OAlg.Data.Ord

Description

Data.Ord enriched with some additional elements.

Synopsis

module Data.Ord
fcompare :: Ord i => (a -> i) -> a -> a -> Ordering
wcompare :: (w -> w -> Ordering) -> (a -> w) -> a -> a -> Ordering
coCompare :: (a -> a -> Ordering) -> a -> a -> Ordering
compare2 :: (a -> a -> Ordering) -> (b -> b -> Ordering) -> (a, b) -> (a, b) -> Ordering
sortFst :: Ord a => [(a, b)] -> [(a, b)]
sortFstBy :: (a -> a -> Ordering) -> [(a, b)] -> [(a, b)]
sortSnd :: Ord b => [(a, b)] -> [(a, b)]
sortSndBy :: (b -> b -> Ordering) -> [(a, b)] -> [(a, b)]
data Closure x
- = NegInf
- | It x
- | PosInf
cmin :: Ord x => [x] -> Closure x
cmax :: Ord x => [x] -> Closure x
cspan :: Ord x => [x] -> Span x
type Span x = (Closure x, Closure x)
enumSpan :: (Enum i, Ord i) => i -> Closure i -> [i]

Documentation

fcompare :: Ord i => (a -> i) -> a -> a -> Ordering Source #

comparing according to the mapped values.

wcompare :: (w -> w -> Ordering) -> (a -> w) -> a -> a -> Ordering Source #

comparing according to the given ordering relation on the mapped values.

the reverse ordering

compare2 :: (a -> a -> Ordering) -> (b -> b -> Ordering) -> (a, b) -> (a, b) -> Ordering Source #

comparing of pairs.

sortFst :: Ord a => [(a, b)] -> [(a, b)] Source #

sorting according to the first component.

sortFstBy :: (a -> a -> Ordering) -> [(a, b)] -> [(a, b)] Source #

sorting according to the first component.

sortSnd :: Ord b => [(a, b)] -> [(a, b)] Source #

sorting according to the second component.

sortSndBy :: (b -> b -> Ordering) -> [(a, b)] -> [(a, b)] Source #

sorting according to the second component.

the closer of a linear ordered x.

Constructors

Instances details

Read x => Read (Closure x) Source #
Instance details Defined in OAlg.Data.Ord Methods readsPrec :: Int -> ReadS (Closure x) # readList :: ReadS [Closure x] # readPrec :: ReadPrec (Closure x) # readListPrec :: ReadPrec [Closure x] #
Show x => Show (Closure x) Source #
Instance details Defined in OAlg.Data.Ord Methods showsPrec :: Int -> Closure x -> ShowS # show :: Closure x -> String # showList :: [Closure x] -> ShowS #
Eq x => Eq (Closure x) Source #
Instance details Defined in OAlg.Data.Ord Methods (==) :: Closure x -> Closure x -> Bool # (/=) :: Closure x -> Closure x -> Bool #
Ord x => Ord (Closure x) Source #
Instance details Defined in OAlg.Data.Ord Methods compare :: Closure x -> Closure x -> Ordering # (<) :: Closure x -> Closure x -> Bool # (<=) :: Closure x -> Closure x -> Bool # (>) :: Closure x -> Closure x -> Bool # (>=) :: Closure x -> Closure x -> Bool # max :: Closure x -> Closure x -> Closure x # min :: Closure x -> Closure x -> Closure x #
Validable x => Validable (Closure x) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Closure x -> Statement Source #

the minimum of the items of a list, i.e. the biggest lower bound.

Property Let xs be in [x] for a linear ordered x, then holds: For all x in xs holds: cmin xs <= It x.

the maximum of the items of a list, i.e. the smallest upper bound.

Property Let xs be in [x] for a linear ordered x, then holds: For all x in xs holds: It x <= cmax xs.

cspan :: Ord x => [x] -> Span x Source #

(l,u) = cspan xs where l is the minimum and u the maximum of the items in xs.

Example

>>> cspan "aeb"
(It 'a',It 'e')

>>> cspan ""
(PosInf,NegInf)

the span type.

enumSpan :: (Enum i, Ord i) => i -> Closure i -> [i] Source #

enumSpan i0 h enumerates the index, starting by i0 to h.