Copyright	(c) Henning Thielemann 2007
Maintainer	numericprelude@henning-thielemann.de
Stability	provisional
Portability	portable
Safe Haskell	Safe
Language	Haskell98

Algebra.Indexable

Description

An alternative type class for Ord which allows an ordering for dictionaries like Data.Map and Data.Set independently from the ordering with respect to a magnitude.

Synopsis

Documentation

class Eq a => C a where #

Definition of an alternative ordering of objects independent from a notion of magnitude. For an application see MathObj.PartialFraction.

Minimal complete definition

compare

Methods

compare :: a -> a -> Ordering #

Instances

C Integer #
Methods compare :: Integer -> Integer -> Ordering #
C T #
Methods compare :: T -> T -> Ordering #
C a => C [a] #
Methods compare :: [a] -> [a] -> Ordering #
(Ord a, C a) => C (T a) #
Methods compare :: T a -> T a -> Ordering #
(C a, C a) => C (T a) #
Methods compare :: T a -> T a -> Ordering #
C a => C (T a) #
Methods compare :: T a -> T a -> Ordering #
(C a, C b) => C (a, b) #
Methods compare :: (a, b) -> (a, b) -> Ordering #

ordCompare :: Ord a => a -> a -> Ordering #

If the type has already an Ord instance it is certainly the most easiest to define compare to be equal to Ord's compare.

liftCompare :: C b => (a -> b) -> a -> a -> Ordering #

Lift compare implementation from a wrapped object.

data ToOrd a #

Wrap an indexable object such that it can be used in Data.Map and Data.Set.

Instances

Eq a => Eq (ToOrd a) #
Methods (==) :: ToOrd a -> ToOrd a -> Bool # (/=) :: ToOrd a -> ToOrd a -> Bool #
C a => Ord (ToOrd a) #
Methods compare :: ToOrd a -> ToOrd a -> Ordering # (<) :: ToOrd a -> ToOrd a -> Bool # (<=) :: ToOrd a -> ToOrd a -> Bool # (>) :: ToOrd a -> ToOrd a -> Bool # (>=) :: ToOrd a -> ToOrd a -> Bool # max :: ToOrd a -> ToOrd a -> ToOrd a # min :: ToOrd a -> ToOrd a -> ToOrd a #
Show a => Show (ToOrd a) #
Methods showsPrec :: Int -> ToOrd a -> ShowS # show :: ToOrd a -> String # showList :: [ToOrd a] -> ShowS #

toOrd :: a -> ToOrd a #

fromOrd :: ToOrd a -> a #