Pandora.Paradigm.Algebraic

Documentation

module Pandora.Paradigm.Algebraic.One

module Pandora.Paradigm.Algebraic.Zero

module Pandora.Paradigm.Algebraic.Sum

module Pandora.Paradigm.Algebraic.Product

module Pandora.Paradigm.Algebraic.Exponential

module Pandora.Paradigm.Algebraic.Functor

type (:+*+:) l r = (l :+: r) :*: (r :+: l)

type (:*+*:) l r = (l :*: r) :+: (r :*: l)

Orphan instances

Monoidal (-->) (-->) (:*:) (:*:) ((:+:) e)

Methods

unit :: Proxy (:*:) -> (Unit (:*:) --> a) --> (e :+: a)

Monoidal (<--) (-->) (:*:) (:*:) ((:*:) s)

Methods

unit :: Proxy (:*:) -> (Unit (:*:) --> a) <-- (s :*: a)

Monoidal (<--) (-->) (:*:) (:*:) (Flip (:*:) a)

Methods

unit :: Proxy (:*:) -> (Unit (:*:) --> a0) <-- Flip (:*:) a a0

(Monoidal (-->) (-->) (:*:) (:+:) t, Monoidal (-->) (-->) (:*:) (:+:) u) => Monoidal (-->) (-->) (:*:) (:+:) (t <:*:> u)

Methods

unit :: Proxy (:*:) -> (Unit (:+:) --> a) --> (t <:*:> u) a

Monoidal (-->) (-->) (:*:) (:*:) ((->) e :: Type -> Type)

Methods

unit :: Proxy (:*:) -> (Unit (:*:) --> a) --> (e -> a)

Semimonoidal (-->) (:*:) (:+:) ((:+:) e :: Type -> Type)

Methods

mult :: forall (a :: k) (b :: k). ((e :+: a) :*: (e :+: b)) --> (e :+: (a :+: b))

Semimonoidal (-->) (:*:) (:*:) ((:+:) e :: Type -> Type)

Methods

mult :: forall (a :: k) (b :: k). ((e :+: a) :*: (e :+: b)) --> (e :+: (a :*: b))

Semimonoidal (<--) (:*:) (:*:) ((:*:) s :: Type -> Type)

Methods

mult :: forall (a :: k) (b :: k). ((s :*: a) :*: (s :*: b)) <-- (s :*: (a :*: b))

Semimonoidal (<--) (:*:) (:*:) (Flip (:*:) a :: Type -> Type)

Methods

mult :: forall (a0 :: k) (b :: k). (Flip (:*:) a a0 :*: Flip (:*:) a b) <-- Flip (:*:) a (a0 :*: b)

(Semimonoidal (-->) (:*:) (:+:) t, Semimonoidal (-->) (:*:) (:+:) u) => Semimonoidal (-->) (:*:) (:+:) (t <:*:> u :: Type -> Type)

Methods

mult :: forall (a :: k) (b :: k). ((t <:*:> u) a :*: (t <:*:> u) b) --> (t <:*:> u) (a :+: b)

Semimonoidal (-->) (:*:) (:*:) ((->) e :: Type -> Type)

Methods

mult :: forall (a :: k) (b :: k). ((e -> a) :*: (e -> b)) --> (e -> (a :*: b))

(Semimonoidal (-->) (:*:) (:*:) t, Semimonoidal (-->) (:*:) (:*:) u) => Semimonoidal (-->) (:*:) (:*:) (t <:*:> u :: Type -> Type)

Methods

mult :: forall (a :: k) (b :: k). ((t <:*:> u) a :*: (t <:*:> u) b) --> (t <:*:> u) (a :*: b)

Semimonoidal (<--) (:*:) (:*:) ((->) e :: Type -> Type)

Methods

mult :: forall (a :: k) (b :: k). ((e -> a) :*: (e -> b)) <-- (e -> (a :*: b))

(Semimonoidal (<--) (:*:) (:*:) t, Semimonoidal (<--) (:*:) (:*:) u) => Semimonoidal (<--) (:*:) (:*:) (t <:*:> u :: Type -> Type)

Methods

mult :: forall (a :: k) (b :: k). ((t <:*:> u) a :*: (t <:*:> u) b) <-- (t <:*:> u) (a :*: b)

Comonad ((->) :: Type -> Type -> Type) ((:*:) s)

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((:*:) s)

Methods

(<-/-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> (s :*: a) -> u (s :*: b)

(<-/-------) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> (s :*: a) -> u (s :*: b)

(<-/------) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> (s :*: a) -> u (s :*: b)

(<-/-----) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> (s :*: a) -> u (s :*: b)

(<-/----) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> (s :*: a) -> u (s :*: b)

(<-/---) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> (s :*: a) -> u (s :*: b)

(<-/--) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> (s :*: a) -> u (s :*: b)

(Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u) => Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (t <:*:> u)

Methods

(<-/-) :: (Covariant (->) (->) u0, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u0) => (a -> u0 b) -> (t <:*:> u) a -> u0 ((t <:*:> u) b)

(<-/-------) :: (Covariant (->) (->) u0, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u0) => (a -> u0 b) -> (t <:*:> u) a -> u0 ((t <:*:> u) b)

(<-/------) :: (Covariant (->) (->) u0, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u0) => (a -> u0 b) -> (t <:*:> u) a -> u0 ((t <:*:> u) b)

(<-/-----) :: (Covariant (->) (->) u0, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u0) => (a -> u0 b) -> (t <:*:> u) a -> u0 ((t <:*:> u) b)

(<-/----) :: (Covariant (->) (->) u0, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u0) => (a -> u0 b) -> (t <:*:> u) a -> u0 ((t <:*:> u) b)

(<-/---) :: (Covariant (->) (->) u0, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u0) => (a -> u0 b) -> (t <:*:> u) a -> u0 ((t <:*:> u) b)

(<-/--) :: (Covariant (->) (->) u0, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u0) => (a -> u0 b) -> (t <:*:> u) a -> u0 ((t <:*:> u) b)