Data.Semilattice.Order

Total Orderings give rise to Join and Meet semilattices.

Documentation

newtype Order a

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

Constructors

Order

Fields

• getOrder :: a

Instances

Functor Order

Methods

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

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

Foldable 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

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)

Methods

minBound :: Order a

maxBound :: Order a

Enum a => Enum (Order a)

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)

Methods

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

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

Num a => Num (Order a)

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)

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)

Methods

readsPrec :: Int -> ReadS (Order a)

readList :: ReadS [Order a]

readPrec :: ReadPrec (Order a)

readListPrec :: ReadPrec [Order a]

Show a => Show (Order a)

Methods

showsPrec :: Int -> Order a -> ShowS

show :: Order a -> String

showList :: [Order a] -> ShowS

Lower a => Lower (Order a)

Methods

lowerBound :: Order a

Ord a => Join (Order a)

Total Orderings 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)

Methods

(\/) :: Order a -> Order a -> Order a

Upper a => Upper (Order a)

Methods

upperBound :: Order a

Ord a => Meet (Order a)

Total Orderings 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

Methods

(/\) :: Order a -> Order a -> Order a

>>> import Test.QuickCheck