Data.Order.Interval

Documentation

data Interval a

An interval in a poset P.

An interval in a poset P is a subset I of P with the following property:

\( \forall x, y \in I, z \in P: x \leq z \leq y \Rightarrow z \in I \)

Instances

Eq a => Eq (Interval a)

Defined in Data.Order.Interval

Methods

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

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

Show a => Show (Interval a)

Defined in Data.Order.Interval

Methods

showsPrec :: Int -> Interval a -> ShowS

show :: Interval a -> String

showList :: [Interval a] -> ShowS

Preorder a => Preorder (Interval a)

A containment order

Defined in Data.Order.Interval

Methods

(<~) :: Interval a -> Interval a -> Bool

(>~) :: Interval a -> Interval a -> Bool

(?~) :: Interval a -> Interval a -> Bool

(~~) :: Interval a -> Interval a -> Bool

(/~) :: Interval a -> Interval a -> Bool

plt :: Interval a -> Interval a -> Bool

pgt :: Interval a -> Interval a -> Bool

similar :: Interval a -> Interval a -> Bool

pmax :: Interval a -> Interval a -> Maybe (Interval a)

pmin :: Interval a -> Interval a -> Maybe (Interval a)

pcompare :: Interval a -> Interval a -> Maybe Ordering

imap :: Preorder b => (a -> b) -> Interval a -> Interval b

Map over an interval.

Note this is not a functor, as a non-monotonic map may cause the interval to collapse to the iempty interval.

(...) :: Preorder a => a -> a -> Interval a infix 3

Construct an interval from a pair of points.

Note: Endpoints are preorder-sorted. If pcompare x y = Nothing then the resulting interval will be empty.

iempty :: Interval a

The iempty interval.

>>> iempty
Empty

singleton :: a -> Interval a

Construct an interval containing a single point.

>>> singleton 1
1 ... 1

contains :: Preorder a => Interval a -> a -> Bool

endpts :: Interval a -> Maybe (a, a)

Obtain the endpoints of an interval.