Pandora.Paradigm.Primary.Functor.Product

Documentation

data Product s a

Constructors

s :*: a infixr 1

Instances

Bivariant Product

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

(<->) :: (a -> b) -> (c -> d) -> Product a c -> Product b d

bimap :: (a -> b) -> (c -> d) -> Product a c -> Product b d

Covariant (Product s)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

(<$>) :: (a -> b) -> Product s a -> Product s b

comap :: (a -> b) -> Product s a -> Product s b

(<$) :: a -> Product s b -> Product s a

($>) :: Product s a -> b -> Product s b

void :: Product s a -> Product s ()

loeb :: Product s (a <-| Product s) -> Product s a

(<&>) :: Product s a -> (a -> b) -> Product s b

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

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

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

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

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

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

Extendable (Product s)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

(=>>) :: Product s a -> (Product s a -> b) -> Product s b

(<<=) :: (Product s a -> b) -> Product s a -> Product s b

extend :: (Product s a -> b) -> Product s a -> Product s b

duplicate :: Product s a -> (Product s :. Product s) := a

(=<=) :: (Product s b -> c) -> (Product s a -> b) -> Product s a -> c

(=>=) :: (Product s a -> b) -> (Product s b -> c) -> Product s a -> c

($=>>) :: Covariant u => (Product s a -> b) -> ((u :. Product s) := a) -> (u :. Product s) := b

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

Traversable (Product s)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

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

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

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

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

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

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

Extractable (Product a)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

extract :: a0 <-| Product a

Comonad (Product s)

Defined in Pandora.Paradigm.Primary.Functor.Product

Substructure ('Left :: Type -> Wye Type) (Product s)

Defined in Pandora.Paradigm.Structure

Associated Types

type Substructural 'Left (Product s) a

Methods

substructure :: Tagged 'Left (Product s a) :-. Substructural 'Left (Product s) a

Substructure ('Right :: Type -> Wye Type) (Product s)

Defined in Pandora.Paradigm.Structure

Associated Types

type Substructural 'Right (Product s) a

Methods

substructure :: Tagged 'Right (Product s a) :-. Substructural 'Right (Product s) a

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

Defined in Pandora.Paradigm.Primary.Functor

Methods

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

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

phi :: (Product s a -> b) -> a -> s -> b

psi :: (a -> s -> b) -> Product s a -> b

eta :: a -> ((->) s :. Product s) := a

epsilon :: ((Product s :. (->) s) := a) -> a

(Semigroup s, Semigroup a) => Semigroup (s :*: a)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

(+) :: (s :*: a) -> (s :*: a) -> s :*: a

(Ringoid s, Ringoid a) => Ringoid (s :*: a)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

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

(Monoid s, Monoid a) => Monoid (s :*: a)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

zero :: s :*: a

(Quasiring s, Quasiring a) => Quasiring (s :*: a)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

one :: s :*: a

(Group s, Group a) => Group (s :*: a)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

invert :: (s :*: a) -> s :*: a

(Supremum s, Supremum a) => Supremum (s :*: a)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

(\/) :: (s :*: a) -> (s :*: a) -> s :*: a

(Infimum s, Infimum a) => Infimum (s :*: a)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

(/\) :: (s :*: a) -> (s :*: a) -> s :*: a

(Lattice s, Lattice a) => Lattice (s :*: a)

Defined in Pandora.Paradigm.Primary.Functor.Product

(Setoid s, Setoid a) => Setoid (s :*: a)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

(==) :: (s :*: a) -> (s :*: a) -> Boolean

(/=) :: (s :*: a) -> (s :*: a) -> Boolean

Monotonic a s => Monotonic (s :*: a) s

Defined in Pandora.Paradigm.Structure

Methods

bypass :: (s -> r -> r) -> r -> (s :*: a) -> r

Covariant u => Covariant ((((->) s :: Type -> Type) <:<.>:> (:*:) s) := u)

Defined in Pandora.Paradigm.Inventory.State

Methods

(<$>) :: (a -> b) -> (((->) s <:<.>:> (:*:) s) := u) a -> (((->) s <:<.>:> (:*:) s) := u) b

comap :: (a -> b) -> (((->) s <:<.>:> (:*:) s) := u) a -> (((->) s <:<.>:> (:*:) s) := u) b

