alg-0.2.10.0: Algebraic structures

Safe HaskellNone
LanguageHaskell2010

Relation.Binary.Comparison

Documentation

class Preord a where Source #

Minimal complete definition

(≥) | (≤)

Methods

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

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

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

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

Instances
Preord Bool Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Bool -> Bool -> Bool Source #

(≥) :: Bool -> Bool -> Bool Source #

(<) :: Bool -> Bool -> Bool Source #

(>) :: Bool -> Bool -> Bool Source #

Preord Char Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Char -> Char -> Bool Source #

(≥) :: Char -> Char -> Bool Source #

(<) :: Char -> Char -> Bool Source #

(>) :: Char -> Char -> Bool Source #

Preord Int Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Int -> Int -> Bool Source #

(≥) :: Int -> Int -> Bool Source #

(<) :: Int -> Int -> Bool Source #

(>) :: Int -> Int -> Bool Source #

Preord Int8 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Int8 -> Int8 -> Bool Source #

(≥) :: Int8 -> Int8 -> Bool Source #

(<) :: Int8 -> Int8 -> Bool Source #

(>) :: Int8 -> Int8 -> Bool Source #

Preord Int16 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Int16 -> Int16 -> Bool Source #

(≥) :: Int16 -> Int16 -> Bool Source #

(<) :: Int16 -> Int16 -> Bool Source #

(>) :: Int16 -> Int16 -> Bool Source #

Preord Int32 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Int32 -> Int32 -> Bool Source #

(≥) :: Int32 -> Int32 -> Bool Source #

(<) :: Int32 -> Int32 -> Bool Source #

(>) :: Int32 -> Int32 -> Bool Source #

Preord Int64 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Int64 -> Int64 -> Bool Source #

(≥) :: Int64 -> Int64 -> Bool Source #

(<) :: Int64 -> Int64 -> Bool Source #

(>) :: Int64 -> Int64 -> Bool Source #

Preord Integer Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Integer -> Integer -> Bool Source #

(≥) :: Integer -> Integer -> Bool Source #

(<) :: Integer -> Integer -> Bool Source #

(>) :: Integer -> Integer -> Bool Source #

Preord Natural Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Natural -> Natural -> Bool Source #

(≥) :: Natural -> Natural -> Bool Source #

(<) :: Natural -> Natural -> Bool Source #

(>) :: Natural -> Natural -> Bool Source #

Preord Ordering Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Ordering -> Ordering -> Bool Source #

(≥) :: Ordering -> Ordering -> Bool Source #

(<) :: Ordering -> Ordering -> Bool Source #

(>) :: Ordering -> Ordering -> Bool Source #

Preord Word Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Word -> Word -> Bool Source #

(≥) :: Word -> Word -> Bool Source #

(<) :: Word -> Word -> Bool Source #

(>) :: Word -> Word -> Bool Source #

Preord Word8 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Word8 -> Word8 -> Bool Source #

(≥) :: Word8 -> Word8 -> Bool Source #

(<) :: Word8 -> Word8 -> Bool Source #

(>) :: Word8 -> Word8 -> Bool Source #

Preord Word16 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Word16 -> Word16 -> Bool Source #

(≥) :: Word16 -> Word16 -> Bool Source #

(<) :: Word16 -> Word16 -> Bool Source #

(>) :: Word16 -> Word16 -> Bool Source #

Preord Word32 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Word32 -> Word32 -> Bool Source #

(≥) :: Word32 -> Word32 -> Bool Source #

(<) :: Word32 -> Word32 -> Bool Source #

(>) :: Word32 -> Word32 -> Bool Source #

Preord Word64 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Word64 -> Word64 -> Bool Source #

(≥) :: Word64 -> Word64 -> Bool Source #

(<) :: Word64 -> Word64 -> Bool Source #

(>) :: Word64 -> Word64 -> Bool Source #

Preord () Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: () -> () -> Bool Source #

(≥) :: () -> () -> Bool Source #

(<) :: () -> () -> Bool Source #

(>) :: () -> () -> Bool Source #

Preord a => Preord (Maybe a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Maybe a -> Maybe a -> Bool Source #

