Data.Semigroup.Quantale

Documentation

residuated :: Quantale a => a -> a -> a -> Bool

class (Semigroup a, Prd a) => Quantale a where

Residuated, partially ordered semigroups.

In the interest of usability we abuse terminology slightly and use the term quantale to describe any residuated, partially ordered semigroup. This admits instances of hoops and triangular (co)-norms.

There are several additional properties that apply when the poset structure is lattice-ordered (i.e. a residuated lattice) or when the semigroup is a monoid or semiring. See the associated Properties module.

Minimal complete definition

Nothing

Methods

residr :: a -> Conn a a

residl :: a -> Conn a a

(\\) :: a -> a -> a

(//) :: a -> a -> a

Instances

Quantale Float

Defined in Data.Semigroup.Quantale

Methods

residr :: Float -> Conn Float Float

residl :: Float -> Conn Float Float

(\\) :: Float -> Float -> Float

(//) :: Float -> Float -> Float

Quantale Unsigned

Defined in Data.Dioid.Signed

Methods

residr :: Unsigned -> Conn Unsigned Unsigned

residl :: Unsigned -> Conn Unsigned Unsigned

(\\) :: Unsigned -> Unsigned -> Unsigned

(//) :: Unsigned -> Unsigned -> Unsigned

lower' :: Prd a => Float -> (Float -> a) -> a -> Float

upper' :: Prd a => Float -> (Float -> a) -> a -> Float

incBy :: Yoneda a => Quantale a => a -> Rep a -> Rep a

decBy :: Yoneda a => Quantale a => a -> Rep a -> Rep a