Safe Haskell	None
Language	Haskell2010

Relation.Binary.Comparison

Documentation

class Preord a where #

Methods

(≤) :: a -> a -> Bool infix 4 #

(≥) :: a -> a -> Bool infix 4 #

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

(>) :: a -> a -> Bool infix 4 #

Instances

Preord Bool #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Bool -> Bool -> Bool # (≥) :: Bool -> Bool -> Bool # (<) :: Bool -> Bool -> Bool # (>) :: Bool -> Bool -> Bool #
Preord Char #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Char -> Char -> Bool # (≥) :: Char -> Char -> Bool # (<) :: Char -> Char -> Bool # (>) :: Char -> Char -> Bool #
Preord Int #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Int -> Int -> Bool # (≥) :: Int -> Int -> Bool # (<) :: Int -> Int -> Bool # (>) :: Int -> Int -> Bool #
Preord Int8 #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Int8 -> Int8 -> Bool # (≥) :: Int8 -> Int8 -> Bool # (<) :: Int8 -> Int8 -> Bool # (>) :: Int8 -> Int8 -> Bool #
Preord Int16 #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Int16 -> Int16 -> Bool # (≥) :: Int16 -> Int16 -> Bool # (<) :: Int16 -> Int16 -> Bool # (>) :: Int16 -> Int16 -> Bool #
Preord Int32 #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Int32 -> Int32 -> Bool # (≥) :: Int32 -> Int32 -> Bool # (<) :: Int32 -> Int32 -> Bool # (>) :: Int32 -> Int32 -> Bool #
Preord Int64 #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Int64 -> Int64 -> Bool # (≥) :: Int64 -> Int64 -> Bool # (<) :: Int64 -> Int64 -> Bool # (>) :: Int64 -> Int64 -> Bool #
Preord Integer #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Integer -> Integer -> Bool # (≥) :: Integer -> Integer -> Bool # (<) :: Integer -> Integer -> Bool # (>) :: Integer -> Integer -> Bool #
Preord Natural #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Natural -> Natural -> Bool # (≥) :: Natural -> Natural -> Bool # (<) :: Natural -> Natural -> Bool # (>) :: Natural -> Natural -> Bool #
Preord Ordering #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Ordering -> Ordering -> Bool # (≥) :: Ordering -> Ordering -> Bool # (<) :: Ordering -> Ordering -> Bool # (>) :: Ordering -> Ordering -> Bool #
Preord Word #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Word -> Word -> Bool # (≥) :: Word -> Word -> Bool # (<) :: Word -> Word -> Bool # (>) :: Word -> Word -> Bool #
Preord Word8 #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Word8 -> Word8 -> Bool # (≥) :: Word8 -> Word8 -> Bool # (<) :: Word8 -> Word8 -> Bool # (>) :: Word8 -> Word8 -> Bool #
Preord Word16 #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Word16 -> Word16 -> Bool # (≥) :: Word16 -> Word16 -> Bool # (<) :: Word16 -> Word16 -> Bool # (>) :: Word16 -> Word16 -> Bool #
Preord Word32 #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Word32 -> Word32 -> Bool # (≥) :: Word32 -> Word32 -> Bool # (<) :: Word32 -> Word32 -> Bool # (>) :: Word32 -> Word32 -> Bool #
Preord Word64 #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Word64 -> Word64 -> Bool # (≥) :: Word64 -> Word64 -> Bool # (<) :: Word64 -> Word64 -> Bool # (>) :: Word64 -> Word64 -> Bool #
Preord () #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: () -> () -> Bool # (≥) :: () -> () -> Bool # (<) :: () -> () -> Bool # (>) :: () -> () -> Bool #
Preord a => Preord (Maybe a) #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Maybe a -> Maybe a -> Bool # (≥) :: Maybe a -> Maybe a -> Bool # (<) :: Maybe a -> Maybe a -> Bool # (>) :: Maybe a -> Maybe a -> Bool #
Preord (Sum Natural) #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Sum Natural -> Sum Natural -> Bool # (≥) :: Sum Natural -> Sum Natural -> Bool # (<) :: Sum Natural -> Sum Natural -> Bool # (>) :: Sum Natural -> Sum Natural -> Bool #
(Preord a, Preord b) => Preord (Lexical (Either a b)) #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Lexical (Either a b) -> Lexical (Either a b) -> Bool # (≥) :: Lexical (Either a b) -> Lexical (Either a b) -> Bool # (<) :: Lexical (Either a b) -> Lexical (Either a b) -> Bool # (>) :: Lexical (Either a b) -> Lexical (Either a b) -> Bool #
(PartialOrd a, PartialOrd b) => Preord (Lexical (a, b)) #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Lexical (a, b) -> Lexical (a, b) -> Bool # (≥) :: Lexical (a, b) -> Lexical (a, b) -> Bool # (<) :: Lexical (a, b) -> Lexical (a, b) -> Bool # (>) :: Lexical (a, b) -> Lexical (a, b) -> Bool #
Bits a => Preord (BitSet a) #
Instance details Defined in Data.BitSet Methods (≤) :: BitSet a -> BitSet a -> Bool # (≥) :: BitSet a -> BitSet a -> Bool # (<) :: BitSet a -> BitSet a -> Bool # (>) :: BitSet a -> BitSet a -> Bool #
(Preord a, Preord b) => Preord (Either a b) #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Either a b -> Either a b -> Bool # (≥) :: Either a b -> Either a b -> Bool # (<) :: Either a b -> Either a b -> Bool # (>) :: Either a b -> Either a b -> Bool #
(Preord a, Preord b) => Preord (a, b) #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: (a, b) -> (a, b) -> Bool # (≥) :: (a, b) -> (a, b) -> Bool # (<) :: (a, b) -> (a, b) -> Bool # (>) :: (a, b) -> (a, b) -> Bool #