(≥) :: Maybe a -> Maybe a -> Bool Source #

(<) :: Maybe a -> Maybe a -> Bool Source #

(>) :: Maybe a -> Maybe a -> Bool Source #

Preord (Sum Natural) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Sum Natural -> Sum Natural -> Bool Source #

(≥) :: Sum Natural -> Sum Natural -> Bool Source #

(<) :: Sum Natural -> Sum Natural -> Bool Source #

(>) :: Sum Natural -> Sum Natural -> Bool Source #

Preord a => Preord (Down a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Down a -> Down a -> Bool Source #

(≥) :: Down a -> Down a -> Bool Source #

(<) :: Down a -> Down a -> Bool Source #

(>) :: Down a -> Down a -> Bool Source #

Bits a => Preord (Min (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

(≤) :: Min (BitSet a) -> Min (BitSet a) -> Bool Source #

(≥) :: Min (BitSet a) -> Min (BitSet a) -> Bool Source #

(<) :: Min (BitSet a) -> Min (BitSet a) -> Bool Source #

(>) :: Min (BitSet a) -> Min (BitSet a) -> Bool Source #

Bits a => Preord (Max (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

(≤) :: Max (BitSet a) -> Max (BitSet a) -> Bool Source #

(≥) :: Max (BitSet a) -> Max (BitSet a) -> Bool Source #

(<) :: Max (BitSet a) -> Max (BitSet a) -> Bool Source #

(>) :: Max (BitSet a) -> Max (BitSet a) -> Bool Source #

Preord a => Preord (Lexical (Maybe a)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Lexical (Maybe a) -> Lexical (Maybe a) -> Bool Source #

(≥) :: Lexical (Maybe a) -> Lexical (Maybe a) -> Bool Source #

(<) :: Lexical (Maybe a) -> Lexical (Maybe a) -> Bool Source #

(>) :: Lexical (Maybe a) -> Lexical (Maybe a) -> Bool Source #

(Preord a, Preord b) => Preord (Lexical (Either a b)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Lexical (Either a b) -> Lexical (Either a b) -> Bool Source #

(≥) :: Lexical (Either a b) -> Lexical (Either a b) -> Bool Source #

(<) :: Lexical (Either a b) -> Lexical (Either a b) -> Bool Source #

(>) :: Lexical (Either a b) -> Lexical (Either a b) -> Bool Source #

(PartialOrd a, PartialOrd b) => Preord (Lexical (a, b)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Lexical (a, b) -> Lexical (a, b) -> Bool Source #

(≥) :: Lexical (a, b) -> Lexical (a, b) -> Bool Source #

(<) :: Lexical (a, b) -> Lexical (a, b) -> Bool Source #

(>) :: Lexical (a, b) -> Lexical (a, b) -> Bool Source #

(PartialOrd a, PartialOrd b, PartialOrd c) => Preord (Lexical (a, b, c)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Lexical (a, b, c) -> Lexical (a, b, c) -> Bool Source #

(≥) :: Lexical (a, b, c) -> Lexical (a, b, c) -> Bool Source #

(<) :: Lexical (a, b, c) -> Lexical (a, b, c) -> Bool Source #

(>) :: Lexical (a, b, c) -> Lexical (a, b, c) -> Bool Source #

Bits a => Preord (BitSet a) Source # 
Instance details

Defined in Data.BitSet

Methods

(≤) :: BitSet a -> BitSet a -> Bool Source #

(≥) :: BitSet a -> BitSet a -> Bool Source #

(<) :: BitSet a -> BitSet a -> Bool Source #

(>) :: BitSet a -> BitSet a -> Bool Source #

(Preord a, Preord b) => Preord (Either a b) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Either a b -> Either a b -> Bool Source #

(≥) :: Either a b -> Either a b -> Bool Source #

(<) :: Either a b -> Either a b -> Bool Source #

(>) :: Either a b -> Either a b -> Bool Source #

(Preord a, Preord b) => Preord (a, b) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: (a, b) -> (a, b) -> Bool Source #

