Numeric.Coalgebra.Incidence

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)

Methods

comult :: (Interval' a -> r) -> Interval' a -> Interval' a -> r

(Eq a, Bounded a, Commutative r, Monoidal r, Semiring r) => CounitalCoalgebra r (Interval' a)

Methods

counit :: (Interval' a -> r) -> r

Eq a => Eq (Interval' a)

Methods

(==) :: Interval' a -> Interval' a -> Bool

(/=) :: Interval' a -> Interval' a -> Bool

Data a => Data (Interval' a)

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)

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)

Methods

readsPrec :: Int -> ReadS (Interval' a)

readList :: ReadS [Interval' a]

readPrec :: ReadPrec (Interval' a)

readListPrec :: ReadPrec [Interval' a]

Show a => Show (Interval' a)

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