Pandora.Paradigm.Schemes.UT

Documentation

newtype UT ct cu t u a

Constructors

UT ((u :. t) := a)

Instances

Monad u => Catchable e (Conclusion e <.:> u :: Type -> Type)

Defined in Pandora.Paradigm.Primary.Functor.Conclusion

Methods

catch :: forall (a :: k). (Conclusion e <.:> u) a -> (e -> (Conclusion e <.:> u) a) -> (Conclusion e <.:> u) a

(Covariant t, Covariant u) => Covariant (t <.:> u)

Defined in Pandora.Paradigm.Schemes.UT

Methods

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

comap :: (a -> b) -> (t <.:> u) a -> (t <.:> u) b

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

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

void :: (t <.:> u) a -> (t <.:> u) ()

loeb :: (t <.:> u) (a <:= (t <.:> u)) -> (t <.:> u) a

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

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

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

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

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

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

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

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

(.#...) :: ((t <.:> u) ~ v a, (t <.:> u) ~ 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

(.#....) :: ((t <.:> u) ~ v a, (t <.:> u) ~ v b, (t <.:> u) ~ 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 u0 => b -> (((t <.:> u) :. u0) := a) -> ((t <.:> u) :. u0) := b

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

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

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

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

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

(Traversable t, Bindable t, Applicative u, Monad u) => Bindable (t <.:> u)

Defined in Pandora.Paradigm.Schemes.UT

Methods

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

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

bind :: (a -> (t <.:> u) b) -> (t <.:> u) a -> (t <.:> u) b

join :: (((t <.:> u) :. (t <.:> u)) := a) -> (t <.:> u) a

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

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

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

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

(Applicative t, Applicative u) => Applicative (t <.:> u)

Defined in Pandora.Paradigm.Schemes.UT

Methods

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

apply :: (t <.:> u) (a -> b) -> (t <.:> u) a -> (t <.:> u) b

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

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

forever :: (t <.:> u) a -> (t <.:> u) b

(<%>) :: (t <.:> u) a -> (t <.:> u) (a -> b) -> (t <.:> u) b

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

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

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

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

(Semigroup e, Extendable u) => Extendable (((->) e :: Type -> Type) <.:> u)

Defined in Pandora.Paradigm.Inventory.Imprint

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

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

(Extractable t, Extractable u) => Extractable (t <.:> u)

Defined in Pandora.Paradigm.Schemes.UT

Methods

extract :: a <:= (t <.:> u)

(Pointable t, Pointable u) => Pointable (t <.:> u)

Defined in Pandora.Paradigm.Schemes.UT

Methods

point :: a :=> (t <.:> u)

pass :: (t <.:> u) ()

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

Defined in Pandora.Paradigm.Inventory.Accumulator

Methods

point :: a :=> ((:*:) e <.:> u)

pass :: ((:*:) e <.:> u) ()

(Covariant (t <.:> v), Covariant (w <:.> u), Adjoint v u, Adjoint t w) => Adjoint (t <.:> v) (w <:.> u)

Defined in Pandora.Paradigm.Schemes

Methods

(-|) :: a -> ((t <.:> v) a -> b) -> (w <:.> u) b

(|-) :: (t <.:> v) a -> (a -> (w <:.> u) b) -> b

phi :: ((t <.:> v) a -> b) -> a -> (w <:.> u) b

psi :: (a -> (w <:.> u) b) -> (t <.:> v) a -> b

eta :: a -> ((w <:.> u) :. (t <.:> v)) := a

epsilon :: (((t <.:> v) :. (w <:.> u)) := a) -> a

(-|$) :: Covariant v0 => v0 a -> ((t <.:> v) a -> b) -> v0 ((w <:.> u) b)

($|-) :: Covariant v0 => v0 ((t <.:> v) a) -> (a -> (w <:.> u) b) -> v0 b

($$|-) :: (Covariant v0, Covariant w0) => ((v0 :. (w0 :. (t <.:> v))) := a) -> (a -> (w <:.> u) b) -> (v0 :. w0) := b

($$$|-) :: (Covariant v0, Covariant w0, Covariant x) => ((v0 :. (w0 :. (x :. (t <.:> v)))) := a) -> (a -> (w <:.> u) b) -> (v0 :. (w0 :. x)) := b

($$$$|-) :: (Covariant v0, Covariant w0, Covariant x, Covariant y) => ((v0 :. (w0 :. (x :. (y :. (t <.:> v))))) := a) -> (a -> (w <:.> u) b) -> (v0 :. (w0 :. (x :. y))) := b

(Covariant (t <.:> v), Covariant (w <.:> u), Adjoint t u, Adjoint v w) => Adjoint (t <.:> v) (w <.:> u)

Defined in Pandora.Paradigm.Schemes

Methods

(-|) :: a -> ((t <.:> v) a -> b) -> (w <.:> u) b

(|-) :: (t <.:> v) a -> (a -> (w <.:> u) b) -> b

phi :: ((t <.:> v) a -> b) -> a -> (w <.:> u) b

psi :: (a -> (w <.:> u) b) -> (t <.:> v) a -> b

eta :: a -> ((w <.:> u) :. (t <.:> v)) := a

epsilon :: (((t <.:> v) :. (w <.:> u)) := a) -> a

(-|$) :: Covariant v0 => v0 a -> ((t <.:> v) a -> b) -> v0 ((w <.:> u) b)

($|-) :: Covariant v0 => v0 ((t <.:> v) a) -> (a -> (w <.:> u) b) -> v0 b

($$|-) :: (Covariant v0, Covariant w0) => ((v0 :. (w0 :. (t <.:> v))) := a) -> (a -> (w <.:> u) b) -> (v0 :. w0) := b