(<$) :: a -> (((->) s <:<.>:> (:*:) s) := u) b -> (((->) s <:<.>:> (:*:) s) := u) a

($>) :: (((->) s <:<.>:> (:*:) s) := u) a -> b -> (((->) s <:<.>:> (:*:) s) := u) b

void :: (((->) s <:<.>:> (:*:) s) := u) a -> (((->) s <:<.>:> (:*:) s) := u) ()

loeb :: (((->) s <:<.>:> (:*:) s) := u) (a <-| (((->) s <:<.>:> (:*:) s) := u)) -> (((->) s <:<.>:> (:*:) s) := u) a

(<&>) :: (((->) s <:<.>:> (:*:) s) := u) a -> (a -> b) -> (((->) s <:<.>:> (:*:) s) := u) b

(<$$>) :: Covariant u0 => (a -> b) -> (((((->) s <:<.>:> (:*:) s) := u) :. u0) := a) -> ((((->) s <:<.>:> (:*:) s) := u) :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> (((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. v)) := a) -> ((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> (((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. (v :. w))) := a) -> ((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => (((((->) s <:<.>:> (:*:) s) := u) :. u0) := a) -> (a -> b) -> ((((->) s <:<.>:> (:*:) s) := u) :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => (((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. v)) := a) -> (a -> b) -> ((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => (((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> ((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. (v :. w))) := b

Covariant u => Covariant (((:*:) p <:<.>:> ((->) p :: Type -> Type)) := u)

Defined in Pandora.Paradigm.Inventory.Store

Methods

(<$>) :: (a -> b) -> (((:*:) p <:<.>:> (->) p) := u) a -> (((:*:) p <:<.>:> (->) p) := u) b

comap :: (a -> b) -> (((:*:) p <:<.>:> (->) p) := u) a -> (((:*:) p <:<.>:> (->) p) := u) b

(<$) :: a -> (((:*:) p <:<.>:> (->) p) := u) b -> (((:*:) p <:<.>:> (->) p) := u) a

($>) :: (((:*:) p <:<.>:> (->) p) := u) a -> b -> (((:*:) p <:<.>:> (->) p) := u) b

void :: (((:*:) p <:<.>:> (->) p) := u) a -> (((:*:) p <:<.>:> (->) p) := u) ()

loeb :: (((:*:) p <:<.>:> (->) p) := u) (a <-| (((:*:) p <:<.>:> (->) p) := u)) -> (((:*:) p <:<.>:> (->) p) := u) a

(<&>) :: (((:*:) p <:<.>:> (->) p) := u) a -> (a -> b) -> (((:*:) p <:<.>:> (->) p) := u) b

(<$$>) :: Covariant u0 => (a -> b) -> (((((:*:) p <:<.>:> (->) p) := u) :. u0) := a) -> ((((:*:) p <:<.>:> (->) p) := u) :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> (((((:*:) p <:<.>:> (->) p) := u) :. (u0 :. v)) := a) -> ((((:*:) p <:<.>:> (->) p) := u) :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> (((((:*:) p <:<.>:> (->) p) := u) :. (u0 :. (v :. w))) := a) -> ((((:*:) p <:<.>:> (->) p) := u) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => (((((:*:) p <:<.>:> (->) p) := u) :. u0) := a) -> (a -> b) -> ((((:*:) p <:<.>:> (->) p) := u) :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => (((((:*:) p <:<.>:> (->) p) := u) :. (u0 :. v)) := a) -> (a -> b) -> ((((:*:) p <:<.>:> (->) p) := u) :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => (((((:*:) p <:<.>:> (->) p) := u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> ((((:*:) p <:<.>:> (->) p) := u) :. (u0 :. (v :. w))) := b

Covariant u => Covariant ((:*:) e <.:> u)

