Pandora.Paradigm.Structure.Modification.Comprehension

Documentation

newtype Comprehension t a

Constructors

Comprehension ((t <:.> Construction t) := a)

Instances

Covariant (t <:.> Construction t) => Covariant (Comprehension t)

Defined in Pandora.Paradigm.Structure.Modification.Comprehension

Methods

(<$>) :: (a -> b) -> Comprehension t a -> Comprehension t b

comap :: (a -> b) -> Comprehension t a -> Comprehension t b

(<$) :: a -> Comprehension t b -> Comprehension t a

($>) :: Comprehension t a -> b -> Comprehension t b

void :: Comprehension t a -> Comprehension t ()

loeb :: Comprehension t (a <:= Comprehension t) -> Comprehension t a

(<&>) :: Comprehension t a -> (a -> b) -> Comprehension t b

(<$$>) :: Covariant u => (a -> b) -> ((Comprehension t :. u) := a) -> (Comprehension t :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Comprehension t :. (u :. v)) := a) -> (Comprehension t :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Comprehension t :. (u :. (v :. w))) := a) -> (Comprehension t :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Comprehension t :. u) := a) -> (a -> b) -> (Comprehension t :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Comprehension t :. (u :. v)) := a) -> (a -> b) -> (Comprehension t :. (u :. v)) := b

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

(.#..) :: (Comprehension t ~ v a, Category v) => v c d -> ((v a :. v b) := c) -> (v a :. v b) := d

(.#...) :: (Comprehension t ~ v a, Comprehension t ~ v b, Category v, Covariant (v a), Covariant (v b)) => v d e -> ((v a :. (v b :. v c)) := d) -> (v a :. (v b :. v c)) := e

(.#....) :: (Comprehension t ~ v a, Comprehension t ~ v b, Comprehension t ~ v c, Category v, Covariant (v a), Covariant (v b), Covariant (v c)) => v e f -> ((v a :. (v b :. (v c :. v d))) := e) -> (v a :. (v b :. (v c :. v d))) := f

(<$$) :: Covariant u => b -> ((Comprehension t :. u) := a) -> (Comprehension t :. u) := b

(<$$$) :: (Covariant u, Covariant v) => b -> ((Comprehension t :. (u :. v)) := a) -> (Comprehension t :. (u :. v)) := b

(<$$$$) :: (Covariant u, Covariant v, Covariant w) => b -> ((Comprehension t :. (u :. (v :. w))) := a) -> (Comprehension t :. (u :. (v :. w))) := b

($$>) :: Covariant u => ((Comprehension t :. u) := a) -> b -> (Comprehension t :. u) := b

($$$>) :: (Covariant u, Covariant v) => ((Comprehension t :. (u :. v)) := a) -> b -> (Comprehension t :. (u :. v)) := b

($$$$>) :: (Covariant u, Covariant v, Covariant w) => ((Comprehension t :. (u :. (v :. w))) := a) -> b -> (Comprehension t :. (u :. (v :. w))) := b

(forall a. Semigroup ((t <:.> Construction t) := a), Bindable t) => Bindable (Comprehension t)

Defined in Pandora.Paradigm.Structure.Modification.Comprehension

Methods

(>>=) :: Comprehension t a -> (a -> Comprehension t b) -> Comprehension t b

(=<<) :: (a -> Comprehension t b) -> Comprehension t a -> Comprehension t b

bind :: (a -> Comprehension t b) -> Comprehension t a -> Comprehension t b

join :: ((Comprehension t :. Comprehension t) := a) -> Comprehension t a

(>=>) :: (a -> Comprehension t b) -> (b -> Comprehension t c) -> a -> Comprehension t c

(<=<) :: (b -> Comprehension t c) -> (a -> Comprehension t b) -> a -> Comprehension t c

($>>=) :: Covariant u => ((u :. Comprehension t) := a) -> (a -> Comprehension t b) -> (u :. Comprehension t) := b

(forall a. Semigroup ((t <:.> Construction t) := a), Bindable t, Pointable t ((->) :: Type -> Type -> Type), Avoidable t) => Applicative (Comprehension t)

Defined in Pandora.Paradigm.Structure.Modification.Comprehension

Methods

(<*>) :: Comprehension t (a -> b) -> Comprehension t a -> Comprehension t b

apply :: Comprehension t (a -> b) -> Comprehension t a -> Comprehension t b

(*>) :: Comprehension t a -> Comprehension t b -> Comprehension t b

(<*) :: Comprehension t a -> Comprehension t b -> Comprehension t a

forever :: Comprehension t a -> Comprehension t b

(<%>) :: Comprehension t a -> Comprehension t (a -> b) -> Comprehension t b

(<**>) :: Applicative u => ((Comprehension t :. u) := (a -> b)) -> ((Comprehension t :. u) := a) -> (Comprehension t :. u) := b

