Pandora.Paradigm.Basis.Twister

Documentation

data Twister t a

Constructors

Twister a ((t :. Twister t) := a)

Instances

Covariant Stack

Defined in Pandora.Paradigm.Structure.Stack

Methods

(<$>) :: (a -> b) -> Stack a -> Stack b

comap :: (a -> b) -> Stack a -> Stack b

(<$) :: a -> Stack b -> Stack a

($>) :: Stack a -> b -> Stack b

void :: Stack a -> Stack ()

loeb :: Stack (a <-| Stack) -> Stack a

(<&>) :: Stack a -> (a -> b) -> Stack b

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

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

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

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

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

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

Covariant Graph

Defined in Pandora.Paradigm.Structure.Graph

Methods

(<$>) :: (a -> b) -> Graph a -> Graph b

comap :: (a -> b) -> Graph a -> Graph b

(<$) :: a -> Graph b -> Graph a

($>) :: Graph a -> b -> Graph b

void :: Graph a -> Graph ()

loeb :: Graph (a <-| Graph) -> Graph a

(<&>) :: Graph a -> (a -> b) -> Graph b

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

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

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

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

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

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

Covariant Binary

Defined in Pandora.Paradigm.Structure.Binary

Methods

(<$>) :: (a -> b) -> Binary a -> Binary b

comap :: (a -> b) -> Binary a -> Binary b

(<$) :: a -> Binary b -> Binary a

($>) :: Binary a -> b -> Binary b

void :: Binary a -> Binary ()

loeb :: Binary (a <-| Binary) -> Binary a

(<&>) :: Binary a -> (a -> b) -> Binary b

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

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

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

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

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

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

Applicative Stack

Defined in Pandora.Paradigm.Structure.Stack

Methods

(<*>) :: Stack (a -> b) -> Stack a -> Stack b

apply :: Stack (a -> b) -> Stack a -> Stack b

(*>) :: Stack a -> Stack b -> Stack b

(<*) :: Stack a -> Stack b -> Stack a

forever :: Stack a -> Stack b

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

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

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

Alternative Stack

Defined in Pandora.Paradigm.Structure.Stack

Methods

(<+>) :: Stack a -> Stack a -> Stack a

alter :: Stack a -> Stack a -> Stack a

Avoidable Stack

Defined in Pandora.Paradigm.Structure.Stack

Methods

empty :: Stack a

Pointable Stack

Defined in Pandora.Paradigm.Structure.Stack

Methods

point :: a |-> Stack

Pointable Binary

Defined in Pandora.Paradigm.Structure.Binary

Methods

point :: a |-> Binary

Traversable Stack

Defined in Pandora.Paradigm.Structure.Stack

Methods

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

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

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

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

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

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

Traversable Graph

Defined in Pandora.Paradigm.Structure.Graph

Methods

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

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

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

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

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

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

Traversable Binary

Defined in Pandora.Paradigm.Structure.Binary

Methods

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

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

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

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

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

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

Lowerable Twister

Defined in Pandora.Paradigm.Basis.Twister

Methods

lower :: Extractable u => Twister u ~> u

Covariant t => Covariant (Twister t)

Defined in Pandora.Paradigm.Basis.Twister

Methods

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

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

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

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

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

loeb :: Twister t (a <-| Twister t) -> Twister t a

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

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

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

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

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

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

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

Alternative t => Bindable (Twister t)

Defined in Pandora.Paradigm.Basis.Twister

Methods

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

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

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

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

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

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

Applicative t => Applicative (Twister t)

Defined in Pandora.Paradigm.Basis.Twister

Methods

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

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

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

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

forever :: Twister t a -> Twister t b

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

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

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

Covariant t => Extendable (Twister t)

Defined in Pandora.Paradigm.Basis.Twister

Methods

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

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

extend :: (Twister t a -> b) -> Twister t a -> Twister t b

duplicate :: Twister t a -> (Twister t :. Twister t) := a

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

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

Avoidable t => Pointable (Twister t)

Defined in Pandora.Paradigm.Basis.Twister

Methods

point :: a |-> Twister t

(Avoidable t, Alternative t) => Monad (Twister t)

