Data.Semilattice.N5

Documentation

newtype N5 a

Lift a Semifield into a non-modular lattice.

See https://en.wikipedia.org/wiki/Modular_lattice#Examples

Constructors

N5

Fields

• unN5 :: a

Instances

Functor N5

Defined in Data.Semilattice.N5

Methods

fmap :: (a -> b) -> N5 a -> N5 b

(<$) :: a -> N5 b -> N5 a

(Minimal a, Semifield a) => Eq (N5 a)

Defined in Data.Semilattice.N5

Methods

(==) :: N5 a -> N5 a -> Bool

(/=) :: N5 a -> N5 a -> Bool

Show a => Show (N5 a)

Defined in Data.Semilattice.N5

Methods

showsPrec :: Int -> N5 a -> ShowS

show :: N5 a -> String

showList :: [N5 a] -> ShowS

(Additive - Semigroup) a => Semigroup (Additive (N5 a))

Defined in Data.Semilattice.N5

Methods

(<>) :: Additive (N5 a) -> Additive (N5 a) -> Additive (N5 a)

sconcat :: NonEmpty (Additive (N5 a)) -> Additive (N5 a)

stimes :: Integral b => b -> Additive (N5 a) -> Additive (N5 a)

(Multiplicative - Semigroup) a => Semigroup (Multiplicative (N5 a))

Defined in Data.Semilattice.N5

Methods

(<>) :: Multiplicative (N5 a) -> Multiplicative (N5 a) -> Multiplicative (N5 a)

sconcat :: NonEmpty (Multiplicative (N5 a)) -> Multiplicative (N5 a)

stimes :: Integral b => b -> Multiplicative (N5 a) -> Multiplicative (N5 a)

(Minimal a, Semifield a) => Semigroup (Meet (N5 a))

Defined in Data.Semilattice.N5

Methods

(<>) :: Meet (N5 a) -> Meet (N5 a) -> Meet (N5 a)

sconcat :: NonEmpty (Meet (N5 a)) -> Meet (N5 a)

stimes :: Integral b => b -> Meet (N5 a) -> Meet (N5 a)

(Minimal a, Semifield a) => Semigroup (Join (N5 a))

Defined in Data.Semilattice.N5

Methods

(<>) :: Join (N5 a) -> Join (N5 a) -> Join (N5 a)

sconcat :: NonEmpty (Join (N5 a)) -> Join (N5 a)

stimes :: Integral b => b -> Join (N5 a) -> Join (N5 a)

(Additive - Monoid) a => Monoid (Additive (N5 a))

Defined in Data.Semilattice.N5

Methods

mempty :: Additive (N5 a)

mappend :: Additive (N5 a) -> Additive (N5 a) -> Additive (N5 a)

mconcat :: [Additive (N5 a)] -> Additive (N5 a)

(Multiplicative - Monoid) a => Monoid (Multiplicative (N5 a))

Defined in Data.Semilattice.N5

Methods

mempty :: Multiplicative (N5 a)

mappend :: Multiplicative (N5 a) -> Multiplicative (N5 a) -> Multiplicative (N5 a)

mconcat :: [Multiplicative (N5 a)] -> Multiplicative (N5 a)

(Minimal a, Semifield a) => Monoid (Meet (N5 a))

Defined in Data.Semilattice.N5

Methods

mempty :: Meet (N5 a)

mappend :: Meet (N5 a) -> Meet (N5 a) -> Meet (N5 a)

mconcat :: [Meet (N5 a)] -> Meet (N5 a)

(Minimal a, Semifield a) => Monoid (Join (N5 a))

Defined in Data.Semilattice.N5

Methods

mempty :: Join (N5 a)

mappend :: Join (N5 a) -> Join (N5 a) -> Join (N5 a)

mconcat :: [Join (N5 a)] -> Join (N5 a)

(Additive - Group) a => Group (Additive (N5 a))

Defined in Data.Semilattice.N5

Methods

inv :: Additive (N5 a) -> Additive (N5 a)

greplicate :: Integer -> Additive (N5 a) -> Additive (N5 a)