class PartialEq a where #

Methods

(≡) :: a -> a -> Bool infix 4 #

(≢) :: a -> a -> Bool infix 4 #

Instances

PartialEq Bool #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Bool -> Bool -> Bool # (≢) :: Bool -> Bool -> Bool #
PartialEq Char #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Char -> Char -> Bool # (≢) :: Char -> Char -> Bool #
PartialEq Int #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Int -> Int -> Bool # (≢) :: Int -> Int -> Bool #
PartialEq Int8 #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Int8 -> Int8 -> Bool # (≢) :: Int8 -> Int8 -> Bool #
PartialEq Int16 #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Int16 -> Int16 -> Bool # (≢) :: Int16 -> Int16 -> Bool #
PartialEq Int32 #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Int32 -> Int32 -> Bool # (≢) :: Int32 -> Int32 -> Bool #
PartialEq Int64 #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Int64 -> Int64 -> Bool # (≢) :: Int64 -> Int64 -> Bool #
PartialEq Integer #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Integer -> Integer -> Bool # (≢) :: Integer -> Integer -> Bool #
PartialEq Natural #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Natural -> Natural -> Bool # (≢) :: Natural -> Natural -> Bool #
PartialEq Ordering #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Ordering -> Ordering -> Bool # (≢) :: Ordering -> Ordering -> Bool #
PartialEq Word #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Word -> Word -> Bool # (≢) :: Word -> Word -> Bool #
PartialEq Word8 #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Word8 -> Word8 -> Bool # (≢) :: Word8 -> Word8 -> Bool #
PartialEq Word16 #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Word16 -> Word16 -> Bool # (≢) :: Word16 -> Word16 -> Bool #
PartialEq Word32 #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Word32 -> Word32 -> Bool # (≢) :: Word32 -> Word32 -> Bool #
PartialEq Word64 #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Word64 -> Word64 -> Bool # (≢) :: Word64 -> Word64 -> Bool #
PartialEq () #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: () -> () -> Bool # (≢) :: () -> () -> Bool #
PartialEq a => PartialEq (Maybe a) #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Maybe a -> Maybe a -> Bool # (≢) :: Maybe a -> Maybe a -> Bool #
PartialEq (Sum Natural) #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Sum Natural -> Sum Natural -> Bool # (≢) :: Sum Natural -> Sum Natural -> Bool #
PartialEq a => PartialEq (Lexical a) #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Lexical a -> Lexical a -> Bool # (≢) :: Lexical a -> Lexical a -> Bool #
Bits a => PartialEq (BitSet a) #
Instance details Defined in Data.BitSet Methods (≡) :: BitSet a -> BitSet a -> Bool # (≢) :: BitSet a -> BitSet a -> Bool #
(PartialEq a, PartialEq b) => PartialEq (Either a b) #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Either a b -> Either a b -> Bool # (≢) :: Either a b -> Either a b -> Bool #
(PartialEq a, PartialEq b) => PartialEq (a, b) #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: (a, b) -> (a, b) -> Bool # (≢) :: (a, b) -> (a, b) -> Bool #

