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Language	Haskell98

Data.Semiring.Directed

Contents

Directed semirings

Description

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.

Synopsis

newtype Directed = Directed {
- getDirected :: Ordering
}

Directed semirings

newtype Directed Source #

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

Instances details

Data Directed Source #	Since: 0.7
Instance details 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 Source #	Since: 0.7
Instance details Defined in Data.Semiring.Directed Methods minBound :: Directed # maxBound :: Directed #
Enum Directed Source #	Since: 0.7
Instance details 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 Source #
Instance details 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 Source #	Since: 0.7
Instance details Defined in Data.Semiring.Directed Methods readsPrec :: Int -> ReadS Directed # readList :: ReadS [Directed] # readPrec :: ReadPrec Directed # readListPrec :: ReadPrec [Directed] #
Show Directed Source #	Since: 0.7
Instance details Defined in Data.Semiring.Directed Methods showsPrec :: Int -> Directed -> ShowS # show :: Directed -> String # showList :: [Directed] -> ShowS #
Eq Directed Source #	Since: 0.7
Instance details Defined in Data.Semiring.Directed Methods (==) :: Directed -> Directed -> Bool # (/=) :: Directed -> Directed -> Bool #
Semiring Directed Source #	Since: 0.7
Instance details Defined in Data.Semiring.Directed Methods plus :: Directed -> Directed -> Directed Source # zero :: Directed Source # times :: Directed -> Directed -> Directed Source # one :: Directed Source # fromNatural :: Natural -> Directed Source #
type Rep Directed Source #	Since: 0.7
Instance details 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)))