(≥) :: (a, b) -> (a, b) -> Bool Source #

(<) :: (a, b) -> (a, b) -> Bool Source #

(>) :: (a, b) -> (a, b) -> Bool Source #

(Preord a, Preord b, Preord c) => Preord (a, b, c) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: (a, b, c) -> (a, b, c) -> Bool Source #

(≥) :: (a, b, c) -> (a, b, c) -> Bool Source #

(<) :: (a, b, c) -> (a, b, c) -> Bool Source #

(>) :: (a, b, c) -> (a, b, c) -> Bool Source #

class PartialEq a where Source #

Minimal complete definition

(≡) | (≢)

Methods

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

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

Instances
PartialEq Bool Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Bool -> Bool -> Bool Source #

(≢) :: Bool -> Bool -> Bool Source #

PartialEq Char Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Char -> Char -> Bool Source #

(≢) :: Char -> Char -> Bool Source #

PartialEq Int Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Int -> Int -> Bool Source #

(≢) :: Int -> Int -> Bool Source #

PartialEq Int8 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Int8 -> Int8 -> Bool Source #

(≢) :: Int8 -> Int8 -> Bool Source #

PartialEq Int16 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Int16 -> Int16 -> Bool Source #

(≢) :: Int16 -> Int16 -> Bool Source #

PartialEq Int32 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Int32 -> Int32 -> Bool Source #

(≢) :: Int32 -> Int32 -> Bool Source #

PartialEq Int64 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Int64 -> Int64 -> Bool Source #

(≢) :: Int64 -> Int64 -> Bool Source #

PartialEq Integer Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Integer -> Integer -> Bool Source #

(≢) :: Integer -> Integer -> Bool Source #

PartialEq Natural Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Natural -> Natural -> Bool Source #

(≢) :: Natural -> Natural -> Bool Source #

PartialEq Ordering Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Ordering -> Ordering -> Bool Source #

(≢) :: Ordering -> Ordering -> Bool Source #

PartialEq Word Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Word -> Word -> Bool Source #

(≢) :: Word -> Word -> Bool Source #

PartialEq Word8 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Word8 -> Word8 -> Bool Source #

(≢) :: Word8 -> Word8 -> Bool Source #

PartialEq Word16 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Word16 -> Word16 -> Bool Source #

(≢) :: Word16 -> Word16 -> Bool Source #

PartialEq Word32 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Word32 -> Word32 -> Bool Source #

(≢) :: Word32 -> Word32 -> Bool Source #

PartialEq Word64 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Word64 -> Word64 -> Bool Source #

(≢) :: Word64 -> Word64 -> Bool Source #

PartialEq () Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: () -> () -> Bool Source #

(≢) :: () -> () -> Bool Source #

PartialEq a => PartialEq [a] Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: [a] -> [a] -> Bool Source #

(≢) :: [a] -> [a] -> Bool Source #

PartialEq a => PartialEq (Maybe a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Maybe a -> Maybe a -> Bool Source #

(≢) :: Maybe a -> Maybe a -> Bool Source #

PartialEq a => PartialEq (Ratio a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Ratio a -> Ratio a -> Bool Source #

(≢) :: Ratio a -> Ratio a -> Bool Source #

PartialEq (Sum Natural) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Sum Natural -> Sum Natural -> Bool Source #

(≢) :: Sum Natural -> Sum Natural -> Bool Source #

PartialEq a => PartialEq (Down a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Down a -> Down a -> Bool Source #

(≢) :: Down a -> Down a -> Bool Source #

Bits a => PartialEq (Min (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

(≡) :: Min (BitSet a) -> Min (BitSet a) -> Bool Source #

(≢) :: Min (BitSet a) -> Min (BitSet a) -> Bool Source #

Bits a => PartialEq (Max (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

(≡) :: Max (BitSet a) -> Max (BitSet a) -> Bool Source #

(≢) :: Max (BitSet a) -> Max (BitSet a) -> Bool Source #

PartialEq a => PartialEq (Lexical a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Lexical a -> Lexical a -> Bool Source #

