Data.Semiring.Directed

A "directed semiring" refers to the semiring composed of the union of upwards directed sets as multiplication, and intersection of downwards directed sets as addition.

Directed semirings

newtype Directed

Wrapper for the semiring of upwards and downwards directed sets.

For the individual join/meet monoids associated with either algebra, see Max Ordering, and Min Ordering@.

Constructors

Directed

Fields

• getDirected :: Ordering

  Since: 0.7

Instances

Data Directed

Since: 0.7

Defined in Data.Semiring.Directed

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Directed -> c Directed

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Directed

toConstr :: Directed -> Constr

dataTypeOf :: Directed -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Directed)

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Directed)

gmapT :: (forall b. Data b => b -> b) -> Directed -> Directed

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Directed -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Directed -> r

gmapQ :: (forall d. Data d => d -> u) -> Directed -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Directed -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Directed -> m Directed

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Directed -> m Directed

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Directed -> m Directed

Bounded Directed

Since: 0.7

Defined in Data.Semiring.Directed

Methods

minBound :: Directed

maxBound :: Directed

Enum Directed

Since: 0.7

Defined in Data.Semiring.Directed

Methods

succ :: Directed -> Directed

pred :: Directed -> Directed

toEnum :: Int -> Directed

fromEnum :: Directed -> Int

enumFrom :: Directed -> [Directed]

enumFromThen :: Directed -> Directed -> [Directed]

enumFromTo :: Directed -> Directed -> [Directed]

enumFromThenTo :: Directed -> Directed -> Directed -> [Directed]

Generic Directed

Defined in Data.Semiring.Directed

Associated Types

type Rep Directed :: Type -> Type

Methods

from :: Directed -> Rep Directed x

to :: Rep Directed x -> Directed

Read Directed

Since: 0.7

Defined in Data.Semiring.Directed

Methods

readsPrec :: Int -> ReadS Directed

readList :: ReadS [Directed]

readPrec :: ReadPrec Directed

readListPrec :: ReadPrec [Directed]

Show Directed

Since: 0.7

Defined in Data.Semiring.Directed

Methods

showsPrec :: Int -> Directed -> ShowS

show :: Directed -> String

showList :: [Directed] -> ShowS

Eq Directed

Since: 0.7

Defined in Data.Semiring.Directed

Methods

(==) :: Directed -> Directed -> Bool

(/=) :: Directed -> Directed -> Bool

Semiring Directed

Since: 0.7

Defined in Data.Semiring.Directed

Methods

plus :: Directed -> Directed -> Directed

zero :: Directed

times :: Directed -> Directed -> Directed

one :: Directed

fromNatural :: Natural -> Directed

type Rep Directed

Since: 0.7

Defined in Data.Semiring.Directed

type Rep Directed = D1 ('MetaData "Directed" "Data.Semiring.Directed" "semirings-0.7-IT1UKobn80nYNk4WFT2qF" 'True) (C1 ('MetaCons "Directed" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDirected") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Ordering)))