{-# LANGUAGE DerivingVia #-}

-- |
-- Module      : Data.HBifunctor
-- Copyright   : (c) Justin Le 2019
-- License     : BSD3
--
-- Maintainer  : justin@jle.im
-- Stability   : experimental
-- Portability : non-portable
--
-- This module provides an abstraction for "two-argument functor
-- combinators", 'HBifunctor', as well as some useful combinators.
module Data.HBifunctor (
    HBifunctor(..)
  , WrappedHBifunctor(..)
  , overHBifunctor
  -- * Simple Instances
  , LeftF(..)
  , RightF(..)
  ) where

import           Control.Natural.IsoF
import           Data.Biapplicative
import           Data.Bifunctor.TH
import           Data.Coerce
import           Data.Data
import           Data.Deriving
import           Data.HFunctor
import           Data.HFunctor.HTraversable
import           Data.HFunctor.Internal
import           Data.HFunctor.Interpret
import           GHC.Generics

-- | Lift two isomorphisms on each side of a bifunctor to become an
-- isomorphism between the two bifunctor applications.
--
-- Basically, if @f@ and @f'@ are isomorphic, and @g@ and @g'@ are
-- isomorphic, then @t f g@ is isomorphic to @t f' g'@.
overHBifunctor
    :: HBifunctor t
    => (f <~> f')
    -> (g <~> g')
    -> t f g <~> t f' g'
overHBifunctor :: forall {k} (t :: (k -> *) -> (k -> *) -> k -> *) (f :: k -> *)
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g))

-- | An 'HBifunctor' that ignores its second input.  Like
-- a 'GHC.Generics.:+:' with no 'GHC.Generics.R1'/right branch.
--
-- This is 'Data.Bifunctors.Joker.Joker' from "Data.Bifunctors.Joker", but
-- given a more sensible name for its purpose.
newtype LeftF f g a = LeftF { forall {k} {k} (f :: k -> *) (g :: k) (a :: k). LeftF f g a -> f a
runLeftF :: f a }
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toConstr :: LeftF f g a -> Constr
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dataTypeOf :: LeftF f g a -> DataType
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       (c :: * -> *).
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(forall d. Data d => c (t d)) -> Maybe (c (LeftF f g a))
dataCast1 :: forall (t :: * -> *) (c :: * -> *).
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$cdataCast2 :: forall k (f :: k -> *) k (g :: k) (a :: k) (t :: * -> * -> *)
       (c :: * -> *).
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(forall d e. (Data d, Data e) => c (t d e))
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(forall d e. (Data d, Data e) => c (t d e))
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Data)

deriveShow1 ''LeftF
deriveRead1 ''LeftF
deriveEq1 ''LeftF
deriveOrd1 ''LeftF
deriveBifunctor ''LeftF
deriveBifoldable ''LeftF
deriveBitraversable ''LeftF

instance Applicative f => Biapplicative (LeftF f) where
    bipure :: forall a b. a -> b -> LeftF f a b
bipure a
_ b
y = f b -> LeftF f a b
forall {k} {k} (f :: k -> *) (g :: k) (a :: k). f a -> LeftF f g a
LeftF (b -> f b
forall a. a -> f a
forall (f :: * -> *) a. Applicative f => a -> f a
pure b
y)
    LeftF f (c -> d)
x <<*>> :: forall a b c d.
LeftF f (a -> b) (c -> d) -> LeftF f a c -> LeftF f b d
<<*>> LeftF f c
y = f d -> LeftF f b d
forall {k} {k} (f :: k -> *) (g :: k) (a :: k). f a -> LeftF f g a
LeftF (f (c -> d)
x f (c -> d) -> f c -> f d
forall a b. f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> f c
y)

instance HBifunctor LeftF where
    hbimap :: forall (f :: k -> *) (j :: k -> *) (g :: k -> *) (l :: k -> *).
(f ~> j) -> (g ~> l) -> LeftF f g ~> LeftF j l
hbimap f ~> j
f g ~> l
_ (LeftF f x
x) = j x -> LeftF j l x
forall {k} {k} (f :: k -> *) (g :: k) (a :: k). f a -> LeftF f g a
LeftF (f x -> j x
f ~> j
f f x
x)