(≢) :: Lexical a -> Lexical a -> Bool Source #

Bits a => PartialEq (BitSet a) Source # 
Instance details

Defined in Data.BitSet

Methods

(≡) :: BitSet a -> BitSet a -> Bool Source #

(≢) :: BitSet a -> BitSet a -> Bool Source #

(PartialEq a, PartialEq b) => PartialEq (Either a b) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Either a b -> Either a b -> Bool Source #

(≢) :: Either a b -> Either a b -> Bool Source #

(PartialEq a, PartialEq b) => PartialEq (a, b) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: (a, b) -> (a, b) -> Bool Source #

(≢) :: (a, b) -> (a, b) -> Bool Source #

(PartialEq a, PartialEq b, PartialEq c) => PartialEq (a, b, c) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: (a, b, c) -> (a, b, c) -> Bool Source #

(≢) :: (a, b, c) -> (a, b, c) -> Bool Source #

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

Instances
Eq Bool Source # 
Instance details

Defined in Relation.Binary.Comparison

Eq Char Source # 
Instance details

Defined in Relation.Binary.Comparison

Eq Int Source # 
Instance details

Defined in Relation.Binary.Comparison

Eq Int8 Source # 
Instance details

Defined in Relation.Binary.Comparison

Eq Int16 Source # 
Instance details

Defined in Relation.Binary.Comparison

Eq Int32 Source # 
Instance details

Defined in Relation.Binary.Comparison

Eq Int64 Source # 
Instance details

Defined in Relation.Binary.Comparison

Eq Integer Source # 
Instance details

Defined in Relation.Binary.Comparison

Eq Natural Source # 
Instance details

Defined in Relation.Binary.Comparison

Eq Ordering Source # 
Instance details

Defined in Relation.Binary.Comparison

Eq Word Source # 
Instance details

Defined in Relation.Binary.Comparison

Eq Word8 Source # 
Instance details

Defined in Relation.Binary.Comparison

Eq Word16 Source # 
Instance details

Defined in Relation.Binary.Comparison

Eq Word32 Source # 
Instance details

Defined in Relation.Binary.Comparison

Eq Word64 Source # 
Instance details

Defined in Relation.Binary.Comparison

Eq () Source # 
Instance details

Defined in Relation.Binary.Comparison

Eq a => Eq (Maybe a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Eq (Sum Natural) Source # 
Instance details

Defined in Relation.Binary.Comparison

Eq a => Eq (Down a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Bits a => Eq (Min (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Bits a => Eq (Max (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Eq a => Eq (Lexical (Maybe a)) Source # 
Instance details

Defined in Relation.Binary.Comparison

(Eq a, Eq b) => Eq (Lexical (Either a b)) Source # 
Instance details

Defined in Relation.Binary.Comparison

(PartialOrd a, PartialOrd b, Eq a, Eq b) => Eq (Lexical (a, b)) Source # 
Instance details

Defined in Relation.Binary.Comparison

(PartialOrd a, PartialOrd b, PartialOrd c, Eq a, Eq b, Eq c) => Eq (Lexical (a, b, c)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Bits a => Eq (BitSet a) Source # 
Instance details

Defined in Data.BitSet

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

Minimal complete definition

Nothing

Methods

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

Instances
PartialOrd Bool Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Bool -> Bool -> Maybe Ordering Source #

PartialOrd Char Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Char -> Char -> Maybe Ordering Source #

PartialOrd Int Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Int -> Int -> Maybe Ordering Source #

PartialOrd Int8 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Int8 -> Int8 -> Maybe Ordering Source #

PartialOrd Int16 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Int16 -> Int16 -> Maybe Ordering Source #

PartialOrd Int32 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Int32 -> Int32 -> Maybe Ordering Source #

PartialOrd Int64 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Int64 -> Int64 -> Maybe Ordering Source #

PartialOrd Integer Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Integer -> Integer -> Maybe Ordering Source #

PartialOrd Natural Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Natural -> Natural -> Maybe Ordering Source #

PartialOrd Ordering Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Ordering -> Ordering -> Maybe Ordering Source #

PartialOrd Word Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Word -> Word -> Maybe Ordering Source #