Defined in Pandora.Paradigm.Inventory.Accumulator

Methods

(<$>) :: (a -> b) -> ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b

comap :: (a -> b) -> ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b

(<$) :: a -> ((:*:) e <.:> u) b -> ((:*:) e <.:> u) a

($>) :: ((:*:) e <.:> u) a -> b -> ((:*:) e <.:> u) b

void :: ((:*:) e <.:> u) a -> ((:*:) e <.:> u) ()

loeb :: ((:*:) e <.:> u) (a <-| ((:*:) e <.:> u)) -> ((:*:) e <.:> u) a

(<&>) :: ((:*:) e <.:> u) a -> (a -> b) -> ((:*:) e <.:> u) b

(<$$>) :: Covariant u0 => (a -> b) -> ((((:*:) e <.:> u) :. u0) := a) -> (((:*:) e <.:> u) :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> ((((:*:) e <.:> u) :. (u0 :. v)) := a) -> (((:*:) e <.:> u) :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> ((((:*:) e <.:> u) :. (u0 :. (v :. w))) := a) -> (((:*:) e <.:> u) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => ((((:*:) e <.:> u) :. u0) := a) -> (a -> b) -> (((:*:) e <.:> u) :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => ((((:*:) e <.:> u) :. (u0 :. v)) := a) -> (a -> b) -> (((:*:) e <.:> u) :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((((:*:) e <.:> u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> (((:*:) e <.:> u) :. (u0 :. (v :. w))) := b

Covariant u => Covariant ((:*:) e <:.> u)

Defined in Pandora.Paradigm.Inventory.Equipment

Methods

(<$>) :: (a -> b) -> ((:*:) e <:.> u) a -> ((:*:) e <:.> u) b

comap :: (a -> b) -> ((:*:) e <:.> u) a -> ((:*:) e <:.> u) b

(<$) :: a -> ((:*:) e <:.> u) b -> ((:*:) e <:.> u) a

($>) :: ((:*:) e <:.> u) a -> b -> ((:*:) e <:.> u) b

void :: ((:*:) e <:.> u) a -> ((:*:) e <:.> u) ()

loeb :: ((:*:) e <:.> u) (a <-| ((:*:) e <:.> u)) -> ((:*:) e <:.> u) a

(<&>) :: ((:*:) e <:.> u) a -> (a -> b) -> ((:*:) e <:.> u) b

(<$$>) :: Covariant u0 => (a -> b) -> ((((:*:) e <:.> u) :. u0) := a) -> (((:*:) e <:.> u) :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> ((((:*:) e <:.> u) :. (u0 :. v)) := a) -> (((:*:) e <:.> u) :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> ((((:*:) e <:.> u) :. (u0 :. (v :. w))) := a) -> (((:*:) e <:.> u) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => ((((:*:) e <:.> u) :. u0) := a) -> (a -> b) -> (((:*:) e <:.> u) :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => ((((:*:) e <:.> u) :. (u0 :. v)) := a) -> (a -> b) -> (((:*:) e <:.> u) :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((((:*:) e <:.> u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> (((:*:) e <:.> u) :. (u0 :. (v :. w))) := b

Bindable u => Bindable ((((->) s :: Type -> Type) <:<.>:> (:*:) s) := u)

Defined in Pandora.Paradigm.Inventory.State

Methods

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

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

bind :: (a -> (((->) s <:<.>:> (:*:) s) := u) b) -> (((->) s <:<.>:> (:*:) s) := u) a -> (((->) s <:<.>:> (:*:) s) := u) b

join :: (((((->) s <:<.>:> (:*:) s) := u) :. (((->) s <:<.>:> (:*:) s) := u)) := a) -> (((->) s <:<.>:> (:*:) s) := u) a

(>=>) :: (a -> (((->) s <:<.>:> (:*:) s) := u) b) -> (b -> (((->) s <:<.>:> (:*:) s) := u) c) -> a -> (((->) s <:<.>:> (:*:) s) := u) c

(<=<) :: (b -> (((->) s <:<.>:> (:*:) s) := u) c) -> (a -> (((->) s <:<.>:> (:*:) s) := u) b) -> a -> (((->) s <:<.>:> (:*:) s) := u) c

($>>=) :: Covariant u0 => (a -> (((->) s <:<.>:> (:*:) s) := u) b) -> ((u0 :. (((->) s <:<.>:> (:*:) s) := u)) := a) -> (u0 :. (((->) s <:<.>:> (:*:) s) := u)) := b

(<>>=) :: ((((->) s <:<.>:> (:*:) s) := u) b -> c) -> (a -> (((->) s <:<.>:> (:*:) s) := u) b) -> (((->) s <:<.>:> (:*:) s) := u) a -> c

(Semigroup e, Pointable u, Bindable u) => Bindable ((:*:) e <.:> u)

