Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Ord.Linear.Internal.Ord

Synopsis

class Eq a => Ord a where
- compare :: a %1 -> a %1 -> Ordering
- (<=) :: a %1 -> a %1 -> Bool
- (<) :: a %1 -> a %1 -> Bool
- (>) :: a %1 -> a %1 -> Bool
- (>=) :: a %1 -> a %1 -> Bool
data Ordering
- = LT
- | EQ
- | GT
min :: (Dupable a, Ord a) => a %1 -> a %1 -> a
max :: (Dupable a, Ord a) => a %1 -> a %1 -> a

Documentation

class Eq a => Ord a where Source #

Linear Orderings

Linear orderings provide a strict order. The laws for (<=) for all \(a,b,c\):

reflexivity: \(a \leq a \)
antisymmetry: \((a \leq b) \land (b \leq a) \rightarrow (a = b) \)
transitivity: \((a \leq b) \land (b \leq c) \rightarrow (a \leq c) \)

and these "agree" with <:

x <= y = not (y > x)
x >= y = not (y < x)

Unlike in the non-linear setting, a linear compare doesn't follow from <= since it requires calls: one to <= and one to ==. However, from a linear compare it is easy to implement the others. Hence, the minimal complete definition only contains compare.

Minimal complete definition

compare

Methods

compare :: a %1 -> a %1 -> Ordering Source #

compare x y returns an Ordering which is one of GT (greater than), EQ (equal), or LT (less than) which should be understood as "x is (compare x y) y".