PartialOrd Word8 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Word8 -> Word8 -> Maybe Ordering Source #

PartialOrd Word16 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Word16 -> Word16 -> Maybe Ordering Source #

PartialOrd Word32 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Word32 -> Word32 -> Maybe Ordering Source #

PartialOrd Word64 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Word64 -> Word64 -> Maybe Ordering Source #

PartialOrd () Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: () -> () -> Maybe Ordering Source #

PartialOrd a => PartialOrd (Maybe a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

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

PartialOrd (Sum Natural) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Sum Natural -> Sum Natural -> Maybe Ordering Source #

PartialOrd a => PartialOrd (Down a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

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

Bits a => PartialOrd (Min (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

tryCompare :: Min (BitSet a) -> Min (BitSet a) -> Maybe Ordering Source #

Bits a => PartialOrd (Max (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

tryCompare :: Max (BitSet a) -> Max (BitSet a) -> Maybe Ordering Source #

PartialOrd a => PartialOrd (Lexical (Maybe a)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Lexical (Maybe a) -> Lexical (Maybe a) -> Maybe Ordering Source #

(PartialOrd a, PartialOrd b) => PartialOrd (Lexical (Either a b)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Lexical (Either a b) -> Lexical (Either a b) -> Maybe Ordering Source #

(PartialOrd a, PartialOrd b) => PartialOrd (Lexical (a, b)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Lexical (a, b) -> Lexical (a, b) -> Maybe Ordering Source #

(PartialOrd a, PartialOrd b, PartialOrd c) => PartialOrd (Lexical (a, b, c)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Lexical (a, b, c) -> Lexical (a, b, c) -> Maybe Ordering Source #

Bits a => PartialOrd (BitSet a) Source # 
Instance details

Defined in Data.BitSet

Methods

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

(PartialOrd a, PartialOrd b) => PartialOrd (Either a b) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Either a b -> Either a b -> Maybe Ordering Source #

(PartialOrd a, PartialOrd b) => PartialOrd (a, b) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: (a, b) -> (a, b) -> Maybe Ordering Source #

(PartialOrd a, PartialOrd b, PartialOrd c) => PartialOrd (a, b, c) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: (a, b, c) -> (a, b, c) -> Maybe Ordering Source #

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

Minimal complete definition

Nothing

Methods

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

Instances
Ord Bool Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Bool -> Bool -> Ordering Source #

Ord Char Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Char -> Char -> Ordering Source #

Ord Int Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Int -> Int -> Ordering Source #

Ord Int8 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Int8 -> Int8 -> Ordering Source #

Ord Int16 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Int16 -> Int16 -> Ordering Source #

Ord Int32 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Int32 -> Int32 -> Ordering Source #

Ord Int64 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Int64 -> Int64 -> Ordering Source #

Ord Integer Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Integer -> Integer -> Ordering Source #

Ord Natural Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Natural -> Natural -> Ordering Source #

Ord Ordering Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Ordering -> Ordering -> Ordering Source #

Ord Word Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Word -> Word -> Ordering Source #

Ord Word8 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Word8 -> Word8 -> Ordering Source #

Ord Word16 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Word16 -> Word16 -> Ordering Source #

Ord Word32 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Word32 -> Word32 -> Ordering Source #

Ord Word64 Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Word64 -> Word64 -> Ordering Source #

Ord () Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: () -> () -> Ordering Source #

Ord (Sum Natural) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Sum Natural -> Sum Natural -> Ordering Source #

Ord a => Ord (Down a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Down a -> Down a -> Ordering Source #

Ord a => Ord (Lexical (Maybe a)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Lexical (Maybe a) -> Lexical (Maybe a) -> Ordering Source #

(Ord a, Ord b) => Ord (Lexical (Either a b)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Lexical (Either a b) -> Lexical (Either a b) -> Ordering Source #

(Ord a, Ord b) => Ord (Lexical (a, b)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Lexical (a, b) -> Lexical (a, b) -> Ordering Source #

