Algebra.Indexable

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.

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.

Methods

compare :: a -> a -> Ordering

Instances

C Integer

Defined in Algebra.Indexable

Methods

compare :: Integer -> Integer -> Ordering

C T

Defined in Number.Peano

Methods

compare :: T -> T -> Ordering

C a => C [a]

Defined in Algebra.Indexable

Methods

compare :: [a] -> [a] -> Ordering

(Ord a, C a) => C (T a)

Defined in Number.Ratio

Methods

compare :: T a -> T a -> Ordering

(C a, C a) => C (T a)

Defined in MathObj.Polynomial

Methods

compare :: T a -> T a -> Ordering

C a => C (T a)

Defined in Number.Complex

Methods

compare :: T a -> T a -> Ordering

(C a, C b) => C (a, b)

Defined in Algebra.Indexable

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)

Defined in Algebra.Indexable

Methods

(==) :: ToOrd a -> ToOrd a -> Bool

(/=) :: ToOrd a -> ToOrd a -> Bool

C a => Ord (ToOrd a)

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)

Defined in Algebra.Indexable

Methods

showsPrec :: Int -> ToOrd a -> ShowS

show :: ToOrd a -> String

showList :: [ToOrd a] -> ShowS

toOrd :: a -> ToOrd a

fromOrd :: ToOrd a -> a