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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	Since: semirings-0.7
Instance details Defined in Data.Semiring.Directed type Rep Directed = D1 ('MetaData "Directed" "Data.Semiring.Directed" "semirings-0.7-GfH8CFjnoFgLT6ACdLwAYA" 'True) (C1 ('MetaCons "Directed" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDirected") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Ordering)))

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-GfH8CFjnoFgLT6ACdLwAYA" 'True) (C1 ('MetaCons "Directed" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDirected") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Ordering)))