Safe Haskell	None
Language	Haskell2010

Data.Semilattice.Order

Description

Total Orderings give rise to Join and Meet semilattices.

Synopsis

newtype Order a = Order {
- getOrder :: a
}

Documentation

newtype Order a Source #

A Join- and Meet-semilattice for any total Ordering.

Constructors

Order
Fields getOrder :: a

Instances

Functor Order Source #
Instance details Defined in Data.Semilattice.Order Methods fmap :: (a -> b) -> Order a -> Order b # (<$) :: a -> Order b -> Order a #
Foldable Order Source #
Instance details Defined in Data.Semilattice.Order Methods fold :: Monoid m => Order m -> m # foldMap :: Monoid m => (a -> m) -> Order a -> m # foldr :: (a -> b -> b) -> b -> Order a -> b # foldr' :: (a -> b -> b) -> b -> Order a -> b # foldl :: (b -> a -> b) -> b -> Order a -> b # foldl' :: (b -> a -> b) -> b -> Order a -> b # foldr1 :: (a -> a -> a) -> Order a -> a # foldl1 :: (a -> a -> a) -> Order a -> a # toList :: Order a -> [a] # null :: Order a -> Bool # length :: Order a -> Int # elem :: Eq a => a -> Order a -> Bool # maximum :: Ord a => Order a -> a # minimum :: Ord a => Order a -> a # sum :: Num a => Order a -> a # product :: Num a => Order a -> a #
Traversable Order Source #
Instance details Defined in Data.Semilattice.Order Methods traverse :: Applicative f => (a -> f b) -> Order a -> f (Order b) # sequenceA :: Applicative f => Order (f a) -> f (Order a) # mapM :: Monad m => (a -> m b) -> Order a -> m (Order b) # sequence :: Monad m => Order (m a) -> m (Order a) #
Bounded a => Bounded (Order a) Source #
Instance details Defined in Data.Semilattice.Order Methods minBound :: Order a # maxBound :: Order a #
Enum a => Enum (Order a) Source #
Instance details Defined in Data.Semilattice.Order Methods succ :: Order a -> Order a # pred :: Order a -> Order a # toEnum :: Int -> Order a # fromEnum :: Order a -> Int # enumFrom :: Order a -> [Order a] # enumFromThen :: Order a -> Order a -> [Order a] # enumFromTo :: Order a -> Order a -> [Order a] # enumFromThenTo :: Order a -> Order a -> Order a -> [Order a] #
Eq a => Eq (Order a) Source #
Instance details Defined in Data.Semilattice.Order Methods (==) :: Order a -> Order a -> Bool # (/=) :: Order a -> Order a -> Bool #
Num a => Num (Order a) Source #
Instance details Defined in Data.Semilattice.Order Methods (+) :: Order a -> Order a -> Order a # (-) :: Order a -> Order a -> Order a # (*) :: Order a -> Order a -> Order a # negate :: Order a -> Order a # abs :: Order a -> Order a # signum :: Order a -> Order a # fromInteger :: Integer -> Order a #
Ord a => Ord (Order a) Source #
Instance details Defined in Data.Semilattice.Order Methods compare :: Order a -> Order a -> Ordering # (<) :: Order a -> Order a -> Bool # (<=) :: Order a -> Order a -> Bool # (>) :: Order a -> Order a -> Bool # (>=) :: Order a -> Order a -> Bool # max :: Order a -> Order a -> Order a # min :: Order a -> Order a -> Order a #
Read a => Read (Order a) Source #
Instance details Defined in Data.Semilattice.Order Methods readsPrec :: Int -> ReadS (Order a) # readList :: ReadS [Order a] # readPrec :: ReadPrec (Order a) # readListPrec :: ReadPrec [Order a] #
Show a => Show (Order a) Source #
Instance details Defined in Data.Semilattice.Order Methods showsPrec :: Int -> Order a -> ShowS # show :: Order a -> String # showList :: [Order a] -> ShowS #
Lower a => Lower (Order a) Source #
Instance details Defined in Data.Semilattice.Order Methods lowerBound :: Order a Source #
Ord a => Join (Order a) Source #	Total `Ord`erings give rise to a join semilattice satisfying: Idempotence: Order x \/ Order x == Order x Associativity: Order a \/ (Order b \/ Order c) == (Order a \/ Order b) \/ Order c Commutativity: Order a \/ Order b == Order b \/ Order a Identity: lowerBound \/ Order a == Order (a :: Int) Absorption: upperBound \/ Order a == (upperBound :: Order Int) Distributivity: Order a \/ Order b /\ Order c == (Order a \/ Order b) /\ (Order a \/ Order c)
Instance details Defined in Data.Semilattice.Order Methods (\/) :: Order a -> Order a -> Order a Source #
Upper a => Upper (Order a) Source #
Instance details Defined in Data.Semilattice.Order Methods upperBound :: Order a Source #
Ord a => Meet (Order a) Source #	Total `Ord`erings give rise to a meet semilattice satisfying: Idempotence: Order x /\ Order x == Order x Associativity: Order a /\ (Order b /\ Order c) == (Order a /\ Order b) /\ Order c Commutativity: Order a /\ Order b == Order b /\ Order a Identity: upperBound /\ Order a == Order (a :: Int) Absorption: lowerBound /\ Order a == (lowerBound :: Order Int) Distributivity: Order a /\ (Order b \/ Order c) == Order a /\ Order b \/ Order a /\ Order c
Instance details Defined in Data.Semilattice.Order Methods (/\) :: Order a -> Order a -> Order a Source #

>>> import Test.QuickCheck