class (Preord a, PartialEq a) => Eq a #

Instances

Eq Bool #
Instance details Defined in Relation.Binary.Comparison
Eq Char #
Instance details Defined in Relation.Binary.Comparison
Eq Int #
Instance details Defined in Relation.Binary.Comparison
Eq Int8 #
Instance details Defined in Relation.Binary.Comparison
Eq Int16 #
Instance details Defined in Relation.Binary.Comparison
Eq Int32 #
Instance details Defined in Relation.Binary.Comparison
Eq Int64 #
Instance details Defined in Relation.Binary.Comparison
Eq Integer #
Instance details Defined in Relation.Binary.Comparison
Eq Natural #
Instance details Defined in Relation.Binary.Comparison
Eq Ordering #
Instance details Defined in Relation.Binary.Comparison
Eq Word #
Instance details Defined in Relation.Binary.Comparison
Eq Word8 #
Instance details Defined in Relation.Binary.Comparison
Eq Word16 #
Instance details Defined in Relation.Binary.Comparison
Eq Word32 #
Instance details Defined in Relation.Binary.Comparison
Eq Word64 #
Instance details Defined in Relation.Binary.Comparison
Eq () #
Instance details Defined in Relation.Binary.Comparison
Eq a => Eq (Maybe a) #
Instance details Defined in Relation.Binary.Comparison
Eq (Sum Natural) #
Instance details Defined in Relation.Binary.Comparison
(Eq a, Eq b) => Eq (Lexical (Either a b)) #
Instance details Defined in Relation.Binary.Comparison
(PartialOrd a, PartialOrd b, Eq a, Eq b) => Eq (Lexical (a, b)) #
Instance details Defined in Relation.Binary.Comparison
Bits a => Eq (BitSet a) #
Instance details Defined in Data.BitSet

class (Preord a, PartialEq a) => PartialOrd a where #

Methods

tryCompare :: a -> a -> Maybe Ordering #

Instances

PartialOrd Bool #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Bool -> Bool -> Maybe Ordering #
PartialOrd Char #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Char -> Char -> Maybe Ordering #
PartialOrd Int #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Int -> Int -> Maybe Ordering #
PartialOrd Int8 #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Int8 -> Int8 -> Maybe Ordering #
PartialOrd Int16 #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Int16 -> Int16 -> Maybe Ordering #
PartialOrd Int32 #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Int32 -> Int32 -> Maybe Ordering #
PartialOrd Int64 #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Int64 -> Int64 -> Maybe Ordering #
PartialOrd Integer #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Integer -> Integer -> Maybe Ordering #
PartialOrd Natural #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Natural -> Natural -> Maybe Ordering #
PartialOrd Ordering #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Ordering -> Ordering -> Maybe Ordering #
PartialOrd Word #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Word -> Word -> Maybe Ordering #
PartialOrd Word8 #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Word8 -> Word8 -> Maybe Ordering #
PartialOrd Word16 #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Word16 -> Word16 -> Maybe Ordering #
PartialOrd Word32 #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Word32 -> Word32 -> Maybe Ordering #
PartialOrd Word64 #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Word64 -> Word64 -> Maybe Ordering #
PartialOrd () #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: () -> () -> Maybe Ordering #
PartialOrd a => PartialOrd (Maybe a) #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Maybe a -> Maybe a -> Maybe Ordering #
PartialOrd (Sum Natural) #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Sum Natural -> Sum Natural -> Maybe Ordering #
(PartialOrd a, PartialOrd b) => PartialOrd (Lexical (Either a b)) #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Lexical (Either a b) -> Lexical (Either a b) -> Maybe Ordering #
(PartialOrd a, PartialOrd b) => PartialOrd (Lexical (a, b)) #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Lexical (a, b) -> Lexical (a, b) -> Maybe Ordering #
Bits a => PartialOrd (BitSet a) #
Instance details Defined in Data.BitSet Methods tryCompare :: BitSet a -> BitSet a -> Maybe Ordering #
(PartialOrd a, PartialOrd b) => PartialOrd (Either a b) #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Either a b -> Either a b -> Maybe Ordering #
(PartialOrd a, PartialOrd b) => PartialOrd (a, b) #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: (a, b) -> (a, b) -> Maybe Ordering #