(Multiplicative - Group) a => Group (Multiplicative (N5 a))

Defined in Data.Semilattice.N5

Methods

inv :: Multiplicative (N5 a) -> Multiplicative (N5 a)

greplicate :: Integer -> Multiplicative (N5 a) -> Multiplicative (N5 a)

(Additive - Group) a => Loop (Additive (N5 a))

Defined in Data.Semilattice.N5

Methods

lempty :: Additive (N5 a)

lreplicate :: Natural -> Additive (N5 a) -> Additive (N5 a)

(Multiplicative - Group) a => Loop (Multiplicative (N5 a))

Defined in Data.Semilattice.N5

Methods

lempty :: Multiplicative (N5 a)

lreplicate :: Natural -> Multiplicative (N5 a) -> Multiplicative (N5 a)

(Additive - Group) a => Quasigroup (Additive (N5 a))

Defined in Data.Semilattice.N5

Methods

(//) :: Additive (N5 a) -> Additive (N5 a) -> Additive (N5 a)

(\\) :: Additive (N5 a) -> Additive (N5 a) -> Additive (N5 a)

(Multiplicative - Group) a => Quasigroup (Multiplicative (N5 a))

Defined in Data.Semilattice.N5

Methods

(//) :: Multiplicative (N5 a) -> Multiplicative (N5 a) -> Multiplicative (N5 a)

(\\) :: Multiplicative (N5 a) -> Multiplicative (N5 a) -> Multiplicative (N5 a)

(Additive - Group) a => Magma (Additive (N5 a))

Defined in Data.Semilattice.N5

Methods

(<<) :: Additive (N5 a) -> Additive (N5 a) -> Additive (N5 a)

(Multiplicative - Group) a => Magma (Multiplicative (N5 a))

Defined in Data.Semilattice.N5

Methods

(<<) :: Multiplicative (N5 a) -> Multiplicative (N5 a) -> Multiplicative (N5 a)

Semifield a => Semifield (N5 a)

Defined in Data.Semilattice.N5

Field a => Field (N5 a)

Defined in Data.Semilattice.N5

Presemiring a => Presemiring (N5 a)

Defined in Data.Semilattice.N5

Semiring a => Semiring (N5 a)

Defined in Data.Semilattice.N5

Ring a => Ring (N5 a)

Defined in Data.Semilattice.N5

(Bound a, Semifield a) => Maximal (N5 a)

Defined in Data.Semilattice.N5

Methods

maximal :: N5 a

(Minimal a, Semifield a) => Minimal (N5 a)

Defined in Data.Semilattice.N5

Methods

minimal :: N5 a

(Minimal a, Semifield a) => Prd (N5 a)

Defined in Data.Semilattice.N5

Methods

(<=) :: N5 a -> N5 a -> Bool

(>=) :: N5 a -> N5 a -> Bool

(<) :: N5 a -> N5 a -> Bool

(>) :: N5 a -> N5 a -> Bool

(?~) :: N5 a -> N5 a -> Bool

(=~) :: N5 a -> N5 a -> Bool

(/~) :: N5 a -> N5 a -> Bool

(~~) :: N5 a -> N5 a -> Bool

(!~) :: N5 a -> N5 a -> Bool

pcompare :: N5 a -> N5 a -> Maybe Ordering

(Minimal a, Semifield a) => Lattice (N5 a)

Defined in Data.Semilattice.N5

n5 :: (Minimal a, Semifield a, Minimal b, Semifield b) => Conn a b -> Conn (N5 a) (N5 b)

n5' :: Semifield a => Minimal a => Bound b => Trip a (Nan b) -> Trip (N5 a) b

n5l :: Semifield a => Minimal a => Maximal b => Conn a (Nan b) -> Conn (N5 a) b

n5r :: Semifield b => Minimal a => Minimal b => Conn (Nan a) b -> Conn a (N5 b)

joinN5 :: Minimal a => Semifield a => N5 a -> N5 a -> N5 a

meetN5 :: Minimal a => Semifield a => N5 a -> N5 a -> N5 a