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module Numeric.Order.Class
( Order(..)
, orderOrd
) where
import Data.Int
import Data.Word
import Data.Set
import Numeric.Natural.Internal
-- a partial order (a, <=)
class Order a where
(<~) :: a -> a -> Bool
a <~ b = maybe False (<= EQ) (order a b)
(<) :: a -> a -> Bool
a < b = order a b == Just LT
(>~) :: a -> a -> Bool
a >~ b = b <~ a
(>) :: a -> a -> Bool
a > b = order a b == Just GT
(~~) :: a -> a -> Bool
a ~~ b = order a b == Just EQ
(/~) :: a -> a -> Bool
a /~ b = order a b /= Just EQ
order :: a -> a -> Maybe Ordering
order a b
| a <~ b = Just $ if b <~ a
then EQ
else LT
| b <~ a = Just GT
| otherwise = Nothing
comparable :: a -> a -> Bool
comparable a b = maybe False (const True) (order a b)
orderOrd :: Ord a => a -> a -> Maybe Ordering
orderOrd a b = Just (compare a b)
instance Order Bool where order = orderOrd
instance Order Integer where order = orderOrd
instance Order Int where order = orderOrd
instance Order Int8 where order = orderOrd
instance Order Int16 where order = orderOrd
instance Order Int32 where order = orderOrd
instance Order Int64 where order = orderOrd
instance Order Natural where order = orderOrd
instance Order Word where order = orderOrd
instance Order Word8 where order = orderOrd
instance Order Word16 where order = orderOrd
instance Order Word32 where order = orderOrd
instance Order Word64 where order = orderOrd
instance Ord a => Order (Set a) where
(<~) = isSubsetOf
instance Order () where
order _ _ = Just EQ
_ <~ _ = True
comparable _ _ = True
instance (Order a, Order b) => Order (a, b) where
(a,b) <~ (i,j) = a <~ i && b <~ j
instance (Order a, Order b, Order c) => Order (a, b, c) where
(a,b,c) <~ (i,j,k) = a <~ i && b <~ j && c <~ k
instance (Order a, Order b, Order c, Order d) => Order (a, b, c, d) where
(a,b,c,d) <~ (i,j,k,l) = a <~ i && b <~ j && c <~ k && d <~ l
instance (Order a, Order b, Order c, Order d, Order e) => Order (a, b, c, d, e) where
(a,b,c,d,e) <~ (i,j,k,l,m) = a <~ i && b <~ j && c <~ k && d <~ l && e <~ m
|