class (PartialOrd a, Eq a) => Ord a where #

Methods

compare :: a -> a -> Ordering #

Instances

Ord Bool #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Bool -> Bool -> Ordering #
Ord Char #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Char -> Char -> Ordering #
Ord Int #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Int -> Int -> Ordering #
Ord Int8 #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Int8 -> Int8 -> Ordering #
Ord Int16 #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Int16 -> Int16 -> Ordering #
Ord Int32 #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Int32 -> Int32 -> Ordering #
Ord Int64 #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Int64 -> Int64 -> Ordering #
Ord Integer #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Integer -> Integer -> Ordering #
Ord Natural #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Natural -> Natural -> Ordering #
Ord Ordering #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Ordering -> Ordering -> Ordering #
Ord Word #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Word -> Word -> Ordering #
Ord Word8 #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Word8 -> Word8 -> Ordering #
Ord Word16 #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Word16 -> Word16 -> Ordering #
Ord Word32 #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Word32 -> Word32 -> Ordering #
Ord Word64 #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Word64 -> Word64 -> Ordering #
Ord () #
Instance details Defined in Relation.Binary.Comparison Methods compare :: () -> () -> Ordering #
Ord (Sum Natural) #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Sum Natural -> Sum Natural -> Ordering #
(Ord a, Ord b) => Ord (Lexical (Either a b)) #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Lexical (Either a b) -> Lexical (Either a b) -> Ordering #
(Ord a, Ord b) => Ord (Lexical (a, b)) #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Lexical (a, b) -> Lexical (a, b) -> Ordering #

newtype Lexical a #

Constructors

Lexical a

Instances

Semigroup a => Semigroup (Lexical a) #
Instance details Defined in Relation.Binary.Comparison Methods (<>) :: Lexical a -> Lexical a -> Lexical a # sconcat :: NonEmpty (Lexical a) -> Lexical a # stimes :: Integral b => b -> Lexical a -> Lexical a #
Monoid a => Monoid (Lexical a) #
Instance details Defined in Relation.Binary.Comparison Methods mempty :: Lexical a # mappend :: Lexical a -> Lexical a -> Lexical a # mconcat :: [Lexical a] -> Lexical a #
Group a => Group (Lexical a) #
Instance details Defined in Relation.Binary.Comparison Methods invert :: Lexical a -> Lexical a #
(Ord a, Ord b) => Ord (Lexical (Either a b)) #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Lexical (Either a b) -> Lexical (Either a b) -> Ordering #
(Ord a, Ord b) => Ord (Lexical (a, b)) #
Instance details Defined in Relation.Binary.Comparison Methods compare :: Lexical (a, b) -> Lexical (a, b) -> Ordering #
(PartialOrd a, PartialOrd b) => PartialOrd (Lexical (Either a b)) #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Lexical (Either a b) -> Lexical (Either a b) -> Maybe Ordering #
(PartialOrd a, PartialOrd b) => PartialOrd (Lexical (a, b)) #
Instance details Defined in Relation.Binary.Comparison Methods tryCompare :: Lexical (a, b) -> Lexical (a, b) -> Maybe Ordering #
(Eq a, Eq b) => Eq (Lexical (Either a b)) #
Instance details Defined in Relation.Binary.Comparison
(PartialOrd a, PartialOrd b, Eq a, Eq b) => Eq (Lexical (a, b)) #
Instance details Defined in Relation.Binary.Comparison
PartialEq a => PartialEq (Lexical a) #
Instance details Defined in Relation.Binary.Comparison Methods (≡) :: Lexical a -> Lexical a -> Bool # (≢) :: Lexical a -> Lexical a -> Bool #
(Preord a, Preord b) => Preord (Lexical (Either a b)) #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Lexical (Either a b) -> Lexical (Either a b) -> Bool # (≥) :: Lexical (Either a b) -> Lexical (Either a b) -> Bool # (<) :: Lexical (Either a b) -> Lexical (Either a b) -> Bool # (>) :: Lexical (Either a b) -> Lexical (Either a b) -> Bool #
(PartialOrd a, PartialOrd b) => Preord (Lexical (a, b)) #
Instance details Defined in Relation.Binary.Comparison Methods (≤) :: Lexical (a, b) -> Lexical (a, b) -> Bool # (≥) :: Lexical (a, b) -> Lexical (a, b) -> Bool # (<) :: Lexical (a, b) -> Lexical (a, b) -> Bool # (>) :: Lexical (a, b) -> Lexical (a, b) -> Bool #

class (Monoid a, Abelian a, PartialOrd a) => Monus a where #

Minimal complete definition

monus

Methods

monus :: a -> a -> a #

Instances

Monus (Sum Natural) #
Instance details Defined in Relation.Binary.Comparison Methods monus :: Sum Natural -> Sum Natural -> Sum Natural #

(∸) :: Monus (Sum a) => a -> a -> a #