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

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

(<$$>) :: 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

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

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

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

Traversable (Product a)

Defined in Pandora.Paradigm.Basis.Product

Methods

(->>) :: (Pointable u, Applicative u) => Product a a0 -> (a0 -> u b) -> (u :. Product a) := b

traverse :: (Pointable u, Applicative u) => (a0 -> u b) -> Product a a0 -> (u :. Product a) := b

sequence :: (Pointable u, Applicative u) => (Product a :. u) a0 -> (u :. Product a) := a0

(->>>) :: (Pointable u, Applicative u, Traversable v) => ((v :. Product a) := a0) -> (a0 -> u b) -> (u :. (v :. Product a)) := b

(->>>>) :: (Pointable u, Applicative u, Traversable v, Traversable w) => ((w :. (v :. Product a)) := a0) -> (a0 -> u b) -> (u :. (w :. (v :. Product a))) := b

(->>>>>) :: (Pointable u, Applicative u, Traversable v, Traversable w, Traversable j) => ((j :. (w :. (v :. Product a))) := a0) -> (a0 -> u b) -> (u :. (j :. (w :. (v :. Product a)))) := b

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

Defined in Pandora.Paradigm.Basis.Product

Methods

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

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

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

zero :: 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

Covariant u => Covariant (TUV Co Co Co ((->) s :: Type -> Type) u ((:*:) s))

Defined in Pandora.Paradigm.Inventory.Stateful

Methods

(<$>) :: (a -> b) -> TUV Co Co Co ((->) s) u ((:*:) s) a -> TUV Co Co Co ((->) s) u ((:*:) s) b

comap :: (a -> b) -> TUV Co Co Co ((->) s) u ((:*:) s) a -> TUV Co Co Co ((->) s) u ((:*:) s) b

(<$) :: a -> TUV Co Co Co ((->) s) u ((:*:) s) b -> TUV Co Co Co ((->) s) u ((:*:) s) a

($>) :: TUV Co Co Co ((->) s) u ((:*:) s) a -> b -> TUV Co Co Co ((->) s) u ((:*:) s) b

void :: TUV Co Co Co ((->) s) u ((:*:) s) a -> TUV Co Co Co ((->) s) u ((:*:) s) ()

loeb :: TUV Co Co Co ((->) s) u ((:*:) s) (TUV Co Co Co ((->) s) u ((:*:) s) a -> a) -> TUV Co Co Co ((->) s) u ((:*:) s) a

(<&>) :: TUV Co Co Co ((->) s) u ((:*:) s) a -> (a -> b) -> TUV Co Co Co ((->) s) u ((:*:) s) b

(<$$>) :: Covariant u0 => (a -> b) -> ((TUV Co Co Co ((->) s) u ((:*:) s) :. u0) := a) -> (TUV Co Co Co ((->) s) u ((:*:) s) :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> ((TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. v)) := a) -> (TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> ((TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. (v :. w))) := a) -> (TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => ((TUV Co Co Co ((->) s) u ((:*:) s) :. u0) := a) -> (a -> b) -> (TUV Co Co Co ((->) s) u ((:*:) s) :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => ((TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. v)) := a) -> (a -> b) -> (TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. (v :. w))) := a) -> (a -> b) -> (TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. (v :. w))) := b

Bindable u => Bindable (TUV Co Co Co ((->) s :: Type -> Type) u ((:*:) s))

Defined in Pandora.Paradigm.Inventory.Stateful

Methods

(>>=) :: TUV Co Co Co ((->) s) u ((:*:) s) a -> (a -> TUV Co Co Co ((->) s) u ((:*:) s) b) -> TUV Co Co Co ((->) s) u ((:*:) s) b

(=<<) :: (a -> TUV Co Co Co ((->) s) u ((:*:) s) b) -> TUV Co Co Co ((->) s) u ((:*:) s) a -> TUV Co Co Co ((->) s) u ((:*:) s) b

bind :: (a -> TUV Co Co Co ((->) s) u ((:*:) s) b) -> TUV Co Co Co ((->) s) u ((:*:) s) a -> TUV Co Co Co ((->) s) u ((:*:) s) b

join :: ((TUV Co Co Co ((->) s) u ((:*:) s) :. TUV Co Co Co ((->) s) u ((:*:) s)) := a) -> TUV Co Co Co ((->) s) u ((:*:) s) a

(>=>) :: (a -> TUV Co Co Co ((->) s) u ((:*:) s) b) -> (b -> TUV Co Co Co ((->) s) u ((:*:) s) c) -> a -> TUV Co Co Co ((->) s) u ((:*:) s) c

(<=<) :: (b -> TUV Co Co Co ((->) s) u ((:*:) s) c) -> (a -> TUV Co Co Co ((->) s) u ((:*:) s) b) -> a -> TUV Co Co Co ((->) s) u ((:*:) s) c

Bindable u => Applicative (TUV Co Co Co ((->) s :: Type -> Type) u ((:*:) s))

Defined in Pandora.Paradigm.Inventory.Stateful

Methods

(<*>) :: TUV Co Co Co ((->) s) u ((:*:) s) (a -> b) -> TUV Co Co Co ((->) s) u ((:*:) s) a -> TUV Co Co Co ((->) s) u ((:*:) s) b

apply :: TUV Co Co Co ((->) s) u ((:*:) s) (a -> b) -> TUV Co Co Co ((->) s) u ((:*:) s) a -> TUV Co Co Co ((->) s) u ((:*:) s) b

(*>) :: TUV Co Co Co ((->) s) u ((:*:) s) a -> TUV Co Co Co ((->) s) u ((:*:) s) b -> TUV Co Co Co ((->) s) u ((:*:) s) b

(<*) :: TUV Co Co Co ((->) s) u ((:*:) s) a -> TUV Co Co Co ((->) s) u ((:*:) s) b -> TUV Co Co Co ((->) s) u ((:*:) s) a

forever :: TUV Co Co Co ((->) s) u ((:*:) s) a -> TUV Co Co Co ((->) s) u ((:*:) s) b

(<**>) :: Applicative u0 => ((TUV Co Co Co ((->) s) u ((:*:) s) :. u0) := (a -> b)) -> ((TUV Co Co Co ((->) s) u ((:*:) s) :. u0) := a) -> (TUV Co Co Co ((->) s) u ((:*:) s) :. u0) := b

(<***>) :: (Applicative u0, Applicative v) => ((TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. v)) := (a -> b)) -> ((TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. v)) := a) -> (TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. v)) := b

(<****>) :: (Applicative u0, Applicative v, Applicative w) => ((TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. (v :. w))) := (a -> b)) -> ((TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. (v :. w))) := a) -> (TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. (v :. w))) := b

Pointable u => Pointable (TUV Co Co Co ((->) s :: Type -> Type) u ((:*:) s))

Defined in Pandora.Paradigm.Inventory.Stateful

Methods

point :: a -> TUV Co Co Co ((->) s) u ((:*:) s) a

Monad u => Monad (TUV Co Co Co ((->) s :: Type -> Type) u ((:*:) s))

Defined in Pandora.Paradigm.Inventory.Stateful

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

curry :: ((a :*: b) -> c) -> a -> b -> c

uncurry :: (a -> b -> c) -> (a :*: b) -> c