(Ord a, Ord b, Ord c) => Ord (Lexical (a, b, c)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Lexical (a, b, c) -> Lexical (a, b, c) -> Ordering Source #

newtype Lexical a Source #

Constructors

Lexical a 
Instances
Semigroup a => Semigroup (Lexical a) Source # 
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) Source # 
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) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

invert :: Lexical a -> Lexical a Source #

Ord a => Ord (Lexical (Maybe a)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Lexical (Maybe a) -> Lexical (Maybe a) -> Ordering Source #

(Ord a, Ord b) => Ord (Lexical (Either a b)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Lexical (Either a b) -> Lexical (Either a b) -> Ordering Source #

(Ord a, Ord b) => Ord (Lexical (a, b)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Lexical (a, b) -> Lexical (a, b) -> Ordering Source #

(Ord a, Ord b, Ord c) => Ord (Lexical (a, b, c)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

compare :: Lexical (a, b, c) -> Lexical (a, b, c) -> Ordering Source #

PartialOrd a => PartialOrd (Lexical (Maybe a)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Lexical (Maybe a) -> Lexical (Maybe a) -> Maybe Ordering Source #

(PartialOrd a, PartialOrd b) => PartialOrd (Lexical (Either a b)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Lexical (Either a b) -> Lexical (Either a b) -> Maybe Ordering Source #

(PartialOrd a, PartialOrd b) => PartialOrd (Lexical (a, b)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Lexical (a, b) -> Lexical (a, b) -> Maybe Ordering Source #

(PartialOrd a, PartialOrd b, PartialOrd c) => PartialOrd (Lexical (a, b, c)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

tryCompare :: Lexical (a, b, c) -> Lexical (a, b, c) -> Maybe Ordering Source #

Eq a => Eq (Lexical (Maybe a)) Source # 
Instance details

Defined in Relation.Binary.Comparison

(Eq a, Eq b) => Eq (Lexical (Either a b)) Source # 
Instance details

Defined in Relation.Binary.Comparison

(PartialOrd a, PartialOrd b, Eq a, Eq b) => Eq (Lexical (a, b)) Source # 
Instance details

Defined in Relation.Binary.Comparison

(PartialOrd a, PartialOrd b, PartialOrd c, Eq a, Eq b, Eq c) => Eq (Lexical (a, b, c)) Source # 
Instance details

Defined in Relation.Binary.Comparison

PartialEq a => PartialEq (Lexical a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≡) :: Lexical a -> Lexical a -> Bool Source #

(≢) :: Lexical a -> Lexical a -> Bool Source #

Preord a => Preord (Lexical (Maybe a)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Lexical (Maybe a) -> Lexical (Maybe a) -> Bool Source #

(≥) :: Lexical (Maybe a) -> Lexical (Maybe a) -> Bool Source #

(<) :: Lexical (Maybe a) -> Lexical (Maybe a) -> Bool Source #

(>) :: Lexical (Maybe a) -> Lexical (Maybe a) -> Bool Source #

(Preord a, Preord b) => Preord (Lexical (Either a b)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Lexical (Either a b) -> Lexical (Either a b) -> Bool Source #

(≥) :: Lexical (Either a b) -> Lexical (Either a b) -> Bool Source #

(<) :: Lexical (Either a b) -> Lexical (Either a b) -> Bool Source #

(>) :: Lexical (Either a b) -> Lexical (Either a b) -> Bool Source #

(PartialOrd a, PartialOrd b) => Preord (Lexical (a, b)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Lexical (a, b) -> Lexical (a, b) -> Bool Source #

(≥) :: Lexical (a, b) -> Lexical (a, b) -> Bool Source #

(<) :: Lexical (a, b) -> Lexical (a, b) -> Bool Source #

(>) :: Lexical (a, b) -> Lexical (a, b) -> Bool Source #

(PartialOrd a, PartialOrd b, PartialOrd c) => Preord (Lexical (a, b, c)) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(≤) :: Lexical (a, b, c) -> Lexical (a, b, c) -> Bool Source #

