{-# LANGUAGE DeriveGeneric, DeriveTraversable, FlexibleInstances, KindSignatures, MultiParamTypeClasses, TypeFamilies, TypeOperators, UndecidableInstances #-}

-- | Operations on /sums/, combining effects into a /signature/.
--
-- @since 0.1.0.0
module Control.Effect.Sum
( -- * Membership
  Member(..)
, Members
  -- * Sums
, (:+:)(..)
) where

import Control.Effect.Class
import Data.Kind (Constraint)
import GHC.Generics (Generic1)

-- | Higher-order sums are used to combine multiple effects into a signature, typically by chaining on the right.
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       (m :: * -> *) (f :: * -> *) a.
(Traversable (f m), Traversable (g m), Applicative f) =>
(:+:) f g m (f a) -> f ((:+:) f g m a)
traverse :: (a -> f b) -> (:+:) f g m a -> f ((:+:) f g m b)
$ctraverse :: forall (f :: (* -> *) -> * -> *) (g :: (* -> *) -> * -> *)
       (m :: * -> *) (f :: * -> *) a b.
(Traversable (f m), Traversable (g m), Applicative f) =>
(a -> f b) -> (:+:) f g m a -> f ((:+:) f g m b)
$cp2Traversable :: forall (f :: (* -> *) -> * -> *) (g :: (* -> *) -> * -> *)
       (m :: * -> *).
(Traversable (f m), Traversable (g m)) =>
Foldable ((:+:) f g m)
$cp1Traversable :: forall (f :: (* -> *) -> * -> *) (g :: (* -> *) -> * -> *)
       (m :: * -> *).
(Traversable (f m), Traversable (g m)) =>
Functor ((:+:) f g m)
Traversable)

infixr 4 :+:

instance (HFunctor f, HFunctor g) => HFunctor (f :+: g)
instance (Effect f, Effect g)     => Effect   (f :+: g)


-- | The class of types present in a signature.
--
--   This is based on Wouter Swierstra’s design described in [Data types à la carte](http://www.cs.ru.nl/~W.Swierstra/Publications/DataTypesALaCarte.pdf). As described therein, overlapping instances are required in order to distinguish e.g. left-occurrence from right-recursion.
--
--   It should not generally be necessary for you to define new 'Member' instances, but these are not specifically prohibited if you wish to get creative.
--
-- @since 0.1.0.0
class Member (sub :: (* -> *) -> (* -> *)) sup where
  -- | Inject a member of a signature into the signature.
  inj :: sub m a -> sup m a

-- | Reflexivity: @t@ is a member of itself.
instance Member t t where
  inj :: t m a -> t m a
inj = t m a -> t m a
forall a. a -> a
id

-- | Left-recursion: if @t@ is a member of @l1 ':+:' l2 ':+:' r@, then we can inject it into @(l1 ':+:' l2) ':+:' r@ by injection into a right-recursive signature, followed by left-association.
instance {-# OVERLAPPABLE #-}
         Member t (l1 :+: l2 :+: r)
      => Member t ((l1 :+: l2) :+: r) where
  inj :: t m a -> (:+:) (l1 :+: l2) r m a
inj = (:+:) l1 (l2 :+: r) m a -> (:+:) (l1 :+: l2) r m a
forall (f :: (* -> *) -> * -> *) (g :: (* -> *) -> * -> *)
       (g :: (* -> *) -> * -> *) (m :: * -> *) k.
(:+:) f (g :+: g) m k -> (:+:) (f :+: g) g m k
reassoc ((:+:) l1 (l2 :+: r) m a -> (:+:) (l1 :+: l2) r m a)
-> (t m a -> (:+:) l1 (l2 :+: r) m a)
-> t m a
-> (:+:) (l1 :+: l2) r m a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. t m a -> (:+:) l1 (l2 :+: r) m a
forall (sub :: (* -> *) -> * -> *) (sup :: (* -> *) -> * -> *)
       (m :: * -> *) a.
Member sub sup =>
sub m a -> sup m a
inj where
    reassoc :: (:+:) f (g :+: g) m k -> (:+:) (f :+: g) g m k
reassoc (L l :: f m k
l)     = (:+:) f g m k -> (:+:) (f :+: g) g m k
forall (f :: (* -> *) -> * -> *) (g :: (* -> *) -> * -> *)
       (m :: * -> *) k.
f m k -> (:+:) f g m k
L (f m k -> (:+:) f g m k
forall (f :: (* -> *) -> * -> *) (g :: (* -> *) -> * -> *)
       (m :: * -> *) k.
f m k -> (:+:) f g m k
L f m k
l)
    reassoc (R (L l :: g m k
l)) = (:+:) f g m k -> (:+:) (f :+: g) g m k
forall (f :: (* -> *) -> * -> *) (g :: (* -> *) -> * -> *)
       (m :: * -> *) k.
f m k -> (:+:) f g m k
L (g m k -> (:+:) f g m k
forall (f :: (* -> *) -> * -> *) (g :: (* -> *) -> * -> *)
       (m :: * -> *) k.
g m k -> (:+:) f g m k
R g m k
l)
    reassoc (R (R r :: g m k
r)) = g m k -> (:+:) (f :+: g) g m k
forall (f :: (* -> *) -> * -> *) (g :: (* -> *) -> * -> *)
       (m :: * -> *) k.
g m k -> (:+:) f g m k
R g m k
r

-- | Left-occurrence: if @t@ is at the head of a signature, we can inject it in O(1).
instance {-# OVERLAPPABLE #-}
         Member l (l :+: r) where
  inj :: l m a -> (:+:) l r m a
inj = l m a -> (:+:) l r m a
forall (f :: (* -> *) -> * -> *) (g :: (* -> *) -> * -> *)
       (m :: * -> *) k.
f m k -> (:+:) f g m k
L

-- | Right-recursion: if @t@ is a member of @r@, we can inject it into @r@ in O(n), followed by lifting that into @l ':+:' r@ in O(1).
instance {-# OVERLAPPABLE #-}
         Member l r
      => Member l (l' :+: r) where
  inj :: l m a -> (:+:) l' r m a
inj = r m a -> (:+:) l' r m a
forall (f :: (* -> *) -> * -> *) (g :: (* -> *) -> * -> *)
       (m :: * -> *) k.
g m k -> (:+:) f g m k
R (r m a -> (:+:) l' r m a)
-> (l m a -> r m a) -> l m a -> (:+:) l' r m a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. l m a -> r m a
forall (sub :: (* -> *) -> * -> *) (sup :: (* -> *) -> * -> *)
       (m :: * -> *) a.
Member sub sup =>
sub m a -> sup m a
inj


-- | Decompose sums on the left into multiple 'Member' constraints.
--
-- Note that while this, and by extension 'Control.Algebra.Has', can be used to group together multiple membership checks into a single (composite) constraint, large signatures on the left can slow compiles down due to [a problem with recursive type families](https://gitlab.haskell.org/ghc/ghc/issues/8095).
--
-- @since 1.0.0.0
type family Members sub sup :: Constraint where
  Members (l :+: r) u = (Members l u, Members r u)
  Members t         u = Member t u