Pandora.Paradigm.Basis.Product

Documentation

data Product a b

Constructors

a :*: b infixr 1

Instances

Covariant (Product a)

Defined in Pandora.Paradigm.Basis.Product

Methods

(<$>) :: (a0 -> b) -> Product a a0 -> Product a b

comap :: (a0 -> b) -> Product a a0 -> Product a b

(<$) :: a0 -> Product a b -> Product a a0

($>) :: Product a a0 -> b -> Product a b

void :: Product a a0 -> Product a ()

loeb :: Product a (Product a a0 -> a0) -> Product a a0

(<$$>) :: Covariant u => (a0 -> b) -> Product a (u a0) -> Product a (u b)

(<$$$>) :: (Covariant u, Covariant v) => (a0 -> b) -> Product a (u (v a0)) -> Product a (u (v b))

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a0 -> b) -> Product a (u (v (w a0))) -> Product a (u (v (w b)))

Extendable (Product a)

Defined in Pandora.Paradigm.Basis.Product

Methods

(=>>) :: Product a a0 -> (Product a a0 -> b) -> Product a b

(<<=) :: (Product a a0 -> b) -> Product a a0 -> Product a b

extend :: (Product a a0 -> b) -> Product a a0 -> Product a b

duplicate :: Product a a0 -> (Product a :.: Product a) a0

(=<=) :: (Product a b -> c) -> (Product a a0 -> b) -> Product a a0 -> c

(=>=) :: (Product a a0 -> b) -> (Product a b -> c) -> Product a a0 -> c

Extractable (Product a)

Defined in Pandora.Paradigm.Basis.Product

Methods

extract :: Product a a0 -> a0

Comonad (Product a)

Defined in Pandora.Paradigm.Basis.Product

Adjoint (Product a) ((->) a :: Type -> Type)

Defined in Pandora.Paradigm.Basis.Product

Methods

phi :: (Product a a0 -> b) -> a0 -> a -> b

psi :: (a0 -> a -> b) -> Product a a0 -> b

eta :: a0 -> ((->) a :.: Product a) a0

epsilon :: (Product a :.: (->) a) a0 -> a0

(Semigroup a, Semigroup b) => Semigroup (Product a b)

Defined in Pandora.Paradigm.Basis.Product

Methods

(<>) :: Product a b -> Product a b -> Product a b

(Ringoid a, Ringoid b) => Ringoid (Product a b)

Defined in Pandora.Paradigm.Basis.Product

Methods

(><) :: Product a b -> Product a b -> Product a b

(Monoid a, Monoid b) => Monoid (Product a b)

Defined in Pandora.Paradigm.Basis.Product

Methods

unit :: Product a b

(Group a, Group b) => Group (Product a b)

Defined in Pandora.Paradigm.Basis.Product

Methods

inverse :: Product a b -> Product a b

(Supremum a, Supremum b) => Supremum (Product a b)

Defined in Pandora.Paradigm.Basis.Product

Methods

(\/) :: Product a b -> Product a b -> Product a b

(Infimum a, Infimum b) => Infimum (Product a b)

Defined in Pandora.Paradigm.Basis.Product

Methods

(/\) :: Product a b -> Product a b -> Product a b

(Lattice a, Lattice b) => Lattice (Product a b)

Defined in Pandora.Paradigm.Basis.Product

(Setoid a, Setoid b) => Setoid (Product a b)

Defined in Pandora.Paradigm.Basis.Product

Methods

(==) :: Product a b -> Product a b -> Boolean

(/=) :: Product a b -> Product a b -> Boolean

type (:*:) = Product infixr 1

type family Has x xs where ...

Equations

Has x (x :*: xs) = ()

Has x (y :*: xs) = Has x xs

Has x x = ()

type family Injective xs ys where ...

Equations

Injective (x :*: xs) ys = (Has x ys, Injective xs ys)

Injective x (x :*: ys) = ()

Injective x (y :*: ys) = Has x ys

Injective x x = ()

delta :: a -> a :*: a

swap :: (a :*: b) -> b :*: a

attached :: (a :*: b) -> a