Data.Ord.Linear

Documentation

class Eq a => Ord a where

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 infix 4

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

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

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

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

Instances

Ord Int16

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: Int16 %1 -> Int16 %1 -> Ordering

(<=) :: Int16 %1 -> Int16 %1 -> Bool

(<) :: Int16 %1 -> Int16 %1 -> Bool

(>) :: Int16 %1 -> Int16 %1 -> Bool

(>=) :: Int16 %1 -> Int16 %1 -> Bool

Ord Int32

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: Int32 %1 -> Int32 %1 -> Ordering

(<=) :: Int32 %1 -> Int32 %1 -> Bool

(<) :: Int32 %1 -> Int32 %1 -> Bool

(>) :: Int32 %1 -> Int32 %1 -> Bool

(>=) :: Int32 %1 -> Int32 %1 -> Bool

Ord Int64

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: Int64 %1 -> Int64 %1 -> Ordering

(<=) :: Int64 %1 -> Int64 %1 -> Bool

(<) :: Int64 %1 -> Int64 %1 -> Bool

(>) :: Int64 %1 -> Int64 %1 -> Bool

(>=) :: Int64 %1 -> Int64 %1 -> Bool

Ord Int8

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: Int8 %1 -> Int8 %1 -> Ordering

(<=) :: Int8 %1 -> Int8 %1 -> Bool

(<) :: Int8 %1 -> Int8 %1 -> Bool

(>) :: Int8 %1 -> Int8 %1 -> Bool

(>=) :: Int8 %1 -> Int8 %1 -> Bool

Ord Word16

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: Word16 %1 -> Word16 %1 -> Ordering

(<=) :: Word16 %1 -> Word16 %1 -> Bool

(<) :: Word16 %1 -> Word16 %1 -> Bool

(>) :: Word16 %1 -> Word16 %1 -> Bool

(>=) :: Word16 %1 -> Word16 %1 -> Bool

Ord Word32

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: Word32 %1 -> Word32 %1 -> Ordering

(<=) :: Word32 %1 -> Word32 %1 -> Bool

(<) :: Word32 %1 -> Word32 %1 -> Bool

(>) :: Word32 %1 -> Word32 %1 -> Bool

(>=) :: Word32 %1 -> Word32 %1 -> Bool

Ord Word64

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: Word64 %1 -> Word64 %1 -> Ordering

(<=) :: Word64 %1 -> Word64 %1 -> Bool

(<) :: Word64 %1 -> Word64 %1 -> Bool

(>) :: Word64 %1 -> Word64 %1 -> Bool

(>=) :: Word64 %1 -> Word64 %1 -> Bool

Ord Word8

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: Word8 %1 -> Word8 %1 -> Ordering

(<=) :: Word8 %1 -> Word8 %1 -> Bool

(<) :: Word8 %1 -> Word8 %1 -> Bool

(>) :: Word8 %1 -> Word8 %1 -> Bool

(>=) :: Word8 %1 -> Word8 %1 -> Bool

Ord Ordering

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: Ordering %1 -> Ordering %1 -> Ordering

(<=) :: Ordering %1 -> Ordering %1 -> Bool

(<) :: Ordering %1 -> Ordering %1 -> Bool

(>) :: Ordering %1 -> Ordering %1 -> Bool

(>=) :: Ordering %1 -> Ordering %1 -> Bool

Ord ()

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: () %1 -> () %1 -> Ordering

(<=) :: () %1 -> () %1 -> Bool

(<) :: () %1 -> () %1 -> Bool

(>) :: () %1 -> () %1 -> Bool

(>=) :: () %1 -> () %1 -> Bool

Ord Bool

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: Bool %1 -> Bool %1 -> Ordering

(<=) :: Bool %1 -> Bool %1 -> Bool

(<) :: Bool %1 -> Bool %1 -> Bool

(>) :: Bool %1 -> Bool %1 -> Bool

(>=) :: Bool %1 -> Bool %1 -> Bool

Ord Char

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: Char %1 -> Char %1 -> Ordering

(<=) :: Char %1 -> Char %1 -> Bool

(<) :: Char %1 -> Char %1 -> Bool

(>) :: Char %1 -> Char %1 -> Bool

(>=) :: Char %1 -> Char %1 -> Bool

Ord Double

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: Double %1 -> Double %1 -> Ordering

(<=) :: Double %1 -> Double %1 -> Bool

(<) :: Double %1 -> Double %1 -> Bool

(>) :: Double %1 -> Double %1 -> Bool

(>=) :: Double %1 -> Double %1 -> Bool

Ord Int

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: Int %1 -> Int %1 -> Ordering

(<=) :: Int %1 -> Int %1 -> Bool

(<) :: Int %1 -> Int %1 -> Bool

(>) :: Int %1 -> Int %1 -> Bool

(>=) :: Int %1 -> Int %1 -> Bool

Ord a => Ord (Ur a)