(<***>) :: (Applicative u, Applicative v) => ((Comprehension t :. (u :. v)) := (a -> b)) -> ((Comprehension t :. (u :. v)) := a) -> (Comprehension t :. (u :. v)) := b

(<****>) :: (Applicative u, Applicative v, Applicative w) => ((Comprehension t :. (u :. (v :. w))) := (a -> b)) -> ((Comprehension t :. (u :. (v :. w))) := a) -> (Comprehension t :. (u :. (v :. w))) := b

Applicative (Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

Methods

(<*>) :: Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) (a -> b) -> Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) a -> Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) b

apply :: Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) (a -> b) -> Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) a -> Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) b

(*>) :: Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) a -> Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) b -> Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) b

(<*) :: Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) a -> Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) b -> Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) a

forever :: Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) a -> Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) b

(<%>) :: Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) a -> Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) (a -> b) -> Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) b

(<**>) :: Applicative u => ((Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) :. u) := (a -> b)) -> ((Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) :. u) := a) -> (Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) :. u) := b

(<***>) :: (Applicative u, Applicative v) => ((Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) :. (u :. v)) := (a -> b)) -> ((Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) :. (u :. v)) := a) -> (Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) :. (u :. v)) := b

(<****>) :: (Applicative u, Applicative v, Applicative w) => ((Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) :. (u :. (v :. w))) := (a -> b)) -> ((Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) :. (u :. (v :. w))) := a) -> (Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:)) :. (u :. (v :. w))) := b

Alternative t => Alternative (Comprehension t)

Defined in Pandora.Paradigm.Structure.Modification.Comprehension

Methods

(<+>) :: Comprehension t a -> Comprehension t a -> Comprehension t a

alter :: Comprehension t a -> Comprehension t a -> Comprehension t a

(Avoidable t, Alternative t) => Avoidable (Comprehension t)

Defined in Pandora.Paradigm.Structure.Modification.Comprehension

Methods

empty :: Comprehension t a

(forall a. Semigroup ((t <:.> Construction t) := a), Pointable t ((->) :: Type -> Type -> Type), Avoidable t, Bindable t) => Monad (Comprehension t)

Defined in Pandora.Paradigm.Structure.Modification.Comprehension

Methods

(>>=-) :: Comprehension t a -> Comprehension t b -> Comprehension t a

(->>=) :: Comprehension t a -> Comprehension t b -> Comprehension t b

(-=<<) :: Comprehension t a -> Comprehension t b -> Comprehension t b

(=<<-) :: Comprehension t a -> Comprehension t b -> Comprehension t a

Traversable (t <:.> Construction t) => Traversable (Comprehension t)

Defined in Pandora.Paradigm.Structure.Modification.Comprehension

Methods

(->>) :: (Pointable u (->), Applicative u) => Comprehension t a -> (a -> u b) -> (u :. Comprehension t) := b

traverse :: (Pointable u (->), Applicative u) => (a -> u b) -> Comprehension t a -> (u :. Comprehension t) := b

sequence :: (Pointable u (->), Applicative u) => ((Comprehension t :. u) := a) -> (u :. Comprehension t) := a

(->>>) :: (Pointable u (->), Applicative u, Traversable v) => ((v :. Comprehension t) := a) -> (a -> u b) -> (u :. (v :. Comprehension t)) := b

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

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

Interpreted (Comprehension t)

Defined in Pandora.Paradigm.Structure.Modification.Comprehension

Associated Types

type Primary (Comprehension t) a

Methods

run :: Comprehension t a -> Primary (Comprehension t) a

unite :: Primary (Comprehension t) a -> Comprehension t a

(||=) :: Interpreted u => (Primary (Comprehension t) a -> Primary u b) -> Comprehension t a -> u b

(=||) :: Interpreted u => (Comprehension t a -> u b) -> Primary (Comprehension t) a -> Primary u b

(<$||=) :: (Covariant j, Interpreted u) => (Primary (Comprehension t) a -> Primary u b) -> (j := Comprehension t a) -> j := u b

(<$$||=) :: (Covariant j, Covariant k, Interpreted u) => (Primary (Comprehension t) a -> Primary u b) -> ((j :. k) := Comprehension t a) -> (j :. k) := u b

(<$$$||=) :: (Covariant j, Covariant k, Covariant l, Interpreted u) => (Primary (Comprehension t) a -> Primary u b) -> ((j :. (k :. l)) := Comprehension t a) -> (j :. (k :. l)) := u b

(<$$$$||=) :: (Covariant j, Covariant k, Covariant l, Covariant m, Interpreted u) => (Primary (Comprehension t) a -> Primary u b) -> ((j :. (k :. (l :. m))) := Comprehension t a) -> (j :. (k :. (l :. m))) := u b

(=||$>) :: (Covariant j, Interpreted u) => (Comprehension t a -> u b) -> (j := Primary (Comprehension t) a) -> j := Primary u b

