algebra-4.3.1: Constructive abstract algebra

Safe HaskellSafe
LanguageHaskell98

Numeric.Order.Class

Documentation

class Order a where #

Methods

(<~) :: a -> a -> Bool #

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

(>~) :: a -> a -> Bool #

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

(~~) :: a -> a -> Bool #

(/~) :: a -> a -> Bool #

order :: a -> a -> Maybe Ordering #

comparable :: a -> a -> Bool #

Instances

Order Bool # 

Methods

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

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

(>~) :: Bool -> Bool -> Bool #

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

(~~) :: Bool -> Bool -> Bool #

(/~) :: Bool -> Bool -> Bool #

order :: Bool -> Bool -> Maybe Ordering #

comparable :: Bool -> Bool -> Bool #

Order Int # 

Methods

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

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

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

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

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

(/~) :: Int -> Int -> Bool #

order :: Int -> Int -> Maybe Ordering #

comparable :: Int -> Int -> Bool #

Order Int8 # 

Methods

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

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

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

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

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

(/~) :: Int8 -> Int8 -> Bool #

order :: Int8 -> Int8 -> Maybe Ordering #

comparable :: Int8 -> Int8 -> Bool #

Order Int16 # 

Methods

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

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

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

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

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

(/~) :: Int16 -> Int16 -> Bool #

order :: Int16 -> Int16 -> Maybe Ordering #

comparable :: Int16 -> Int16 -> Bool #

Order Int32 # 

Methods

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

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

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

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

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

(/~) :: Int32 -> Int32 -> Bool #

order :: Int32 -> Int32 -> Maybe Ordering #

comparable :: Int32 -> Int32 -> Bool #

Order Int64 # 

Methods

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

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

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

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

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

(/~) :: Int64 -> Int64 -> Bool #

order :: Int64 -> Int64 -> Maybe Ordering #

comparable :: Int64 -> Int64 -> Bool #

Order Integer # 
Order Natural # 
Order Word # 

Methods

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

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

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

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

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

(/~) :: Word -> Word -> Bool #

order :: Word -> Word -> Maybe Ordering #

comparable :: Word -> Word -> Bool #

Order Word8 # 

Methods

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

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

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

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

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

(/~) :: Word8 -> Word8 -> Bool #

order :: Word8 -> Word8 -> Maybe Ordering #

comparable :: Word8 -> Word8 -> Bool #

Order Word16 # 
Order Word32 # 
Order Word64 # 
Order () # 

Methods

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

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

(>~) :: () -> () -> Bool #

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

(~~) :: () -> () -> Bool #

(/~) :: () -> () -> Bool #

order :: () -> () -> Maybe Ordering #

comparable :: () -> () -> Bool #

Ord a => Order (Set a) # 

Methods

(<~) :: Set a -> Set a -> Bool #

(<) :: Set a -> Set a -> Bool #

(>~) :: Set a -> Set a -> Bool #

(>) :: Set a -> Set a -> Bool #

(~~) :: Set a -> Set a -> Bool #

(/~) :: Set a -> Set a -> Bool #

order :: Set a -> Set a -> Maybe Ordering #

comparable :: Set a -> Set a -> Bool #

(Order a, Order b) => Order (a, b) # 

Methods

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

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

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

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

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

(/~) :: (a, b) -> (a, b) -> Bool #

order :: (a, b) -> (a, b) -> Maybe Ordering #

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

(Order a, Order b, Order c) => Order (a, b, c) # 

Methods

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

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

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

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

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

(/~) :: (a, b, c) -> (a, b, c) -> Bool #

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

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

(Order a, Order b, Order c, Order d) => Order (a, b, c, d) # 

Methods

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

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

(>~) :: (a, b, c, d) -> (a, b, c, d) -> Bool #

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

(~~) :: (a, b, c, d) -> (a, b, c, d) -> Bool #

(/~) :: (a, b, c, d) -> (a, b, c, d) -> Bool #

order :: (a, b, c, d) -> (a, b, c, d) -> Maybe Ordering #

comparable :: (a, b, c, d) -> (a, b, c, d) -> Bool #

(Order a, Order b, Order c, Order d, Order e) => Order (a, b, c, d, e) # 

Methods

(<~) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

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

(>~) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

(>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

(~~) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

(/~) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

order :: (a, b, c, d, e) -> (a, b, c, d, e) -> Maybe Ordering #

comparable :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

orderOrd :: Ord a => a -> a -> Maybe Ordering #