(<=) :: a %1 -> a %1 -> Bool infix 4 Source #

(<) :: a %1 -> a %1 -> Bool infix 4 Source #

(>) :: a %1 -> a %1 -> Bool infix 4 Source #

(>=) :: a %1 -> a %1 -> Bool infix 4 Source #

Instances

Instances details

Ord Bool Source #
Instance details Defined in Data.Ord.Linear.Internal.Ord Methods compare :: Bool %1 -> Bool %1 -> Ordering Source # (<=) :: Bool %1 -> Bool %1 -> Bool Source # (<) :: Bool %1 -> Bool %1 -> Bool Source # (>) :: Bool %1 -> Bool %1 -> Bool Source # (>=) :: Bool %1 -> Bool %1 -> Bool Source #
Ord Char Source #
Instance details Defined in Data.Ord.Linear.Internal.Ord Methods compare :: Char %1 -> Char %1 -> Ordering Source # (<=) :: Char %1 -> Char %1 -> Bool Source # (<) :: Char %1 -> Char %1 -> Bool Source # (>) :: Char %1 -> Char %1 -> Bool Source # (>=) :: Char %1 -> Char %1 -> Bool Source #
Ord Double Source #
Instance details Defined in Data.Ord.Linear.Internal.Ord Methods compare :: Double %1 -> Double %1 -> Ordering Source # (<=) :: Double %1 -> Double %1 -> Bool Source # (<) :: Double %1 -> Double %1 -> Bool Source # (>) :: Double %1 -> Double %1 -> Bool Source # (>=) :: Double %1 -> Double %1 -> Bool Source #
Ord Int Source #
Instance details Defined in Data.Ord.Linear.Internal.Ord Methods compare :: Int %1 -> Int %1 -> Ordering Source # (<=) :: Int %1 -> Int %1 -> Bool Source # (<) :: Int %1 -> Int %1 -> Bool Source # (>) :: Int %1 -> Int %1 -> Bool Source # (>=) :: Int %1 -> Int %1 -> Bool Source #
Ord Ordering Source #
Instance details Defined in Data.Ord.Linear.Internal.Ord Methods compare :: Ordering %1 -> Ordering %1 -> Ordering Source # (<=) :: Ordering %1 -> Ordering %1 -> Bool Source # (<) :: Ordering %1 -> Ordering %1 -> Bool Source # (>) :: Ordering %1 -> Ordering %1 -> Bool Source # (>=) :: Ordering %1 -> Ordering %1 -> Bool Source #
Ord () Source #
Instance details Defined in Data.Ord.Linear.Internal.Ord Methods compare :: () %1 -> () %1 -> Ordering Source # (<=) :: () %1 -> () %1 -> Bool Source # (<) :: () %1 -> () %1 -> Bool Source # (>) :: () %1 -> () %1 -> Bool Source # (>=) :: () %1 -> () %1 -> Bool Source #
(Consumable a, Ord a) => Ord [a] Source #
Instance details Defined in Data.Ord.Linear.Internal.Ord Methods compare :: [a] %1 -> [a] %1 -> Ordering Source # (<=) :: [a] %1 -> [a] %1 -> Bool Source # (<) :: [a] %1 -> [a] %1 -> Bool Source # (>) :: [a] %1 -> [a] %1 -> Bool Source # (>=) :: [a] %1 -> [a] %1 -> Bool Source #
(Consumable a, Ord a) => Ord (Maybe a) Source #
Instance details Defined in Data.Ord.Linear.Internal.Ord Methods compare :: Maybe a %1 -> Maybe a %1 -> Ordering Source # (<=) :: Maybe a %1 -> Maybe a %1 -> Bool Source # (<) :: Maybe a %1 -> Maybe a %1 -> Bool Source # (>) :: Maybe a %1 -> Maybe a %1 -> Bool Source # (>=) :: Maybe a %1 -> Maybe a %1 -> Bool Source #
Ord a => Ord (Ur a) Source #
Instance details Defined in Data.Ord.Linear.Internal.Ord Methods compare :: Ur a %1 -> Ur a %1 -> Ordering Source # (<=) :: Ur a %1 -> Ur a %1 -> Bool Source # (<) :: Ur a %1 -> Ur a %1 -> Bool Source # (>) :: Ur a %1 -> Ur a %1 -> Bool Source # (>=) :: Ur a %1 -> Ur a %1 -> Bool Source #
(Consumable a, Consumable b, Ord a, Ord b) => Ord (Either a b) Source #
Instance details Defined in Data.Ord.Linear.Internal.Ord Methods compare :: Either a b %1 -> Either a b %1 -> Ordering Source # (<=) :: Either a b %1 -> Either a b %1 -> Bool Source # (<) :: Either a b %1 -> Either a b %1 -> Bool Source # (>) :: Either a b %1 -> Either a b %1 -> Bool Source # (>=) :: Either a b %1 -> Either a b %1 -> Bool Source #
(Ord a, Ord b) => Ord (a, b) Source #
Instance details Defined in Data.Ord.Linear.Internal.Ord Methods compare :: (a, b) %1 -> (a, b) %1 -> Ordering Source # (<=) :: (a, b) %1 -> (a, b) %1 -> Bool Source # (<) :: (a, b) %1 -> (a, b) %1 -> Bool Source # (>) :: (a, b) %1 -> (a, b) %1 -> Bool Source # (>=) :: (a, b) %1 -> (a, b) %1 -> Bool Source #
(Ord a, Ord b, Ord c) => Ord (a, b, c) Source #
Instance details Defined in Data.Ord.Linear.Internal.Ord Methods compare :: (a, b, c) %1 -> (a, b, c) %1 -> Ordering Source # (<=) :: (a, b, c) %1 -> (a, b, c) %1 -> Bool Source # (<) :: (a, b, c) %1 -> (a, b, c) %1 -> Bool Source # (>) :: (a, b, c) %1 -> (a, b, c) %1 -> Bool Source # (>=) :: (a, b, c) %1 -> (a, b, c) %1 -> Bool Source #
(Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) Source #
Instance details Defined in Data.Ord.Linear.Internal.Ord Methods compare :: (a, b, c, d) %1 -> (a, b, c, d) %1 -> Ordering Source # (<=) :: (a, b, c, d) %1 -> (a, b, c, d) %1 -> Bool Source # (<) :: (a, b, c, d) %1 -> (a, b, c, d) %1 -> Bool Source # (>) :: (a, b, c, d) %1 -> (a, b, c, d) %1 -> Bool Source # (>=) :: (a, b, c, d) %1 -> (a, b, c, d) %1 -> Bool Source #

