Type.Yoko.Natural

Natural transformations and pairs.

Documentation

type NT_ u f = forall t. u t -> f t

newtype NT u f

Natural transformations. We use Unwrap to lighten the user interface at the value level, though it clutters the types a little.

Constructors

NT (forall t. u t -> Unwrap f t)

nt_ :: Proxy (KTSS f) -> (forall t. u t -> Unwrap f t) -> NT u f

appNT :: NT u f -> u t -> Unwrap f t

appNTF :: Wrapper f => NT u f -> NT_ u f

orNT :: NT u f -> NT v f -> NT (u :|| v) f

Defining an NT via type-level backtracking; :|| uses Pred to short-circuit, preferring inhabitation of u over v.

constNT :: Unwrap f t -> NT (:=: t) f

constNT_ :: Proxy (KTSS f) -> Unwrap f t -> NT (:=: t) f

constNTF :: Wrapper f => f t -> NT (:=: t) f

firstNT :: NT_ u g -> NT g f -> NT u f

data NP u f

Natural pairs.

Constructors

forall t . NP (u t) (Unwrap f t)

firstNP :: NT_ u v -> NP u f -> NP v f

Analog to Control.Arrow.first.

newtype ArrowTSS f g a

ArrowTSS can be partially applied, and hence occur as the second argument of NT, where as f _ -> g _ cannot.

Constructors

ArrowTSS (f a -> g a)

Instances

Wrapper (ArrowTSS f g)

appNTtoNP :: (Wrapper f, Wrapper g) => NT u (ArrowTSS f g) -> NP u f -> NP u g