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: Ur a %1 -> Ur a %1 -> Ordering

(<=) :: Ur a %1 -> Ur a %1 -> Bool

(<) :: Ur a %1 -> Ur a %1 -> Bool

(>) :: Ur a %1 -> Ur a %1 -> Bool

(>=) :: Ur a %1 -> Ur a %1 -> Bool

(Consumable a, Ord a) => Ord (Maybe a)

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: Maybe a %1 -> Maybe a %1 -> Ordering

(<=) :: Maybe a %1 -> Maybe a %1 -> Bool

(<) :: Maybe a %1 -> Maybe a %1 -> Bool

(>) :: Maybe a %1 -> Maybe a %1 -> Bool

(>=) :: Maybe a %1 -> Maybe a %1 -> Bool

(Consumable a, Ord a) => Ord [a]

Defined in Data.Ord.Linear.Internal.Ord

Methods

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

(Consumable a, Consumable b, Ord a, Ord b) => Ord (Either a b)

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: Either a b %1 -> Either a b %1 -> Ordering

(<=) :: Either a b %1 -> Either a b %1 -> Bool

(<) :: Either a b %1 -> Either a b %1 -> Bool

(>) :: Either a b %1 -> Either a b %1 -> Bool

(>=) :: Either a b %1 -> Either a b %1 -> Bool

(Ord a, Ord b) => Ord (a, b)

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: (a, b) %1 -> (a, b) %1 -> Ordering

(<=) :: (a, b) %1 -> (a, b) %1 -> Bool

(<) :: (a, b) %1 -> (a, b) %1 -> Bool

(>) :: (a, b) %1 -> (a, b) %1 -> Bool

(>=) :: (a, b) %1 -> (a, b) %1 -> Bool

(Ord a, Ord b, Ord c) => Ord (a, b, c)

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: (a, b, c) %1 -> (a, b, c) %1 -> Ordering

(<=) :: (a, b, c) %1 -> (a, b, c) %1 -> Bool

(<) :: (a, b, c) %1 -> (a, b, c) %1 -> Bool

(>) :: (a, b, c) %1 -> (a, b, c) %1 -> Bool

(>=) :: (a, b, c) %1 -> (a, b, c) %1 -> Bool

(Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d)

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: (a, b, c, d) %1 -> (a, b, c, d) %1 -> Ordering

(<=) :: (a, b, c, d) %1 -> (a, b, c, d) %1 -> Bool

(<) :: (a, b, c, d) %1 -> (a, b, c, d) %1 -> Bool

(>) :: (a, b, c, d) %1 -> (a, b, c, d) %1 -> Bool

(>=) :: (a, b, c, d) %1 -> (a, b, c, d) %1 -> Bool

data Ordering

Constructors

LT

EQ

GT

Instances

Monoid Ordering

Since: base-2.1

Defined in GHC.Base

Methods

mempty :: Ordering

mappend :: Ordering -> Ordering -> Ordering

mconcat :: [Ordering] -> Ordering

Semigroup Ordering

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: Ordering -> Ordering -> Ordering

sconcat :: NonEmpty Ordering -> Ordering

stimes :: Integral b => b -> Ordering -> Ordering

Bounded Ordering

Since: base-2.1

Defined in GHC.Enum

Methods

minBound :: Ordering

maxBound :: Ordering

Enum Ordering

Since: base-2.1

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]

Generic Ordering

Defined in GHC.Generics

Associated Types

type Rep Ordering :: Type -> Type

Methods

from :: Ordering -> Rep Ordering x

to :: Rep Ordering x -> Ordering

Ix Ordering

Since: base-2.1

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

Read Ordering

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Ordering

readList :: ReadS [Ordering]

readPrec :: ReadPrec Ordering

readListPrec :: ReadPrec [Ordering]

Show Ordering

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Ordering -> ShowS

show :: Ordering -> String

showList :: [Ordering] -> ShowS

Eq Ordering

Defined in GHC.Classes

Methods

(==) :: Ordering -> Ordering -> Bool

(/=) :: Ordering -> Ordering -> Bool

Ord Ordering

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

Hashable Ordering

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Ordering -> Int

hash :: Ordering -> Int

Monoid Ordering

Defined in Data.Monoid.Linear.Internal.Monoid

Methods

mempty :: Ordering

Semigroup Ordering

Defined in Data.Monoid.Linear.Internal.Semigroup

Methods

(<>) :: Ordering %1 -> Ordering %1 -> Ordering

Eq Ordering

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: Ordering %1 -> Ordering %1 -> Bool

