Copyright	(c) Ross Paterson 2022
License	BSD-style (see the file LICENSE)
Maintainer	[email protected]
Stability	provisional
Portability	portable
Safe Haskell	None
Language	Haskell2010

Data.YAP.Tropical

Description

An example instance of the algebraic classes: tropical semirings.

Synopsis

data Tropical a
- = Tropical a
- | Infinity
data Schedule a
- = MinusInfinity
- | Schedule a

Documentation

data Tropical a Source #

Tropical semiring

Constructors

Tropical a
Infinity

Instances

Instances details

Bounded a => Bounded (Tropical a) Source #
Instance details Defined in Data.YAP.Tropical Methods minBound :: Tropical a # maxBound :: Tropical a #
Read a => Read (Tropical a) Source #
Instance details Defined in Data.YAP.Tropical Methods readsPrec :: Int -> ReadS (Tropical a) # readList :: ReadS [Tropical a] # readPrec :: ReadPrec (Tropical a) # readListPrec :: ReadPrec [Tropical a] #
Show a => Show (Tropical a) Source #
Instance details Defined in Data.YAP.Tropical Methods showsPrec :: Int -> Tropical a -> ShowS # show :: Tropical a -> String # showList :: [Tropical a] -> ShowS #
Eq a => Eq (Tropical a) Source #
Instance details Defined in Data.YAP.Tropical Methods (==) :: Tropical a -> Tropical a -> Bool # (/=) :: Tropical a -> Tropical a -> Bool #
Ord a => Ord (Tropical a) Source #
Instance details Defined in Data.YAP.Tropical Methods compare :: Tropical a -> Tropical a -> Ordering # (<) :: Tropical a -> Tropical a -> Bool # (<=) :: Tropical a -> Tropical a -> Bool # (>) :: Tropical a -> Tropical a -> Bool # (>=) :: Tropical a -> Tropical a -> Bool # max :: Tropical a -> Tropical a -> Tropical a # min :: Tropical a -> Tropical a -> Tropical a #
Ord a => AdditiveMonoid (Tropical a) Source #
Instance details Defined in Data.YAP.Tropical Methods (+) :: Tropical a -> Tropical a -> Tropical a # zero :: Tropical a # atimes :: ToInteger b => b -> Tropical a -> Tropical a #
(Ord a, AbelianGroup a) => DivisionSemiring (Tropical a) Source #
Instance details Defined in Data.YAP.Tropical Methods recip :: Tropical a -> Tropical a #
(Ord a, AbelianGroup a) => Semifield (Tropical a) Source #
Instance details Defined in Data.YAP.Tropical Methods (/) :: Tropical a -> Tropical a -> Tropical a #
(Ord a, AdditiveMonoid a) => Semiring (Tropical a) Source #
Instance details Defined in Data.YAP.Tropical Methods (*) :: Tropical a -> Tropical a -> Tropical a # one :: Tropical a # fromNatural :: Natural -> Tropical a # rescale :: Tropical a -> Tropical a -> (Tropical a, Tropical a, Tropical a -> Tropical a) #

data Schedule a Source #

Schedule algebra or arctic semiring (dual of Tropical)

Constructors

MinusInfinity
Schedule a

Instances

Instances details

Bounded a => Bounded (Schedule a) Source #
Instance details Defined in Data.YAP.Tropical Methods minBound :: Schedule a # maxBound :: Schedule a #
Read a => Read (Schedule a) Source #
Instance details Defined in Data.YAP.Tropical Methods readsPrec :: Int -> ReadS (Schedule a) # readList :: ReadS [Schedule a] # readPrec :: ReadPrec (Schedule a) # readListPrec :: ReadPrec [Schedule a] #
Show a => Show (Schedule a) Source #
Instance details Defined in Data.YAP.Tropical Methods showsPrec :: Int -> Schedule a -> ShowS # show :: Schedule a -> String # showList :: [Schedule a] -> ShowS #
Eq a => Eq (Schedule a) Source #
Instance details Defined in Data.YAP.Tropical Methods (==) :: Schedule a -> Schedule a -> Bool # (/=) :: Schedule a -> Schedule a -> Bool #
Ord a => Ord (Schedule a) Source #
Instance details Defined in Data.YAP.Tropical Methods compare :: Schedule a -> Schedule a -> Ordering # (<) :: Schedule a -> Schedule a -> Bool # (<=) :: Schedule a -> Schedule a -> Bool # (>) :: Schedule a -> Schedule a -> Bool # (>=) :: Schedule a -> Schedule a -> Bool # max :: Schedule a -> Schedule a -> Schedule a # min :: Schedule a -> Schedule a -> Schedule a #
Ord a => AdditiveMonoid (Schedule a) Source #
Instance details Defined in Data.YAP.Tropical Methods (+) :: Schedule a -> Schedule a -> Schedule a # zero :: Schedule a # atimes :: ToInteger b => b -> Schedule a -> Schedule a #
(Ord a, AbelianGroup a) => DivisionSemiring (Schedule a) Source #
Instance details Defined in Data.YAP.Tropical Methods recip :: Schedule a -> Schedule a #
(Ord a, AbelianGroup a) => Semifield (Schedule a) Source #
Instance details Defined in Data.YAP.Tropical Methods (/) :: Schedule a -> Schedule a -> Schedule a #
(Ord a, AdditiveMonoid a) => Semiring (Schedule a) Source #
Instance details Defined in Data.YAP.Tropical Methods (*) :: Schedule a -> Schedule a -> Schedule a # one :: Schedule a # fromNatural :: Natural -> Schedule a # rescale :: Schedule a -> Schedule a -> (Schedule a, Schedule a, Schedule a -> Schedule a) #