{-# LANGUAGE UndecidableInstances #-}

module Pandora.Paradigm.Primary.Transformer.Jet where

import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)), (-<$$>-))
import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)), (-<<-<<-))
import Pandora.Paradigm.Primary.Algebraic ((-<*>-))

data Jet t a = Jet a (Jet t (t a))

instance Covariant (->) (->) t => Covariant (->) (->) (Jet t) where
	a -> b
f -<$>- :: (a -> b) -> Jet t a -> Jet t b
-<$>- Jet a
x Jet t (t a)
xs = b -> Jet t (t b) -> Jet t b
forall (t :: * -> *) a. a -> Jet t (t a) -> Jet t a
Jet (a -> b
f a
x) (a -> b
f (a -> b) -> Jet t (t a) -> Jet t (t b)
forall (t :: * -> *) (u :: * -> *) (category :: * -> * -> *) a b.
(Covariant category category u, Covariant category category t) =>
category a b -> category (t (u a)) (t (u b))
-<$$>- Jet t (t a)
xs)

instance Traversable (->) (->) t => Traversable (->) (->) (Jet t) where
	a -> u b
f <<- :: (a -> u b) -> Jet t a -> u (Jet t b)
<<- Jet a
x Jet t (t a)
xs = b -> Jet t (t b) -> Jet t b
forall (t :: * -> *) a. a -> Jet t (t a) -> Jet t a
Jet (b -> Jet t (t b) -> Jet t b) -> u b -> u (Jet t (t b) -> Jet t b)
forall (source :: * -> * -> *) (target :: * -> * -> *)
       (t :: * -> *) a b.
Covariant source target t =>
source a b -> target (t a) (t b)
-<$>- a -> u b
f a
x u (Jet t (t b) -> Jet t b) -> u (Jet t (t b)) -> u (Jet t b)
forall (t :: * -> *) a b.
(Covariant (->) (->) t, Semimonoidal (->) (:*:) (:*:) t) =>
t (a -> b) -> t a -> t b
-<*>- a -> u b
f (a -> u b) -> Jet t (t a) -> u (Jet t (t b))
forall (t :: * -> *) (u :: * -> *) (v :: * -> *)
       (category :: * -> * -> *) a b.
(Traversable category category t, Covariant category category u,
 Monoidal category category (:*:) (:*:) u,
 Traversable category category v) =>
category a (u b) -> category (v (t a)) (u (v (t b)))
-<<-<<- Jet t (t a)
xs