{-# LANGUAGE DataKinds                  #-}
{-# LANGUAGE DeriveFunctor              #-}
{-# LANGUAGE DeriveTraversable          #-}
{-# LANGUAGE FlexibleInstances          #-}
{-# LANGUAGE GADTs                      #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE LambdaCase                 #-}
{-# LANGUAGE MultiParamTypeClasses      #-}
{-# LANGUAGE OverloadedStrings          #-}
{-# LANGUAGE PatternSynonyms            #-}
{-# LANGUAGE PolyKinds                  #-}
{-# LANGUAGE RankNTypes                 #-}
{-# LANGUAGE TemplateHaskell            #-}

module Camfort.Helpers.TypeLevel where

import           Data.Functor.Identity

import           Language.Expression.Pretty

--------------------------------------------------------------------------------
--  Types
--------------------------------------------------------------------------------

-- | An existential type containing @f a@ for some type @a@.
data Some f where
  Some :: f a -> Some f

-- | A pair of functorial values over the same ground type, where the first
-- value is meant to add constraints rather than real semantic information. The
-- 'Pretty1' instance ignores the first value.
data PairOf f g a = PairOf (f a) (g a)
  deriving (PairOf f g a -> PairOf f g a -> Bool
(PairOf f g a -> PairOf f g a -> Bool)
-> (PairOf f g a -> PairOf f g a -> Bool) -> Eq (PairOf f g a)
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
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-> (PairOf f g a -> PairOf f g a -> PairOf f g a)
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max :: PairOf f g a -> PairOf f g a -> PairOf f g a
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min :: PairOf f g a -> PairOf f g a -> PairOf f g a
Ord, Int -> PairOf f g a -> ShowS
[PairOf f g a] -> ShowS
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Int -> PairOf f g a -> ShowS
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Int -> PairOf f g a -> ShowS
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traverse :: forall (f :: * -> *) a b.
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sequenceA :: forall (f :: * -> *) a.
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PairOf f g (f a) -> f (PairOf f g a)
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sequence :: forall (m :: * -> *) a.
Monad m =>
PairOf f g (m a) -> m (PairOf f g a)
Traversable)

type SomePair f g = Some (PairOf f g)

--------------------------------------------------------------------------------
--  Patterns
--------------------------------------------------------------------------------

pattern SomePair :: f a -> g a -> Some (PairOf f g)
pattern $mSomePair :: forall {r} {k} {f :: k -> *} {g :: k -> *}.
Some (PairOf f g)
-> (forall {a :: k}. f a -> g a -> r) -> ((# #) -> r) -> r
$bSomePair :: forall {k} (f :: k -> *) (g :: k -> *) (a :: k).
f a -> g a -> Some (PairOf f g)
SomePair x y = Some (PairOf x y)

--------------------------------------------------------------------------------
--  Combinators
--------------------------------------------------------------------------------

traverseSome
  :: Functor m
  => (forall a. f a -> m (g a))
  -> Some f -> m (Some g)
traverseSome :: forall {k} (m :: * -> *) (f :: k -> *) (g :: k -> *).
Functor m =>
(forall (a :: k). f a -> m (g a)) -> Some f -> m (Some g)
traverseSome forall (a :: k). f a -> m (g a)
f (Some f a
x) = g a -> Some g
forall {k} (f :: k -> *) (a :: k). f a -> Some f
Some (g a -> Some g) -> m (g a) -> m (Some g)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> f a -> m (g a)
forall (a :: k). f a -> m (g a)
f f a
x

traversePairOf
  :: Functor m
  => (f a -> g a -> m (f' b, g' b))
  -> PairOf f g a -> m (PairOf f' g' b)
traversePairOf :: forall {k} {k} (m :: * -> *) (f :: k -> *) (a :: k) (g :: k -> *)
       (f' :: k -> *) (b :: k) (g' :: k -> *).
Functor m =>
(f a -> g a -> m (f' b, g' b))
-> PairOf f g a -> m (PairOf f' g' b)
traversePairOf f a -> g a -> m (f' b, g' b)
f (PairOf f a
x g a
y) = (f' b -> g' b -> PairOf f' g' b) -> (f' b, g' b) -> PairOf f' g' b
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry f' b -> g' b -> PairOf f' g' b
forall {k} (f :: k -> *) (g :: k -> *) (a :: k).
f a -> g a -> PairOf f g a
PairOf ((f' b, g' b) -> PairOf f' g' b)
-> m (f' b, g' b) -> m (PairOf f' g' b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> f a -> g a -> m (f' b, g' b)
f f a
x g a
y

mapSome :: (forall a. f a -> g a) -> Some f -> Some g
mapSome :: forall {k} (f :: k -> *) (g :: k -> *).
(forall (a :: k). f a -> g a) -> Some f -> Some g
mapSome forall (a :: k). f a -> g a
f = Identity (Some g) -> Some g
forall a. Identity a -> a
runIdentity (Identity (Some g) -> Some g)
-> (Some f -> Identity (Some g)) -> Some f -> Some g
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (forall (a :: k). f a -> Identity (g a))
-> Some f -> Identity (Some g)
forall {k} (m :: * -> *) (f :: k -> *) (g :: k -> *).
Functor m =>
(forall (a :: k). f a -> m (g a)) -> Some f -> m (Some g)
traverseSome (g a -> Identity (g a)
forall a. a -> Identity a
Identity (g a -> Identity (g a)) -> (f a -> g a) -> f a -> Identity (g a)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. f a -> g a
forall (a :: k). f a -> g a
f)

--------------------------------------------------------------------------------
--  Instances
--------------------------------------------------------------------------------

instance Pretty1 f => Pretty (Some f) where
  prettysPrec :: Int -> Some f -> ShowS
prettysPrec Int
p = \case
    Some f a
x -> Int -> f a -> ShowS
forall (a :: k). Int -> f a -> ShowS
forall {k} (t :: k -> *) (a :: k). Pretty1 t => Int -> t a -> ShowS
prettys1Prec Int
p f a
x

instance Pretty1 g => Pretty1 (PairOf f g) where
  prettys1Prec :: forall (a :: k). Int -> PairOf f g a -> ShowS
prettys1Prec Int
p = \case
    PairOf f a
_ g a
x -> Int -> g a -> ShowS
forall (a :: k). Int -> g a -> ShowS
forall {k} (t :: k -> *) (a :: k). Pretty1 t => Int -> t a -> ShowS
prettys1Prec Int
p g a
x

instance Pretty1 f => Show (Some f) where
  show :: Some f -> String
show = Some f -> String
forall a. Pretty a => a -> String
pretty