Safe Haskell	Safe
Language	Haskell2010

Data.Semigroup.Join

Contents

Orphan instances

Synopsis

(∨) :: (Join - Semigroup) a => a -> a -> a
bottom :: (Join - Monoid) a => a
type JoinSemilattice a = (Prd a, (Join - Semigroup) a)
joinLeq :: Eq a => (Join - Semigroup) a => a -> a -> Bool
joinGeq :: Eq a => (Join - Semigroup) a => a -> a -> Bool
pcompareJoin :: Eq a => (Join - Semigroup) a => a -> a -> Maybe Ordering
newtype Join a = Join {
- unJoin :: a
}

Documentation

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

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 Source #

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

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

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 Source #

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 Source #

Partial version of compare.

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

newtype Join a Source #

A commutative Semigroup under ∨.

Constructors

Join
Fields unJoin :: a

Instances

Functor Join Source #
Instance details Defined in Data.Semigroup.Join Methods fmap :: (a -> b) -> Join a -> Join b # (<$) :: a -> Join b -> Join a #
Applicative Join Source #
Instance details 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) Source #
Instance details Defined in Data.Semigroup.Join Methods (==) :: Join a -> Join a -> Bool # (/=) :: Join a -> Join a -> Bool #
Ord a => Ord (Join a) Source #
Instance details 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) Source #
Instance details Defined in Data.Semigroup.Join Methods showsPrec :: Int -> Join a -> ShowS # show :: Join a -> String # showList :: [Join a] -> ShowS #
Generic (Join a) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details 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 ()) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details Defined in Data.Semigroup.Join Methods mempty :: Join Bool # mappend :: Join Bool -> Join Bool -> Join Bool # mconcat :: [Join Bool] -> Join Bool #
Monoid (Join Int) Source #
Instance details Defined in Data.Semigroup.Join Methods mempty :: Join Int # mappend :: Join Int -> Join Int -> Join Int # mconcat :: [Join Int] -> Join Int #
Monoid (Join Int8) Source #
Instance details Defined in Data.Semigroup.Join Methods mempty :: Join Int8 # mappend :: Join Int8 -> Join Int8 -> Join Int8 # mconcat :: [Join Int8] -> Join Int8 #
Monoid (Join Int16) Source #
Instance details Defined in Data.Semigroup.Join Methods mempty :: Join Int16 # mappend :: Join Int16 -> Join Int16 -> Join Int16 # mconcat :: [Join Int16] -> Join Int16 #
Monoid (Join Int32) Source #
Instance details Defined in Data.Semigroup.Join Methods mempty :: Join Int32 # mappend :: Join Int32 -> Join Int32 -> Join Int32 # mconcat :: [Join Int32] -> Join Int32 #
Monoid (Join Int64) Source #
Instance details Defined in Data.Semigroup.Join Methods mempty :: Join Int64 # mappend :: Join Int64 -> Join Int64 -> Join Int64 # mconcat :: [Join Int64] -> Join Int64 #
Monoid (Join Natural) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details Defined in Data.Semigroup.Join Methods mempty :: Join Word # mappend :: Join Word -> Join Word -> Join Word # mconcat :: [Join Word] -> Join Word #
Monoid (Join Word8) Source #
Instance details Defined in Data.Semigroup.Join Methods mempty :: Join Word8 # mappend :: Join Word8 -> Join Word8 -> Join Word8 # mconcat :: [Join Word8] -> Join Word8 #
Monoid (Join Word16) Source #
Instance details Defined in Data.Semigroup.Join Methods mempty :: Join Word16 # mappend :: Join Word16 -> Join Word16 -> Join Word16 # mconcat :: [Join Word16] -> Join Word16 #
Monoid (Join Word32) Source #
Instance details Defined in Data.Semigroup.Join Methods mempty :: Join Word32 # mappend :: Join Word32 -> Join Word32 -> Join Word32 # mconcat :: [Join Word32] -> Join Word32 #
Monoid (Join Word64) Source #
Instance details Defined in Data.Semigroup.Join Methods mempty :: Join Word64 # mappend :: Join Word64 -> Join Word64 -> Join Word64 # mconcat :: [Join Word64] -> Join Word64 #
Monoid (Join ()) Source #
Instance details Defined in Data.Semigroup.Join Methods mempty :: Join () # mappend :: Join () -> Join () -> Join () # mconcat :: [Join ()] -> Join () #
(Minimal a, Semigroup (Max a)) => Monoid (Join (Max a)) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details Methods mempty :: Meet (Down a) # mappend :: Meet (Down a) -> Meet (Down a) -> Meet (Down a) # mconcat :: [Meet (Down a)] -> Meet (Down a) #