NumHask.Shape

numbers with a shape

Documentation

class HasShape f where

Not everything that has a shape is representable.

todo: Structure is a useful alternative concept/naming convention

Associated Types

type Shape f

Methods

shape :: f a -> Shape f

Instances

Dimensions r => HasShape (Array c r)

Defined in NumHask.Array

Associated Types

type Shape (Array c r) :: Type

Methods

shape :: Array c r a -> Shape (Array c r)

Representable

Representable has most of what's needed to define numbers that have elements (aka scalars) and a fixed shape.

class Distributive f => Representable (f :: Type -> Type) where

A Functor f is Representable if tabulate and index witness an isomorphism to (->) x.

Every Distributive Functor is actually Representable.

Every Representable Functor from Hask to Hask is a right adjoint.

tabulate . index  ≡ id
index . tabulate  ≡ id
tabulate . return ≡ return

Minimal complete definition

Nothing

Associated Types

type Rep (f :: Type -> Type) :: Type

If no definition is provided, this will default to GRep.

Methods

tabulate :: (Rep f -> a) -> f a

fmap f . tabulate ≡ tabulate . fmap f

If no definition is provided, this will default to gtabulate.

index :: f a -> Rep f -> a

If no definition is provided, this will default to gindex.

Instances

Representable Par1

Defined in Data.Functor.Rep

Associated Types

type Rep Par1 :: Type

Methods

tabulate :: (Rep Par1 -> a) -> Par1 a

index :: Par1 a -> Rep Par1 -> a

Representable Complex

Defined in Data.Functor.Rep

Associated Types

type Rep Complex :: Type

Methods

tabulate :: (Rep Complex -> a) -> Complex a

index :: Complex a -> Rep Complex -> a

Representable Identity

Defined in Data.Functor.Rep

Associated Types

type Rep Identity :: Type

Methods

tabulate :: (Rep Identity -> a) -> Identity a

index :: Identity a -> Rep Identity -> a

Representable Dual

Defined in Data.Functor.Rep

Associated Types

type Rep Dual :: Type

Methods

tabulate :: (Rep Dual -> a) -> Dual a

index :: Dual a -> Rep Dual -> a

Representable Sum

Defined in Data.Functor.Rep

Associated Types

type Rep Sum :: Type

Methods

tabulate :: (Rep Sum -> a) -> Sum a

index :: Sum a -> Rep Sum -> a

Representable Product

Defined in Data.Functor.Rep

Associated Types

type Rep Product :: Type

Methods

tabulate :: (Rep Product -> a) -> Product a

index :: Product a -> Rep Product -> a

Representable Range

Defined in NumHask.Data.Range

Associated Types

type Rep Range :: Type

Methods

tabulate :: (Rep Range -> a) -> Range a

index :: Range a -> Rep Range -> a

Representable (U1 :: Type -> Type)

Defined in Data.Functor.Rep

Associated Types

type Rep U1 :: Type

Methods

tabulate :: (Rep U1 -> a) -> U1 a

index :: U1 a -> Rep U1 -> a

Representable f => Representable (Co f)

Defined in Data.Functor.Rep

Associated Types

type Rep (Co f) :: Type

Methods

tabulate :: (Rep (Co f) -> a) -> Co f a

index :: Co f a -> Rep (Co f) -> a

Representable (Proxy :: Type -> Type)

Defined in Data.Functor.Rep

Associated Types

type Rep Proxy :: Type

Methods

tabulate :: (Rep Proxy -> a) -> Proxy a

index :: Proxy a -> Rep Proxy -> a

Representable f => Representable (Cofree f)

Defined in Data.Functor.Rep

Associated Types

type Rep (Cofree f) :: Type

Methods

tabulate :: (Rep (Cofree f) -> a) -> Cofree f a

index :: Cofree f a -> Rep (Cofree f) -> a

Representable f => Representable (Rec1 f)

