) -> Join (IntMap a) -> Join (IntMap a)

mconcat :: [Join (IntMap a)] -> Join (IntMap a)

Monoid (Join IntSet)

Defined in Data.Semigroup.Join

Methods

mempty :: Join IntSet

mappend :: Join IntSet -> Join IntSet -> Join IntSet

mconcat :: [Join IntSet] -> Join IntSet

(Ord k, (Join - Semigroup) a) => Monoid (Join (Map k a))

Defined in Data.Semigroup.Join

Methods

mempty :: Join (Map k a)

mappend :: Join (Map k a) -> Join (Map k a) -> Join (Map k a)

mconcat :: [Join (Map k a)] -> Join (Map k a)

Ord a => Monoid (Join (Set a))

Defined in Data.Semigroup.Join

Methods

mempty :: Join (Set a)

mappend :: Join (Set a) -> Join (Set a) -> Join (Set a)

mconcat :: [Join (Set a)] -> Join (Set a)

(Ord a, Minimal a) => Monoid (Join (MaxMin a))

Defined in Data.Semilattice.MaxMin

Methods

mempty :: Join (MaxMin a)

mappend :: Join (MaxMin a) -> Join (MaxMin a) -> Join (MaxMin a)

mconcat :: [Join (MaxMin a)] -> Join (MaxMin a)

(Minimal a, Semifield a) => Monoid (Join (N5 a))

Defined in Data.Semilattice.N5

Methods

mempty :: Join (N5 a)

mappend :: Join (N5 a) -> Join (N5 a) -> Join (N5 a)

mconcat :: [Join (N5 a)] -> Join (N5 a)

(Join - Monoid) a => Monoid (Join (Top a))

Defined in Data.Semilattice.Top

Methods

mempty :: Join (Top a)

mappend :: Join (Top a) -> Join (Top a) -> Join (Top a)

mconcat :: [Join (Top a)] -> Join (Top a)

type Rep (Join a)

Defined in Data.Semigroup.Join

type Rep (Join a) = D1 (MetaData "Join" "Data.Semigroup.Join" "connections-0.0.3-DlJXNVSUPF02JVkbDQVocy" True) (C1 (MetaCons "Join" PrefixI True) (S1 (MetaSel (Just "unJoin") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

Orphan instances

(Join - Semigroup) (Max a) => Semigroup (Additive (Max a))

Methods

(<>) :: Additive (Max a) -> Additive (Max a) -> Additive (Max a)

sconcat :: NonEmpty (Additive (Max a)) -> Additive (Max a)

stimes :: Integral b => b -> Additive (Max a) -> Additive (Max a)

(Join - Semigroup) a => Semigroup (Meet (Down a))

Methods

(<>) :: Meet (Down a) -> Meet (Down a) -> Meet (Down a)

sconcat :: NonEmpty (Meet (Down a)) -> Meet (Down a)

stimes :: Integral b => b -> Meet (Down a) -> Meet (Down a)

(Join - Monoid) (Max a) => Monoid (Additive (Max a))

Methods

mempty :: Additive (Max a)

mappend :: Additive (Max a) -> Additive (Max a) -> Additive (Max a)

mconcat :: [Additive (Max a)] -> Additive (Max a)

(Join - Monoid) a => Monoid (Meet (Down a))

Methods

mempty :: Meet (Down a)

mappend :: Meet (Down a) -> Meet (Down a) -> Meet (Down a)

mconcat :: [Meet (Down a)] -> Meet (Down a)