Defined in Pandora.Paradigm.Inventory.Accumulator

Methods

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

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

bind :: (a -> ((:*:) e <.:> u) b) -> ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b

join :: ((((:*:) e <.:> u) :. ((:*:) e <.:> u)) := a) -> ((:*:) e <.:> u) a

(>=>) :: (a -> ((:*:) e <.:> u) b) -> (b -> ((:*:) e <.:> u) c) -> a -> ((:*:) e <.:> u) c

(<=<) :: (b -> ((:*:) e <.:> u) c) -> (a -> ((:*:) e <.:> u) b) -> a -> ((:*:) e <.:> u) c

($>>=) :: Covariant u0 => (a -> ((:*:) e <.:> u) b) -> ((u0 :. ((:*:) e <.:> u)) := a) -> (u0 :. ((:*:) e <.:> u)) := b

(<>>=) :: (((:*:) e <.:> u) b -> c) -> (a -> ((:*:) e <.:> u) b) -> ((:*:) e <.:> u) a -> c

Bindable u => Applicative ((((->) s :: Type -> Type) <:<.>:> (:*:) s) := u)

Defined in Pandora.Paradigm.Inventory.State

Methods

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

apply :: (((->) s <:<.>:> (:*:) s) := u) (a -> b) -> (((->) s <:<.>:> (:*:) s) := u) a -> (((->) s <:<.>:> (:*:) s) := u) b

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

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

forever :: (((->) s <:<.>:> (:*:) s) := u) a -> (((->) s <:<.>:> (:*:) s) := u) b

(<**>) :: Applicative u0 => (((((->) s <:<.>:> (:*:) s) := u) :. u0) := (a -> b)) -> (((((->) s <:<.>:> (:*:) s) := u) :. u0) := a) -> ((((->) s <:<.>:> (:*:) s) := u) :. u0) := b

(<***>) :: (Applicative u0, Applicative v) => (((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. v)) := (a -> b)) -> (((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. v)) := a) -> ((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. v)) := b

(<****>) :: (Applicative u0, Applicative v, Applicative w) => (((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. (v :. w))) := (a -> b)) -> (((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. (v :. w))) := a) -> ((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. (v :. w))) := b

(Semigroup e, Applicative u) => Applicative ((:*:) e <.:> u)

Defined in Pandora.Paradigm.Inventory.Accumulator

Methods

(<*>) :: ((:*:) e <.:> u) (a -> b) -> ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b

apply :: ((:*:) e <.:> u) (a -> b) -> ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b

(*>) :: ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b -> ((:*:) e <.:> u) b

(<*) :: ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b -> ((:*:) e <.:> u) a

forever :: ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b

(<**>) :: Applicative u0 => ((((:*:) e <.:> u) :. u0) := (a -> b)) -> ((((:*:) e <.:> u) :. u0) := a) -> (((:*:) e <.:> u) :. u0) := b

(<***>) :: (Applicative u0, Applicative v) => ((((:*:) e <.:> u) :. (u0 :. v)) := (a -> b)) -> ((((:*:) e <.:> u) :. (u0 :. v)) := a) -> (((:*:) e <.:> u) :. (u0 :. v)) := b

(<****>) :: (Applicative u0, Applicative v, Applicative w) => ((((:*:) e <.:> u) :. (u0 :. (v :. w))) := (a -> b)) -> ((((:*:) e <.:> u) :. (u0 :. (v :. w))) := a) -> (((:*:) e <.:> u) :. (u0 :. (v :. w))) := b

Alternative u => Alternative ((((->) s :: Type -> Type) <:<.>:> (:*:) s) := u)

Defined in Pandora.Paradigm.Inventory.State

Methods

(<+>) :: (((->) s <:<.>:> (:*:) s) := u) a -> (((->) s <:<.>:> (:*:) s) := u) a -> (((->) s <:<.>:> (:*:) s) := u) a

alter :: (((->) s <:<.>:> (:*:) s) := u) a -> (((->) s <:<.>:> (:*:) s) := u) a -> (((->) s <:<.>:> (:*:) s) := u) a

Avoidable u => Avoidable ((((->) s :: Type -> Type) <:<.>:> (:*:) s) := u)

Defined in Pandora.Paradigm.Inventory.State

Methods

empty :: (((->) s <:<.>:> (:*:) s) := u) a

Extendable u => Extendable (((:*:) p <:<.>:> ((->) p :: Type -> Type)) := u)