Defined in Data.Functor.Rep

Associated Types

type Rep (Rec1 f) :: Type

Methods

tabulate :: (Rep (Rec1 f) -> a) -> Rec1 f a

index :: Rec1 f a -> Rep (Rec1 f) -> a

Representable w => Representable (TracedT s w)

Defined in Data.Functor.Rep

Associated Types

type Rep (TracedT s w) :: Type

Methods

tabulate :: (Rep (TracedT s w) -> a) -> TracedT s w a

index :: TracedT s w a -> Rep (TracedT s w) -> a

Representable m => Representable (IdentityT m)

Defined in Data.Functor.Rep

Associated Types

type Rep (IdentityT m) :: Type

Methods

tabulate :: (Rep (IdentityT m) -> a) -> IdentityT m a

index :: IdentityT m a -> Rep (IdentityT m) -> a

Representable (Tagged t)

Defined in Data.Functor.Rep

Associated Types

type Rep (Tagged t) :: Type

Methods

tabulate :: (Rep (Tagged t) -> a) -> Tagged t a

index :: Tagged t a -> Rep (Tagged t) -> a

Representable f => Representable (Reverse f)

Defined in Data.Functor.Rep

Associated Types

type Rep (Reverse f) :: Type

Methods

tabulate :: (Rep (Reverse f) -> a) -> Reverse f a

index :: Reverse f a -> Rep (Reverse f) -> a

Representable f => Representable (Backwards f)

Defined in Data.Functor.Rep

Associated Types

type Rep (Backwards f) :: Type

Methods

tabulate :: (Rep (Backwards f) -> a) -> Backwards f a

index :: Backwards f a -> Rep (Backwards f) -> a

Representable ((->) e :: Type -> Type)

Defined in Data.Functor.Rep

Associated Types

type Rep ((->) e) :: Type

Methods

tabulate :: (Rep ((->) e) -> a) -> e -> a

index :: (e -> a) -> Rep ((->) e) -> a

(Representable f, Representable g) => Representable (f :*: g)

Defined in Data.Functor.Rep

Associated Types

type Rep (f :*: g) :: Type

Methods

tabulate :: (Rep (f :*: g) -> a) -> (f :*: g) a

index :: (f :*: g) a -> Rep (f :*: g) -> a

(Representable f, Representable g) => Representable (Product f g)

Defined in Data.Functor.Rep

Associated Types

type Rep (Product f g) :: Type

Methods

tabulate :: (Rep (Product f g) -> a) -> Product f g a

index :: Product f g a -> Rep (Product f g) -> a

Representable m => Representable (ReaderT e m)

Defined in Data.Functor.Rep

Associated Types

type Rep (ReaderT e m) :: Type

Methods

tabulate :: (Rep (ReaderT e m) -> a) -> ReaderT e m a

index :: ReaderT e m a -> Rep (ReaderT e m) -> a

(Dimensions r, Container c) => Representable (Array c r)

Defined in NumHask.Array

Associated Types

type Rep (Array c r) :: Type

Methods

tabulate :: (Rep (Array c r) -> a) -> Array c r a

index :: Array c r a -> Rep (Array c r) -> a

Representable f => Representable (M1 i c f)

Defined in Data.Functor.Rep

Associated Types

type Rep (M1 i c f) :: Type

Methods

tabulate :: (Rep (M1 i c f) -> a) -> M1 i c f a

index :: M1 i c f a -> Rep (M1 i c f) -> a

(Representable f, Representable g) => Representable (f :.: g)

Defined in Data.Functor.Rep

Associated Types

type Rep (f :.: g) :: Type

Methods

tabulate :: (Rep (f :.: g) -> a) -> (f :.: g) a

index :: (f :.: g) a -> Rep (f :.: g) -> a

(Representable f, Representable g) => Representable (Compose f g)

Defined in Data.Functor.Rep

Associated Types

type Rep (Compose f g) :: Type

Methods

tabulate :: (Rep (Compose f g) -> a) -> Compose f g a

index :: Compose f g a -> Rep (Compose f g) -> a