Copyright	(c) Edward Kmett 2014
License	BSD3
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Hask.Power

Description

Documentation

type (⋔) = Power infixr 0 Source

class (Category ((~>) :: i -> i -> *), hom ~ Hom) => Powered hom where Source

Associated Types

type Power :: i -> j -> j Source

Methods

flipped :: forall a u b a' u' b'. Iso (hom a (Power u b)) (hom a' (Power u' b')) (u `Hom` hom a b) (u' `Hom` hom a' b') Source

Instances

Powered * * (->)
Powered Constraint Constraint (\|-)
Powered (i -> ) (Nat * i)
Powered (k -> ) (k -> ) (Lift1 * * k (->))
Powered (k -> k -> ) (k -> k -> ) (Lift2 (k -> ) (k -> ) k k (Lift1 * * k (->)))

flip :: Powered hom => hom a (Power u b) ~> Hom u (hom a b) Source

unflip :: Powered hom => Hom u (hom a b) ~> hom a (Power u b) Source

newtype Power1 v f a Source

Constructors

Power
Fields runPower :: v -> f a

Instances

Monoidal k * f => Monoidal k * (Power1 k v f)
Semimonoidal * k f => Semimonoidal * k (Power1 k v f)
Functor k * f => Functor k * (Power1 k v f)
Corepresentable * (k -> ) (k -> ) (Power1 k)
(Monoidal k * f, Monoid k m) => Monoid * (Power1 k v f m)
(Semimonoidal * k f, Semigroup k m) => Semigroup * (Power1 k v f m)
Contravariant ((k -> ) -> k -> ) * (Power1 k)
Monoidal (k -> ) (k -> ) (Power1 k v)
Semimonoidal (k -> ) (k -> ) (Power1 k v)
Functor (k -> ) (k -> ) (Power1 k v)
Monoid (k -> ) m => Monoid (k -> ) (Power1 k v m)
Semigroup (k -> ) m => Semigroup (k -> ) (Power1 k v m)
type Corep * (k -> ) (k -> ) (Power1 k) = Rel * (k -> *)

Powered * * (->)
Powered Constraint Constraint (\|-)
Powered (i -> ) (Nat * i)
Powered (k -> ) (k -> ) (Lift1 * * k (->))
Powered (k -> k -> ) (k -> k -> ) (Lift2 (k -> ) (k -> ) k k (Lift1 * * k (->)))

Monoidal k * f => Monoidal k * (Power1 k v f)
Semimonoidal * k f => Semimonoidal * k (Power1 k v f)
Functor k * f => Functor k * (Power1 k v f)
Corepresentable * (k -> ) (k -> ) (Power1 k)
(Monoidal k * f, Monoid k m) => Monoid * (Power1 k v f m)
(Semimonoidal * k f, Semigroup k m) => Semigroup * (Power1 k v f m)
Contravariant ((k -> ) -> k -> ) * (Power1 k)
Monoidal (k -> ) (k -> ) (Power1 k v)
Semimonoidal (k -> ) (k -> ) (Power1 k v)
Functor (k -> ) (k -> ) (Power1 k v)
Monoid (k -> ) m => Monoid (k -> ) (Power1 k v m)
Semigroup (k -> ) m => Semigroup (k -> ) (Power1 k v m)
type Corep * (k -> ) (k -> ) (Power1 k) = Rel * (k -> *)