(=||$$>) :: (Covariant j, Covariant k, Interpreted u) => (Comprehension t a -> u b) -> ((j :. k) := Primary (Comprehension t) a) -> (j :. k) := Primary u b

(=||$$$>) :: (Covariant j, Covariant k, Covariant l, Interpreted u) => (Comprehension t a -> u b) -> ((j :. (k :. l)) := Primary (Comprehension t) a) -> (j :. (k :. l)) := Primary u b

(=||$$$$>) :: (Covariant j, Covariant k, Covariant l, Covariant m, Interpreted u) => (Comprehension t a -> u b) -> ((j :. (k :. (l :. m))) := Primary (Comprehension t) a) -> (j :. (k :. (l :. m))) := Primary u b

Nullable (t <:.> Construction t) => Nullable (Comprehension t :: Type -> Type)

Defined in Pandora.Paradigm.Structure.Modification.Comprehension

Methods

null :: forall (a :: k). (Predicate :. Comprehension t) := a

(Avoidable t, Pointable t ((->) :: Type -> Type -> Type)) => Pointable (Comprehension t) ((->) :: Type -> Type -> Type)

Defined in Pandora.Paradigm.Structure.Modification.Comprehension

Methods

point :: a -> Comprehension t a

Morphable ('Into (Comprehension Maybe)) (Tap ((List <:.:> List) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into (Comprehension Maybe)) (Tap ((List <:.:> List) := (:*:))) :: Type -> Type

Methods

morphing :: (Tagged ('Into (Comprehension Maybe)) <:.> Tap ((List <:.:> List) := (:*:))) ~> Morphing ('Into (Comprehension Maybe)) (Tap ((List <:.:> List) := (:*:)))

Covariant_ (t <:.> Construction t) ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) => Covariant_ (Comprehension t) ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type)

Defined in Pandora.Paradigm.Structure.Modification.Comprehension

Methods

(-<$>-) :: (a -> b) -> Comprehension t a -> Comprehension t b

Semigroup ((t <:.> Construction t) := a) => Semigroup (Comprehension t a)

Defined in Pandora.Paradigm.Structure.Modification.Comprehension

Methods

(+) :: Comprehension t a -> Comprehension t a -> Comprehension t a

Monoid ((t <:.> Construction t) := a) => Monoid (Comprehension t a)

Defined in Pandora.Paradigm.Structure.Modification.Comprehension

Methods

zero :: Comprehension t a

Setoid ((t <:.> Construction t) := a) => Setoid (Comprehension t a)

Defined in Pandora.Paradigm.Structure.Modification.Comprehension

Methods

(==) :: Comprehension t a -> Comprehension t a -> Boolean

(!=) :: Comprehension t a -> Comprehension t a -> Boolean

(Covariant t, Covariant_ t ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type), Pointable t ((->) :: Type -> Type -> Type)) => Morphable ('Push :: a -> Morph a) (Comprehension t)

Defined in Pandora.Paradigm.Structure.Modification.Comprehension

Associated Types

type Morphing 'Push (Comprehension t) :: Type -> Type

Methods

morphing :: (Tagged 'Push <:.> Comprehension t) ~> Morphing 'Push (Comprehension t)

type Primary (Comprehension t) a

Defined in Pandora.Paradigm.Structure.Modification.Comprehension

type Primary (Comprehension t) a = (t <:.> Construction t) := a

type Morphing ('Into (Comprehension Maybe)) (Tap ((List <:.:> List) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into (Comprehension Maybe)) (Tap ((List <:.:> List) := (:*:))) = Comprehension Maybe

type Morphing ('Push :: a -> Morph a) (Comprehension t)

Defined in Pandora.Paradigm.Structure.Modification.Comprehension

type Morphing ('Push :: a -> Morph a) (Comprehension t) = (Identity <:.:> Comprehension t) := ((->) :: Type -> Type -> Type)

type Zipper (Comprehension Maybe) (('Left :: a1 -> Wye a1) ::: ('Right :: a2 -> Wye a2) :: k -> k' -> Type)

Defined in Pandora.Paradigm.Structure.Some.List

type Zipper (Comprehension Maybe) (('Left :: a1 -> Wye a1) ::: ('Right :: a2 -> Wye a2) :: k -> k' -> Type) = Tap ((Comprehension Maybe <:.:> Comprehension Maybe) := (:*:))

Orphan instances

(Covariant t, Covariant_ t ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type), Pointable t ((->) :: Type -> Type -> Type)) => Morphable ('Push :: a -> Morph a) (Comprehension t)

Associated Types

type Morphing 'Push (Comprehension t) :: Type -> Type

Methods

morphing :: (Tagged 'Push <:.> Comprehension t) ~> Morphing 'Push (Comprehension t)