($$$|-) :: (Covariant v0, Covariant w0, Covariant x) => ((v0 :. (w0 :. (x :. (t <.:> v)))) := a) -> (a -> (w <.:> u) b) -> (v0 :. (w0 :. x)) := b

($$$$|-) :: (Covariant v0, Covariant w0, Covariant x, Covariant y) => ((v0 :. (w0 :. (x :. (y :. (t <.:> v))))) := a) -> (a -> (w <.:> u) b) -> (v0 :. (w0 :. (x :. y))) := b

(Covariant (v <:.> t), Covariant (w <.:> u), Adjoint t u, Adjoint v w) => Adjoint (v <:.> t) (w <.:> u)

Defined in Pandora.Paradigm.Schemes

Methods

(-|) :: a -> ((v <:.> t) a -> b) -> (w <.:> u) b

(|-) :: (v <:.> t) a -> (a -> (w <.:> u) b) -> b

phi :: ((v <:.> t) a -> b) -> a -> (w <.:> u) b

psi :: (a -> (w <.:> u) b) -> (v <:.> t) a -> b

eta :: a -> ((w <.:> u) :. (v <:.> t)) := a

epsilon :: (((v <:.> t) :. (w <.:> u)) := a) -> a

(-|$) :: Covariant v0 => v0 a -> ((v <:.> t) a -> b) -> v0 ((w <.:> u) b)

($|-) :: Covariant v0 => v0 ((v <:.> t) a) -> (a -> (w <.:> u) b) -> v0 b

($$|-) :: (Covariant v0, Covariant w0) => ((v0 :. (w0 :. (v <:.> t))) := a) -> (a -> (w <.:> u) b) -> (v0 :. w0) := b

($$$|-) :: (Covariant v0, Covariant w0, Covariant x) => ((v0 :. (w0 :. (x :. (v <:.> t)))) := a) -> (a -> (w <.:> u) b) -> (v0 :. (w0 :. x)) := b

($$$$|-) :: (Covariant v0, Covariant w0, Covariant x, Covariant y) => ((v0 :. (w0 :. (x :. (y :. (v <:.> t))))) := a) -> (a -> (w <.:> u) b) -> (v0 :. (w0 :. (x :. y))) := b

Pointable t => Liftable (UT Covariant Covariant t)

Defined in Pandora.Paradigm.Schemes.UT

Methods

lift :: forall (u :: Type -> Type). Covariant u => u ~> UT Covariant Covariant t u

Extractable t => Lowerable (UT Covariant Covariant t)

Defined in Pandora.Paradigm.Schemes.UT

Methods

lower :: forall (u :: Type -> Type). Covariant u => UT Covariant Covariant t u ~> u

Interpreted (UT ct cu t u)

Defined in Pandora.Paradigm.Schemes.UT

Associated Types

type Primary (UT ct cu t u) a

Methods

run :: UT ct cu t u a -> Primary (UT ct cu t u) a

unite :: Primary (UT ct cu t u) a -> UT ct cu t u a

(||=) :: Interpreted u0 => (Primary (UT ct cu t u) a -> Primary u0 b) -> UT ct cu t u a -> u0 b

(=||) :: Interpreted u0 => (UT ct cu t u a -> u0 b) -> Primary (UT ct cu t u) a -> Primary u0 b

(<$||=) :: (Covariant j, Interpreted u0) => (Primary (UT ct cu t u) a -> Primary u0 b) -> (j := UT ct cu t u a) -> j := u0 b

(<$$||=) :: (Covariant j, Covariant k, Interpreted u0) => (Primary (UT ct cu t u) a -> Primary u0 b) -> ((j :. k) := UT ct cu t u a) -> (j :. k) := u0 b

(<$$$||=) :: (Covariant j, Covariant k, Covariant l, Interpreted u0) => (Primary (UT ct cu t u) a -> Primary u0 b) -> ((j :. (k :. l)) := UT ct cu t u a) -> (j :. (k :. l)) := u0 b

(<$$$$||=) :: (Covariant j, Covariant k, Covariant l, Covariant m, Interpreted u0) => (Primary (UT ct cu t u) a -> Primary u0 b) -> ((j :. (k :. (l :. m))) := UT ct cu t u a) -> (j :. (k :. (l :. m))) := u0 b

(=||$>) :: (Covariant j, Interpreted u0) => (UT ct cu t u a -> u0 b) -> (j := Primary (UT ct cu t u) a) -> j := Primary u0 b

(=||$$>) :: (Covariant j, Covariant k, Interpreted u0) => (UT ct cu t u a -> u0 b) -> ((j :. k) := Primary (UT ct cu t u) a) -> (j :. k) := Primary u0 b

(=||$$$>) :: (Covariant j, Covariant k, Covariant l, Interpreted u0) => (UT ct cu t u a -> u0 b) -> ((j :. (k :. l)) := Primary (UT ct cu t u) a) -> (j :. (k :. l)) := Primary u0 b

(=||$$$$>) :: (Covariant j, Covariant k, Covariant l, Covariant m, Interpreted u0) => (UT ct cu t u a -> u0 b) -> ((j :. (k :. (l :. m))) := Primary (UT ct cu t u) a) -> (j :. (k :. (l :. m))) := Primary u0 b

type Primary (UT ct cu t u) a

Defined in Pandora.Paradigm.Schemes.UT

type Primary (UT ct cu t u) a = (u :. t) := a

type (<.:>) = UT Covariant Covariant infixr 3

type (>.:>) = UT Contravariant Covariant infixr 3

type (<.:<) = UT Covariant Contravariant infixr 3

type (>.:<) = UT Contravariant Contravariant infixr 3