Safe Haskell	Safe
Language	Haskell98

Numeric.Coalgebra.Incidence

Synopsis

data Interval' a = Interval' a a
zeta' :: Unital r => Interval' a -> r
moebius' :: (Ring r, LocallyFiniteOrder a) => Interval' a -> r

Documentation

data Interval' a #

the dual incidence algebra basis

Constructors

Interval' a a

Instances

(Eq a, Commutative r, Monoidal r, Semiring r) => Coalgebra r (Interval' a) #
Instance details Defined in Numeric.Coalgebra.Incidence Methods comult :: (Interval' a -> r) -> Interval' a -> Interval' a -> r #
(Eq a, Bounded a, Commutative r, Monoidal r, Semiring r) => CounitalCoalgebra r (Interval' a) #
Instance details Defined in Numeric.Coalgebra.Incidence Methods counit :: (Interval' a -> r) -> r #
Eq a => Eq (Interval' a) #
Instance details Defined in Numeric.Coalgebra.Incidence Methods (==) :: Interval' a -> Interval' a -> Bool # (/=) :: Interval' a -> Interval' a -> Bool #
Data a => Data (Interval' a) #
Instance details Defined in Numeric.Coalgebra.Incidence Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Interval' a -> c (Interval' a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Interval' a) # toConstr :: Interval' a -> Constr # dataTypeOf :: Interval' a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Interval' a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Interval' a)) # gmapT :: (forall b. Data b => b -> b) -> Interval' a -> Interval' a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Interval' a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Interval' a -> r # gmapQ :: (forall d. Data d => d -> u) -> Interval' a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Interval' a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Interval' a -> m (Interval' a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Interval' a -> m (Interval' a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Interval' a -> m (Interval' a) #
Ord a => Ord (Interval' a) #
Instance details Defined in Numeric.Coalgebra.Incidence Methods compare :: Interval' a -> Interval' a -> Ordering # (<) :: Interval' a -> Interval' a -> Bool # (<=) :: Interval' a -> Interval' a -> Bool # (>) :: Interval' a -> Interval' a -> Bool # (>=) :: Interval' a -> Interval' a -> Bool # max :: Interval' a -> Interval' a -> Interval' a # min :: Interval' a -> Interval' a -> Interval' a #
Read a => Read (Interval' a) #
Instance details Defined in Numeric.Coalgebra.Incidence Methods readsPrec :: Int -> ReadS (Interval' a) # readList :: ReadS [Interval' a] # readPrec :: ReadPrec (Interval' a) # readListPrec :: ReadPrec [Interval' a] #
Show a => Show (Interval' a) #
Instance details Defined in Numeric.Coalgebra.Incidence Methods showsPrec :: Int -> Interval' a -> ShowS # show :: Interval' a -> String # showList :: [Interval' a] -> ShowS #

zeta' :: Unital r => Interval' a -> r #

moebius' :: (Ring r, LocallyFiniteOrder a) => Interval' a -> r #