(≥) :: Lexical (a, b, c) -> Lexical (a, b, c) -> Bool Source #

(<) :: Lexical (a, b, c) -> Lexical (a, b, c) -> Bool Source #

(>) :: Lexical (a, b, c) -> Lexical (a, b, c) -> Bool Source #

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

Methods

monus :: a -> a -> a Source #

Instances
Monus (Sum Natural) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

monus :: Sum Natural -> Sum Natural -> Sum Natural Source #

Bits a => Monus (Min (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

monus :: Min (BitSet a) -> Min (BitSet a) -> Min (BitSet a) Source #

Bits a => Monus (Max (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

monus :: Max (BitSet a) -> Max (BitSet a) -> Max (BitSet a) Source #

(∸) :: Monus (Sum a) => a -> a -> a Source #

max :: Ord a => a -> a -> a Source #

min :: Ord a => a -> a -> a Source #

newtype Max a Source #

Constructors

Max 

Fields

Instances
Eq a => Eq (Max a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(==) :: Max a -> Max a -> Bool #

(/=) :: Max a -> Max a -> Bool #

Read a => Read (Max a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

readsPrec :: Int -> ReadS (Max a) #

readList :: ReadS [Max a] #

readPrec :: ReadPrec (Max a) #

readListPrec :: ReadPrec [Max a] #

Show a => Show (Max a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

showsPrec :: Int -> Max a -> ShowS #

show :: Max a -> String #

showList :: [Max a] -> ShowS #

Ord a => Semigroup (Max a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(<>) :: Max a -> Max a -> Max a #

sconcat :: NonEmpty (Max a) -> Max a #

stimes :: Integral b => b -> Max a -> Max a #

Bits a => Semigroup (Max (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

(<>) :: Max (BitSet a) -> Max (BitSet a) -> Max (BitSet a) #

sconcat :: NonEmpty (Max (BitSet a)) -> Max (BitSet a) #

stimes :: Integral b => b -> Max (BitSet a) -> Max (BitSet a) #

Bits a => Monoid (Max (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

mempty :: Max (BitSet a) #

mappend :: Max (BitSet a) -> Max (BitSet a) -> Max (BitSet a) #

mconcat :: [Max (BitSet a)] -> Max (BitSet a) #

Bits a => Bits (Max a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(.&.) :: Max a -> Max a -> Max a #

(.|.) :: Max a -> Max a -> Max a #

xor :: Max a -> Max a -> Max a #

complement :: Max a -> Max a #

shift :: Max a -> Int -> Max a #

rotate :: Max a -> Int -> Max a #

zeroBits :: Max a #

bit :: Int -> Max a #

setBit :: Max a -> Int -> Max a #

clearBit :: Max a -> Int -> Max a #

complementBit :: Max a -> Int -> Max a #

testBit :: Max a -> Int -> Bool #

bitSizeMaybe :: Max a -> Maybe Int #

bitSize :: Max a -> Int #

isSigned :: Max a -> Bool #

shiftL :: Max a -> Int -> Max a #

unsafeShiftL :: Max a -> Int -> Max a #

shiftR :: Max a -> Int -> Max a #

unsafeShiftR :: Max a -> Int -> Max a #

rotateL :: Max a -> Int -> Max a #

rotateR :: Max a -> Int -> Max a #

popCount :: Max a -> Int #

FiniteBits a => FiniteBits (Max a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

finiteBitSize :: Max a -> Int #

countLeadingZeros :: Max a -> Int #

countTrailingZeros :: Max a -> Int #

Bits a => Idempotent (Max (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Bits a => Abelian (Max (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Bits a => Monus (Max (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

monus :: Max (BitSet a) -> Max (BitSet a) -> Max (BitSet a) Source #

Bits a => PartialOrd (Max (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

tryCompare :: Max (BitSet a) -> Max (BitSet a) -> Maybe Ordering Source #

Bits a => Eq (Max (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Bits a => PartialEq (Max (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

