Pandora.Paradigm.Inventory.Store

Documentation

newtype Store p a

Constructors

Store (((:*:) p :. (->) p) := a)

Instances

Interpreted (Store p)

Defined in Pandora.Paradigm.Inventory.Store

Associated Types

type Primary (Store p) a :: Type

Methods

run :: Store p a -> Primary (Store p) a

Covariant (Store p)

Defined in Pandora.Paradigm.Inventory.Store

Methods

(<$>) :: (a -> b) -> Store p a -> Store p b

comap :: (a -> b) -> Store p a -> Store p b

(<$) :: a -> Store p b -> Store p a

($>) :: Store p a -> b -> Store p b

void :: Store p a -> Store p ()

loeb :: Store p (a <-| Store p) -> Store p a

(<&>) :: Store p a -> (a -> b) -> Store p b

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

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

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

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

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

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

Extendable (Store p)

Defined in Pandora.Paradigm.Inventory.Store

Methods

(=>>) :: Store p a -> (Store p a -> b) -> Store p b

(<<=) :: (Store p a -> b) -> Store p a -> Store p b

extend :: (Store p a -> b) -> Store p a -> Store p b

duplicate :: Store p a -> (Store p :. Store p) := a

(=<=) :: (Store p b -> c) -> (Store p a -> b) -> Store p a -> c

(=>=) :: (Store p a -> b) -> (Store p b -> c) -> Store p a -> c

($=>>) :: Covariant u => (Store p a -> b) -> ((u :. Store p) := a) -> (u :. Store p) := b

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

Extractable (Store p)

Defined in Pandora.Paradigm.Inventory.Store

Methods

extract :: a <-| Store p

Comonad (Store p)

Defined in Pandora.Paradigm.Inventory.Store

Comonadic (Store p)

Defined in Pandora.Paradigm.Inventory.Store

Methods

flick :: Covariant u => (Store p :< u) ~> u

bring :: Extractable u => (Store p :< u) ~> Store p

Adjoint (Store s) (State s)

Defined in Pandora.Paradigm.Inventory

Methods

(-|) :: a -> (Store s a -> b) -> State s b

(|-) :: Store s a -> (a -> State s b) -> b

phi :: (Store s a -> b) -> a -> State s b

psi :: (a -> State s b) -> Store s a -> b

eta :: a -> (State s :. Store s) := a

epsilon :: ((Store s :. State s) := a) -> a

type Schematic Comonad (Store p) u

Defined in Pandora.Paradigm.Inventory.Store

type Schematic Comonad (Store p) u = ((:*:) p <:<.>:> ((->) p :: Type -> Type)) := u

type Primary (Store p) a

Defined in Pandora.Paradigm.Inventory.Store

type Primary (Store p) a = ((:*:) p :. ((->) p :: Type -> Type)) := a

type Storable s x = Adaptable x (Store s)

position :: Storable s t => t a -> s

access :: Storable s t => s -> a <-| t

retrofit :: (p -> p) -> Store p ~> Store p

Orphan instances

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

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

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

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

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

Methods

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