Copyright	(c) Erich Gut
License	BSD3
Maintainer	zerich.gut@gmail.com
Safe Haskell	Safe-Inferred
Language	Haskell2010

OAlg.Data.Ord

Contents

Total
Partial

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 Closer x
- = NegInf
- | It x
- | PosInf
cmin :: Ord x => [x] -> Closer x
cmax :: Ord x => [x] -> Closer x
cspan :: Ord x => [x] -> Span x
type Span x = (Closer x, Closer x)
enumSpan :: (Enum i, Ord i) => i -> Closer i -> [i]
class Eq a => POrd a where
- (<<=) :: a -> a -> Bool

Total

module Data.Ord

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.

coCompare :: (a -> a -> Ordering) -> a -> a -> Ordering Source #

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.

data Closer x Source #

the closer of a linear ordered x.

Constructors

NegInf
It x
PosInf

Instances

Instances details

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

cmin :: Ord x => [x] -> Closer x 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.

cmax :: Ord x => [x] -> Closer x Source #

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)

type Span x = (Closer x, Closer x) Source #

the span type.

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

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

Partial

class Eq a => POrd a where Source #

partially ordered types.

Properties Let a be an instance of POrd, then holds:

For all x in a holds: x <<= x.
For all x, y in a holds: If x <<= y and y <<= x then x == y.
For all x, y, z in a holds: If x <<= y and y <<= z then x <<= z.

Methods

(<<=) :: a -> a -> Bool infix 4 Source #

Instances

Instances details

Ord x => POrd (Set x) Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods (<<=) :: Set x -> Set x -> Bool Source #