(≡) :: Max (BitSet a) -> Max (BitSet a) -> Bool Source #

(≢) :: Max (BitSet a) -> Max (BitSet a) -> Bool Source #

Bits a => Preord (Max (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

(≤) :: Max (BitSet a) -> Max (BitSet a) -> Bool Source #

(≥) :: Max (BitSet a) -> Max (BitSet a) -> Bool Source #

(<) :: Max (BitSet a) -> Max (BitSet a) -> Bool Source #

(>) :: Max (BitSet a) -> Max (BitSet a) -> Bool Source #

newtype Min a Source #

Constructors

Min 

Fields

Instances
Eq a => Eq (Min a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(==) :: Min a -> Min a -> Bool #

(/=) :: Min a -> Min a -> Bool #

Read a => Read (Min a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

readsPrec :: Int -> ReadS (Min a) #

readList :: ReadS [Min a] #

readPrec :: ReadPrec (Min a) #

readListPrec :: ReadPrec [Min a] #

Show a => Show (Min a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

showsPrec :: Int -> Min a -> ShowS #

show :: Min a -> String #

showList :: [Min a] -> ShowS #

Ord a => Semigroup (Min a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(<>) :: Min a -> Min a -> Min a #

sconcat :: NonEmpty (Min a) -> Min a #

stimes :: Integral b => b -> Min a -> Min a #

Bits a => Semigroup (Min (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

(<>) :: Min (BitSet a) -> Min (BitSet a) -> Min (BitSet a) #

sconcat :: NonEmpty (Min (BitSet a)) -> Min (BitSet a) #

stimes :: Integral b => b -> Min (BitSet a) -> Min (BitSet a) #

Bits a => Monoid (Min (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

mempty :: Min (BitSet a) #

mappend :: Min (BitSet a) -> Min (BitSet a) -> Min (BitSet a) #

mconcat :: [Min (BitSet a)] -> Min (BitSet a) #

Bits a => Bits (Min a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

(.&.) :: Min a -> Min a -> Min a #

(.|.) :: Min a -> Min a -> Min a #

xor :: Min a -> Min a -> Min a #

complement :: Min a -> Min a #

shift :: Min a -> Int -> Min a #

rotate :: Min a -> Int -> Min a #

zeroBits :: Min a #

bit :: Int -> Min a #

setBit :: Min a -> Int -> Min a #

clearBit :: Min a -> Int -> Min a #

complementBit :: Min a -> Int -> Min a #

testBit :: Min a -> Int -> Bool #

bitSizeMaybe :: Min a -> Maybe Int #

bitSize :: Min a -> Int #

isSigned :: Min a -> Bool #

shiftL :: Min a -> Int -> Min a #

unsafeShiftL :: Min a -> Int -> Min a #

shiftR :: Min a -> Int -> Min a #

unsafeShiftR :: Min a -> Int -> Min a #

rotateL :: Min a -> Int -> Min a #

rotateR :: Min a -> Int -> Min a #

popCount :: Min a -> Int #

FiniteBits a => FiniteBits (Min a) Source # 
Instance details

Defined in Relation.Binary.Comparison

Methods

finiteBitSize :: Min a -> Int #

countLeadingZeros :: Min a -> Int #

countTrailingZeros :: Min a -> Int #

Bits a => Idempotent (Min (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Bits a => Abelian (Min (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Bits a => Monus (Min (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

monus :: Min (BitSet a) -> Min (BitSet a) -> Min (BitSet a) Source #

Bits a => PartialOrd (Min (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

tryCompare :: Min (BitSet a) -> Min (BitSet a) -> Maybe Ordering Source #

Bits a => Eq (Min (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Bits a => PartialEq (Min (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

(≡) :: Min (BitSet a) -> Min (BitSet a) -> Bool Source #

(≢) :: Min (BitSet a) -> Min (BitSet a) -> Bool Source #

Bits a => Preord (Min (BitSet a)) Source # 
Instance details

Defined in Data.BitSet

Methods

(≤) :: Min (BitSet a) -> Min (BitSet a) -> Bool Source #

(≥) :: Min (BitSet a) -> Min (BitSet a) -> Bool Source #

(<) :: Min (BitSet a) -> Min (BitSet a) -> Bool Source #

(>) :: Min (BitSet a) -> Min (BitSet a) -> Bool Source #