Data.Functor.Exp

Exponentiation of a Functor by a Functor.

For reference:

Powers of polynomial monads by David Spivak https://topos.site/blog/2023/09/powers-of-polynomial-monads/

Documentation

newtype Exp1 f g a

Constructors

Exp1

Fields

• unExp1 :: forall r. f r -> (a -> r) -> g r

Instances

FFunctor (Exp1 f)

Defined in Data.Functor.Exp

Methods

ffmap :: forall (g :: Type -> Type) (h :: Type -> Type) x. (Functor g, Functor h) => (g ~> h) -> Exp1 f g x -> Exp1 f h x

Functor f => FMonad (Exp1 f)

g ~ Exp1 Proxy g; Exp1 f (Exp1 f g) ~ Exp1 (f :*: f) g

Defined in Data.Functor.Exp

Methods

fpure :: forall (g :: Type -> Type). Functor g => g ~> Exp1 f g

fbind :: forall (g :: Type -> Type) (h :: Type -> Type) a. (Functor g, Functor h) => (g ~> Exp1 f h) -> Exp1 f g a -> Exp1 f h a

Functor f => FStrong (Exp1 f)

Defined in Data.Functor.Exp

Methods

fstrength :: forall (g :: Type -> Type) (h :: Type -> Type). Functor g => Day (Exp1 f g) h ~> Exp1 f (Day g h)

mapCurried :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => Curried g h ~> Curried (Exp1 f g) (Exp1 f h)

(Comonad f, Monad g) => Alternative (Exp1 f g)

Defined in Data.Functor.Exp

Methods

empty :: Exp1 f g a

(<|>) :: Exp1 f g a -> Exp1 f g a -> Exp1 f g a

some :: Exp1 f g a -> Exp1 f g [a]

many :: Exp1 f g a -> Exp1 f g [a]

(Functor f, Monad g) => Applicative (Exp1 f g)

Defined in Data.Functor.Exp

Methods

pure :: a -> Exp1 f g a

(<*>) :: Exp1 f g (a -> b) -> Exp1 f g a -> Exp1 f g b

liftA2 :: (a -> b -> c) -> Exp1 f g a -> Exp1 f g b -> Exp1 f g c

(*>) :: Exp1 f g a -> Exp1 f g b -> Exp1 f g b

(<*) :: Exp1 f g a -> Exp1 f g b -> Exp1 f g a

Functor (Exp1 f g)

Defined in Data.Functor.Exp

Methods

fmap :: (a -> b) -> Exp1 f g a -> Exp1 f g b

(<$) :: a -> Exp1 f g b -> Exp1 f g a

(Functor f, Monad g) => Monad (Exp1 f g)

Defined in Data.Functor.Exp

Methods

(>>=) :: Exp1 f g a -> (a -> Exp1 f g b) -> Exp1 f g b

(>>) :: Exp1 f g a -> Exp1 f g b -> Exp1 f g b

return :: a -> Exp1 f g a

Functor f => Adjunction ((:*:) f) (Exp1 f)

Defined in FFunctor.Adjunction

Methods

unit :: forall (g :: Type -> Type). Functor g => g ~> Exp1 f (f :*: g)

counit :: forall (g :: Type -> Type). Functor g => (f :*: Exp1 f g) ~> g

leftAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => ((f :*: g) ~> h) -> g ~> Exp1 f h

rightAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (g ~> Exp1 f h) -> (f :*: g) ~> h

(Comonad f, Monad g) => Monoid (Exp1 f g a)

Equivalent to Alt (Exp1 f g) a

Defined in Data.Functor.Exp

Methods

mempty :: Exp1 f g a

mappend :: Exp1 f g a -> Exp1 f g a -> Exp1 f g a

mconcat :: [Exp1 f g a] -> Exp1 f g a

(Comonad f, Monad g) => Semigroup (Exp1 f g a)

Equivalent to Alt (Exp1 f g) a

Defined in Data.Functor.Exp

Methods

(<>) :: Exp1 f g a -> Exp1 f g a -> Exp1 f g a

sconcat :: NonEmpty (Exp1 f g a) -> Exp1 f g a

stimes :: Integral b => b -> Exp1 f g a -> Exp1 f g a

type (:^:) f g = Exp1 g f

toExp1 :: forall f g h. Functor g => ((f :*: g) ~> h) -> g ~> Exp1 f h

fromExp1 :: forall f g h. (g ~> Exp1 f h) -> (f :*: g) ~> h

evalExp1 :: (f :*: Exp1 f g) ~> g

coevalExp1 :: Functor g => g ~> Exp1 f (f :*: g)

fromExp1' :: Functor f => Exp1 f g b -> f a -> g (Either a b)

toExp1' :: Functor g => (forall a. f a -> g (Either a b)) -> Exp1 f g b