Defined in Pandora.Paradigm.Inventory.Store

Methods

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

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

extend :: ((((:*:) p <:<.>:> (->) p) := u) a -> b) -> (((:*:) p <:<.>:> (->) p) := u) a -> (((:*:) p <:<.>:> (->) p) := u) b

duplicate :: (((:*:) p <:<.>:> (->) p) := u) a -> ((((:*:) p <:<.>:> (->) p) := u) :. (((:*:) p <:<.>:> (->) p) := u)) := a

(=<=) :: ((((:*:) p <:<.>:> (->) p) := u) b -> c) -> ((((:*:) p <:<.>:> (->) p) := u) a -> b) -> (((:*:) p <:<.>:> (->) p) := u) a -> c

(=>=) :: ((((:*:) p <:<.>:> (->) p) := u) a -> b) -> ((((:*:) p <:<.>:> (->) p) := u) b -> c) -> (((:*:) p <:<.>:> (->) p) := u) a -> c

($=>>) :: Covariant u0 => ((((:*:) p <:<.>:> (->) p) := u) a -> b) -> ((u0 :. (((:*:) p <:<.>:> (->) p) := u)) := a) -> (u0 :. (((:*:) p <:<.>:> (->) p) := u)) := b

(<<=$) :: Covariant u0 => ((u0 :. (((:*:) p <:<.>:> (->) p) := u)) := a) -> ((((:*:) p <:<.>:> (->) p) := u) a -> b) -> (u0 :. (((:*:) p <:<.>:> (->) p) := u)) := b

Extendable u => Extendable ((:*:) e <:.> u)

Defined in Pandora.Paradigm.Inventory.Equipment

Methods

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

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

extend :: (((:*:) e <:.> u) a -> b) -> ((:*:) e <:.> u) a -> ((:*:) e <:.> u) b

duplicate :: ((:*:) e <:.> u) a -> (((:*:) e <:.> u) :. ((:*:) e <:.> u)) := a

(=<=) :: (((:*:) e <:.> u) b -> c) -> (((:*:) e <:.> u) a -> b) -> ((:*:) e <:.> u) a -> c

(=>=) :: (((:*:) e <:.> u) a -> b) -> (((:*:) e <:.> u) b -> c) -> ((:*:) e <:.> u) a -> c

($=>>) :: Covariant u0 => (((:*:) e <:.> u) a -> b) -> ((u0 :. ((:*:) e <:.> u)) := a) -> (u0 :. ((:*:) e <:.> u)) := b

(<<=$) :: Covariant u0 => ((u0 :. ((:*:) e <:.> u)) := a) -> (((:*:) e <:.> u) a -> b) -> (u0 :. ((:*:) e <:.> u)) := b

Pointable u => Pointable ((((->) s :: Type -> Type) <:<.>:> (:*:) s) := u)

Defined in Pandora.Paradigm.Inventory.State

Methods

point :: a |-> (((->) s <:<.>:> (:*:) s) := u)

(Pointable u, Monoid e) => Pointable ((:*:) e <.:> u)

Defined in Pandora.Paradigm.Inventory.Accumulator

Methods

point :: a |-> ((:*:) e <.:> u)

Monad u => Monad ((((->) s :: Type -> Type) <:<.>:> (:*:) s) := u)

Defined in Pandora.Paradigm.Inventory.State

Methods

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

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

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

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

Extractable u => Extractable (((:*:) p <:<.>:> ((->) p :: Type -> Type)) := u)

Defined in Pandora.Paradigm.Inventory.Store

Methods

extract :: a <-| (((:*:) p <:<.>:> (->) p) := u)

Extractable u => Extractable ((:*:) e <:.> u)

Defined in Pandora.Paradigm.Inventory.Equipment

Methods

extract :: a <-| ((:*:) e <:.> u)

type Substructural ('Left :: Type -> Wye Type) (Product s) a

Defined in Pandora.Paradigm.Structure

type Substructural ('Left :: Type -> Wye Type) (Product s) a = s

type Substructural ('Right :: Type -> Wye Type) (Product s) a

Defined in Pandora.Paradigm.Structure

type Substructural ('Right :: Type -> Wye Type) (Product s) a = a

type (:*:) = Product infixr 1

delta :: a -> a :*: a

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

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