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

class Eq a => C a where
- compare :: a -> a -> Ordering
ordCompare :: Ord a => a -> a -> Ordering
liftCompare :: C b => (a -> b) -> a -> a -> Ordering
data ToOrd a
toOrd :: a -> ToOrd a
fromOrd :: ToOrd a -> a

Documentation

class Eq a => C a where Source #

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

Methods

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

Instances

Instances details

C Integer Source #
Instance details Defined in Algebra.Indexable Methods compare :: Integer -> Integer -> Ordering Source #
C T Source #
Instance details Defined in Number.Peano Methods compare :: T -> T -> Ordering Source #
C a => C [a] Source #
Instance details Defined in Algebra.Indexable Methods compare :: [a] -> [a] -> Ordering Source #
(Ord a, C a) => C (T a) Source #
Instance details Defined in Number.Ratio Methods compare :: T a -> T a -> Ordering Source #
(C a, C a) => C (T a) Source #
Instance details Defined in MathObj.Polynomial Methods compare :: T a -> T a -> Ordering Source #
C a => C (T a) Source #
Instance details Defined in Number.Complex Methods compare :: T a -> T a -> Ordering Source #
(C a, C b) => C (a, b) Source #
Instance details Defined in Algebra.Indexable Methods compare :: (a, b) -> (a, b) -> Ordering Source #

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

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 Source #

Lift compare implementation from a wrapped object.

data ToOrd a Source #

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

Instances

Instances details

Eq a => Eq (ToOrd a) Source #
Instance details Defined in Algebra.Indexable Methods (==) :: ToOrd a -> ToOrd a -> Bool # (/=) :: ToOrd a -> ToOrd a -> Bool #
C a => Ord (ToOrd a) Source #
Instance details Defined in Algebra.Indexable 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) Source #
Instance details Defined in Algebra.Indexable Methods showsPrec :: Int -> ToOrd a -> ShowS # show :: ToOrd a -> String # showList :: [ToOrd a] -> ShowS #

toOrd :: a -> ToOrd a Source #

fromOrd :: ToOrd a -> a Source #