Pandora.Paradigm.Primary.Algebraic

Documentation

module Pandora.Paradigm.Primary.Algebraic.One

module Pandora.Paradigm.Primary.Algebraic.Zero

module Pandora.Paradigm.Primary.Algebraic.Sum

module Pandora.Paradigm.Primary.Algebraic.Product

module Pandora.Paradigm.Primary.Algebraic.Exponential

type Applicative t = (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t, Monoidal (-->) (-->) (:*:) (:*:) t)

type Alternative t = (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:+:) t, Monoidal (-->) (-->) (:*:) (:+:) t)

type Divisible t = (Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:*:) t, Monoidal (-->) (<--) (:*:) (:*:) t)

type Decidable t = (Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:+:) t, Monoidal (-->) (<--) (:*:) (:+:) t)

type Extractable t = Monoidal (<--) (-->) (:*:) (:*:) t

type Pointable t = Monoidal (-->) (-->) (:*:) (:*:) t

(!>-) :: Covariant (->) (->) t => t a -> b -> t b

(!!>-) :: (Covariant (->) (->) t, Covariant (->) (->) u) => t (u a) -> b -> t (u b)

(!!!>-) :: (Covariant (->) (->) t, Covariant (->) (->) u, Covariant (->) (->) v) => t (u (v a)) -> b -> t (u (v b))

(<-*-) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t (a -> b) -> t a -> t b infixl 8

(<-*--) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t (a -> b) -> t a -> t b infixl 7

(<-*---) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t (a -> b) -> t a -> t b infixl 6

(<-*----) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t (a -> b) -> t a -> t b infixl 5

(<-*-----) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t (a -> b) -> t a -> t b infixl 4

(<-*-----) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t (a -> b) -> t a -> t b infixl 4

(<-*------) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t (a -> b) -> t a -> t b infixl 3

(<-*-------) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t (a -> b) -> t a -> t b infixl 2

(<-*--------) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t (a -> b) -> t a -> t b infixl 1

(.-*-) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t b -> t a -> t b infixl 8

(.-*--) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t b -> t a -> t b infixl 7

(.-*---) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t b -> t a -> t b infixl 6

(.-*----) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t b -> t a -> t b infixl 5

(.-*-----) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t b -> t a -> t b infixl 4

(.-*-----) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t b -> t a -> t b infixl 4

(.-*------) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t b -> t a -> t b infixl 3

(.-*-------) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t b -> t a -> t b infixl 2

(.-*--------) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t b -> t a -> t b infixl 1

(<-*-*-) :: (Covariant (->) (->) t, Covariant (->) (->) u, Semimonoidal (-->) (:*:) (:*:) t, Semimonoidal (-->) (:*:) (:*:) u) => t (u (a -> b)) -> t (u a) -> t (u b) infixl 7

(.-*-*-) :: (Covariant (->) (->) t, Covariant (->) (->) u, Semimonoidal (-->) (:*:) (:*:) t, Semimonoidal (-->) (:*:) (:*:) u) => t (u b) -> t (u a) -> t (u b) infixl 7

loop :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t a -> t b

(<-+-) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:+:) t) => t b -> t a -> ((a :+: b) -> r) -> t r infixl 8

(.-+-) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:+:) t) => t a -> t a -> t a infixl 8

void :: Covariant (->) (->) t => t a -> t ()

empty :: Emptiable t => t a

point :: Pointable t => a -> t a

pass :: Pointable t => t ()

extract :: Extractable t => t a -> a

(<-||-) :: forall (m :: * -> * -> *) (p :: * -> * -> *) a b c. (Covariant m m (Flip p c), Interpreted m (Flip p c)) => m a b -> m (p a c) (p b c) infixl 8

(>-||-) :: forall (m :: * -> * -> *) (p :: * -> * -> *) a b c. (Contravariant m m (Flip p c), Interpreted m (Flip p c)) => m a b -> m (p b c) (p a c) infixl 8

(<-|-<-|-) :: forall (m :: * -> * -> *) (p :: * -> * -> *) a b c d. (Covariant m m (p a), Covariant m m (Flip p d), Interpreted m (Flip p d)) => (m a b :*: m c d) -> m (p a c) (p b d) infixl 6

(<-|->-|-) :: forall (m :: * -> * -> *) (p :: * -> * -> *) a b c d. (Covariant m m (Flip p c), Contravariant m m (p a), Interpreted m (Flip p c)) => (m a b :*: m c d) -> m (p a d) (p b c) infixl 6

(>-|-<-|-) :: forall (m :: * -> * -> *) (p :: * -> * -> *) a b c d. (Contravariant m m (Flip p d), Covariant m m (p b), Interpreted m (Flip p d)) => (m a b :*: m c d) -> m (p b c) (p a d) infixl 6

(>-|->-|-) :: forall (m :: * -> * -> *) (p :: * -> * -> *) a b c d. (Contravariant m m (p b), Contravariant m m (Flip p c), Interpreted m (Flip p c)) => (m a b :*: m c d) -> m (p b d) (p a c) infixl 6

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 (-->) (-->) (:*:) (:*:) ((->) 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 (-->) (:*:) (:*:) ((->) 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 (<--) (:*:) (:*:) 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)

(<<--------) :: (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)

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

Methods

(-|) :: ((s :*: a) -> b) -> a -> (s -> b)

(|-) :: (a -> (s -> b)) -> (s :*: a) -> b

(|--) :: (a -> (s -> b)) -> (s :*: a) -> b

(|---) :: (a -> (s -> b)) -> (s :*: a) -> b

(|----) :: (a -> (s -> b)) -> (s :*: a) -> b

(|-----) :: (a -> (s -> b)) -> (s :*: a) -> b

(|------) :: (a -> (s -> b)) -> (s :*: a) -> b

(|-------) :: (a -> (s -> b)) -> (s :*: a) -> b

(|--------) :: (a -> (s -> b)) -> (s :*: a) -> b

(|---------) :: (a -> (s -> b)) -> (s :*: a) -> b

(--|) :: ((s :*: a) -> b) -> a -> (s -> b)

(---|) :: ((s :*: a) -> b) -> a -> (s -> b)

(----|) :: ((s :*: a) -> b) -> a -> (s -> b)

(-----|) :: ((s :*: a) -> b) -> a -> (s -> b)

(------|) :: ((s :*: a) -> b) -> a -> (s -> b)

(-------|) :: ((s :*: a) -> b) -> a -> (s -> b)

(--------|) :: ((s :*: a) -> b) -> a -> (s -> b)

(---------|) :: ((s :*: a) -> b) -> a -> (s -> b)