data Ordering #

Constructors

LT
EQ
GT

Instances

Instances details

Bounded Ordering	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Ordering # maxBound :: Ordering #
Enum Ordering	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Ordering -> Ordering # pred :: Ordering -> Ordering # toEnum :: Int -> Ordering # fromEnum :: Ordering -> Int # enumFrom :: Ordering -> [Ordering] # enumFromThen :: Ordering -> Ordering -> [Ordering] # enumFromTo :: Ordering -> Ordering -> [Ordering] # enumFromThenTo :: Ordering -> Ordering -> Ordering -> [Ordering] #
Eq Ordering
Instance details Defined in GHC.Classes Methods (==) :: Ordering -> Ordering -> Bool # (/=) :: Ordering -> Ordering -> Bool #
Ord Ordering
Instance details Defined in GHC.Classes Methods compare :: Ordering -> Ordering -> Ordering # (<) :: Ordering -> Ordering -> Bool # (<=) :: Ordering -> Ordering -> Bool # (>) :: Ordering -> Ordering -> Bool # (>=) :: Ordering -> Ordering -> Bool # max :: Ordering -> Ordering -> Ordering # min :: Ordering -> Ordering -> Ordering #
Read Ordering	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Ordering # readList :: ReadS [Ordering] # readPrec :: ReadPrec Ordering # readListPrec :: ReadPrec [Ordering] #
Show Ordering	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Ordering -> ShowS # show :: Ordering -> String # showList :: [Ordering] -> ShowS #
Ix Ordering	Since: base-2.1
Instance details Defined in GHC.Ix Methods range :: (Ordering, Ordering) -> [Ordering] # index :: (Ordering, Ordering) -> Ordering -> Int # unsafeIndex :: (Ordering, Ordering) -> Ordering -> Int # inRange :: (Ordering, Ordering) -> Ordering -> Bool # rangeSize :: (Ordering, Ordering) -> Int # unsafeRangeSize :: (Ordering, Ordering) -> Int #
Generic Ordering
Instance details Defined in GHC.Generics Associated Types type Rep Ordering :: Type -> Type # Methods from :: Ordering -> Rep Ordering x # to :: Rep Ordering x -> Ordering #
Semigroup Ordering	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Ordering -> Ordering -> Ordering # sconcat :: NonEmpty Ordering -> Ordering # stimes :: Integral b => b -> Ordering -> Ordering #
Monoid Ordering	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering # mappend :: Ordering -> Ordering -> Ordering # mconcat :: [Ordering] -> Ordering #
Hashable Ordering
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Ordering -> Int # hash :: Ordering -> Int #
Consumable Ordering Source #
Instance details Defined in Data.Unrestricted.Internal.Instances Methods consume :: Ordering %1 -> () Source #
Semigroup Ordering Source #
Instance details Defined in Data.Monoid.Linear.Internal.Semigroup Methods (<>) :: Ordering %1 -> Ordering %1 -> Ordering Source #
Monoid Ordering Source #
Instance details Defined in Data.Monoid.Linear.Internal.Monoid Methods mempty :: Ordering Source #
Dupable Ordering Source #
Instance details Defined in Data.Unrestricted.Internal.Instances Methods dupV :: forall (n :: Nat). KnownNat n => Ordering %1 -> V n Ordering Source # dup2 :: Ordering %1 -> (Ordering, Ordering) Source #
Movable Ordering Source #
Instance details Defined in Data.Unrestricted.Internal.Instances Methods move :: Ordering %1 -> Ur Ordering Source #
Eq Ordering Source #
Instance details Defined in Data.Ord.Linear.Internal.Eq Methods (==) :: Ordering %1 -> Ordering %1 -> Bool Source # (/=) :: Ordering %1 -> Ordering %1 -> Bool Source #
Ord Ordering Source #
Instance details Defined in Data.Ord.Linear.Internal.Ord Methods compare :: Ordering %1 -> Ordering %1 -> Ordering Source # (<=) :: Ordering %1 -> Ordering %1 -> Bool Source # (<) :: Ordering %1 -> Ordering %1 -> Bool Source # (>) :: Ordering %1 -> Ordering %1 -> Bool Source # (>=) :: Ordering %1 -> Ordering %1 -> Bool Source #
type Rep Ordering	Since: base-4.6.0.0
Instance details Defined in GHC.Generics type Rep Ordering = D1 ('MetaData "Ordering" "GHC.Types" "ghc-prim" 'False) (C1 ('MetaCons "LT" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "EQ" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "GT" 'PrefixI 'False) (U1 :: Type -> Type)))

min :: (Dupable a, Ord a) => a %1 -> a %1 -> a Source #

min x y returns the smaller input, or y in case of a tie.

max :: (Dupable a, Ord a) => a %1 -> a %1 -> a Source #

max x y returns the larger input, or y in case of a tie.