(/=) :: Ordering %1 -> Ordering %1 -> Bool

Ord Ordering

Defined in Data.Ord.Linear.Internal.Ord

Methods

compare :: Ordering %1 -> Ordering %1 -> Ordering

(<=) :: Ordering %1 -> Ordering %1 -> Bool

(<) :: Ordering %1 -> Ordering %1 -> Bool

(>) :: Ordering %1 -> Ordering %1 -> Bool

(>=) :: Ordering %1 -> Ordering %1 -> Bool

Consumable Ordering

Defined in Data.Unrestricted.Linear.Internal.Consumable

Methods

consume :: Ordering %1 -> ()

Dupable Ordering

Defined in Data.Unrestricted.Linear.Internal.Dupable

Methods

dupR :: Ordering %1 -> Replicator Ordering

dup2 :: Ordering %1 -> (Ordering, Ordering)

Movable Ordering

Defined in Data.Unrestricted.Linear.Internal.Movable

Methods

move :: Ordering %1 -> Ur Ordering

type Rep Ordering

Since: base-4.6.0.0

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)))

type Rep Ordering

Defined in Generics.Linear.Instances.Base

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

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

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

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

class Eq a where

Testing equality on values.

The laws are that (==) and (/=) are compatible and (==) is an equivalence relation. So, for all x, y, z,

• x == x always
• x == y implies y == x
• x == y and y == z implies x == z
• (x == y) ≌ not (x /= y)

Minimal complete definition

(==) | (/=)

Methods

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

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

Instances

Eq Int16

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: Int16 %1 -> Int16 %1 -> Bool

(/=) :: Int16 %1 -> Int16 %1 -> Bool

Eq Int32

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: Int32 %1 -> Int32 %1 -> Bool

(/=) :: Int32 %1 -> Int32 %1 -> Bool

Eq Int64

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: Int64 %1 -> Int64 %1 -> Bool

(/=) :: Int64 %1 -> Int64 %1 -> Bool

Eq Int8

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: Int8 %1 -> Int8 %1 -> Bool

(/=) :: Int8 %1 -> Int8 %1 -> Bool

Eq Word16

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: Word16 %1 -> Word16 %1 -> Bool

(/=) :: Word16 %1 -> Word16 %1 -> Bool

Eq Word32

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: Word32 %1 -> Word32 %1 -> Bool

(/=) :: Word32 %1 -> Word32 %1 -> Bool

Eq Word64

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: Word64 %1 -> Word64 %1 -> Bool

(/=) :: Word64 %1 -> Word64 %1 -> Bool

Eq Word8

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: Word8 %1 -> Word8 %1 -> Bool

(/=) :: Word8 %1 -> Word8 %1 -> Bool

Eq Ordering

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: Ordering %1 -> Ordering %1 -> Bool

(/=) :: Ordering %1 -> Ordering %1 -> Bool

Eq ()

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: () %1 -> () %1 -> Bool

(/=) :: () %1 -> () %1 -> Bool

Eq Bool

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: Bool %1 -> Bool %1 -> Bool

(/=) :: Bool %1 -> Bool %1 -> Bool

Eq Char

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: Char %1 -> Char %1 -> Bool

(/=) :: Char %1 -> Char %1 -> Bool

Eq Double

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: Double %1 -> Double %1 -> Bool

(/=) :: Double %1 -> Double %1 -> Bool

Eq Int

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: Int %1 -> Int %1 -> Bool

(/=) :: Int %1 -> Int %1 -> Bool

Eq a => Eq (Ur a)

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: Ur a %1 -> Ur a %1 -> Bool

(/=) :: Ur a %1 -> Ur a %1 -> Bool

(Consumable a, Eq a) => Eq (Maybe a)

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: Maybe a %1 -> Maybe a %1 -> Bool

(/=) :: Maybe a %1 -> Maybe a %1 -> Bool

(Consumable a, Eq a) => Eq [a]

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: [a] %1 -> [a] %1 -> Bool

(/=) :: [a] %1 -> [a] %1 -> Bool

(Consumable a, Consumable b, Eq a, Eq b) => Eq (Either a b)

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: Either a b %1 -> Either a b %1 -> Bool

(/=) :: Either a b %1 -> Either a b %1 -> Bool

(Eq a, Eq b) => Eq (a, b)

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: (a, b) %1 -> (a, b) %1 -> Bool

(/=) :: (a, b) %1 -> (a, b) %1 -> Bool

(Eq a, Eq b, Eq c) => Eq (a, b, c)

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: (a, b, c) %1 -> (a, b, c) %1 -> Bool

(/=) :: (a, b, c) %1 -> (a, b, c) %1 -> Bool

(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d)

Defined in Data.Ord.Linear.Internal.Eq

Methods

(==) :: (a, b, c, d) %1 -> (a, b, c, d) %1 -> Bool

(/=) :: (a, b, c, d) %1 -> (a, b, c, d) %1 -> Bool