Defined in Pandora.Paradigm.Basis.Twister

Traversable t => Traversable (Twister t)

Defined in Pandora.Paradigm.Basis.Twister

Methods

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

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

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

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

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

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

Semigroup (Stack a)

Defined in Pandora.Paradigm.Structure.Stack

Methods

(+) :: Stack a -> Stack a -> Stack a

Monoid (Stack a)

Defined in Pandora.Paradigm.Structure.Stack

Methods

zero :: Stack a

Covariant t => Extractable (Twister t)

Defined in Pandora.Paradigm.Basis.Twister

Methods

extract :: a <-| Twister t

Covariant t => Comonad (Twister t)

Defined in Pandora.Paradigm.Basis.Twister

Setoid a => Setoid (Stack a)

Defined in Pandora.Paradigm.Structure.Stack

Methods

(==) :: Stack a -> Stack a -> Boolean

(/=) :: Stack a -> Stack a -> Boolean

Substructure (Left :: Type -> Wye Type) Binary

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Output Left Binary a = (r :: Type)

Methods

sub :: Binary a :-. Output Left Binary a

Substructure (Right :: Type -> Wye Type) Binary

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Output Right Binary a = (r :: Type)

Methods

sub :: Binary a :-. Output Right Binary a

Substructure (Left :: Type -> Wye Type) (Twister Wye)

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Output Left (Twister Wye) a = (r :: Type)

Methods

sub :: Twister Wye a :-. Output Left (Twister Wye) a

Substructure (Right :: Type -> Wye Type) (Twister Wye)

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Output Right (Twister Wye) a = (r :: Type)

Methods

sub :: Twister Wye a :-. Output Right (Twister Wye) a

(Semigroup a, forall b. Semigroup b => Semigroup (t b)) => Semigroup (Twister t a)

Defined in Pandora.Paradigm.Basis.Twister

Methods

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

(Monoid a, forall b. Semigroup b => Monoid (t b)) => Monoid (Twister t a)

Defined in Pandora.Paradigm.Basis.Twister

Methods

zero :: Twister t a

(Setoid a, forall b. Setoid b => Setoid (t b)) => Setoid (Twister t a)

Defined in Pandora.Paradigm.Basis.Twister

Methods

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

(/=) :: Twister t a -> Twister t a -> Boolean

type Nonempty Stack

Defined in Pandora.Paradigm.Structure.Stack

type Nonempty Stack = Twister Maybe

type Nonempty Graph

Defined in Pandora.Paradigm.Structure.Graph

type Nonempty Graph = Twister Edges

type Nonempty Binary

Defined in Pandora.Paradigm.Structure.Binary

type Nonempty Binary = Twister Wye

type Output (Left :: Type -> Wye Type) Binary a

Defined in Pandora.Paradigm.Structure.Binary

type Output (Left :: Type -> Wye Type) Binary a = (Left :: (Any :: Type) -> Wye (Any :: Type)) :# Binary a

type Output (Right :: Type -> Wye Type) Binary a

Defined in Pandora.Paradigm.Structure.Binary

type Output (Right :: Type -> Wye Type) Binary a = (Right :: (Any :: Type) -> Wye (Any :: Type)) :# Binary a

type Output (Left :: Type -> Wye Type) (Twister Wye) a

Defined in Pandora.Paradigm.Structure.Binary

type Output (Left :: Type -> Wye Type) (Twister Wye) a = Maybe ((Left :: (Any :: Type) -> Wye (Any :: Type)) :# Twister Wye a)

type Output (Right :: Type -> Wye Type) (Twister Wye) a

Defined in Pandora.Paradigm.Structure.Binary

type Output (Right :: Type -> Wye Type) (Twister Wye) a = Maybe ((Right :: (Any :: Type) -> Wye (Any :: Type)) :# Twister Wye a)

untwist :: Twister t a -> (t :. Twister t) a

coiterate :: Covariant t => (a |-> t) -> a |-> Twister t

section :: Comonad t => t ~> Twister t