instance HFunctor (LeftF f) where
    hmap :: forall (f :: k -> *) (g :: k -> *).
(f ~> g) -> LeftF f f ~> LeftF f g
hmap f ~> g
_ = LeftF f f x -> LeftF f g x
forall a b. Coercible a b => a -> b
coerce

instance HTraversable (LeftF f) where
    htraverse :: forall (h :: * -> *) (f :: k -> *) (g :: k -> *) (a :: k1).
Applicative h =>
(forall (x :: k). f x -> h (g x)) -> LeftF f f a -> h (LeftF f g a)
htraverse forall (x :: k). f x -> h (g x)
_ = LeftF f g a -> h (LeftF f g a)
forall a. a -> h a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (LeftF f g a -> h (LeftF f g a))
-> (LeftF f f a -> LeftF f g a) -> LeftF f f a -> h (LeftF f g a)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. LeftF f f a -> LeftF f g a
forall a b. Coercible a b => a -> b
coerce

-- | An 'HBifunctor' that ignores its first input.  Like
-- a 'GHC.Generics.:+:' with no 'GHC.Generics.L1'/left branch.
--
-- In its polykinded form (on @f@), it is essentially a higher-order
-- version of 'Data.Tagged.Tagged'.
newtype RightF f g a = RightF { forall {k} {k} (f :: k) (g :: k -> *) (a :: k). RightF f g a -> g a
runRightF :: g a }
  deriving (Int -> RightF f g a -> ShowS
[RightF f g a] -> ShowS
RightF f g a -> String
(Int -> RightF f g a -> ShowS)
-> (RightF f g a -> String)
-> ([RightF f g a] -> ShowS)
-> Show (RightF f g a)
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
forall k (f :: k) k (g :: k -> *) (a :: k).
Show (g a) =>
Int -> RightF f g a -> ShowS
forall k (f :: k) k (g :: k -> *) (a :: k).
Show (g a) =>
[RightF f g a] -> ShowS
forall k (f :: k) k (g :: k -> *) (a :: k).
Show (g a) =>
RightF f g a -> String
$cshowsPrec :: forall k (f :: k) k (g :: k -> *) (a :: k).
Show (g a) =>
Int -> RightF f g a -> ShowS
showsPrec :: Int -> RightF f g a -> ShowS
$cshow :: forall k (f :: k) k (g :: k -> *) (a :: k).
Show (g a) =>
RightF f g a -> String
show :: RightF f g a -> String
$cshowList :: forall k (f :: k) k (g :: k -> *) (a :: k).
Show (g a) =>
[RightF f g a] -> ShowS
showList :: [RightF f g a] -> ShowS
Show, ReadPrec [RightF f g a]
ReadPrec (RightF f g a)
Int -> ReadS (RightF f g a)
ReadS [RightF f g a]
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-> ReadS [RightF f g a]
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-> ReadPrec [RightF f g a]
-> Read (RightF f g a)
forall a.
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forall k (f :: k) k (g :: k -> *) (a :: k).
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Read (g a) =>
ReadPrec (RightF f g a)
forall k (f :: k) k (g :: k -> *) (a :: k).
Read (g a) =>
Int -> ReadS (RightF f g a)
forall k (f :: k) k (g :: k -> *) (a :: k).
Read (g a) =>
ReadS [RightF f g a]
$creadsPrec :: forall k (f :: k) k (g :: k -> *) (a :: k).
Read (g a) =>
Int -> ReadS (RightF f g a)
readsPrec :: Int -> ReadS (RightF f g a)
$creadList :: forall k (f :: k) k (g :: k -> *) (a :: k).
Read (g a) =>
ReadS [RightF f g a]
readList :: ReadS [RightF f g a]
$creadPrec :: forall k (f :: k) k (g :: k -> *) (a :: k).
Read (g a) =>
ReadPrec (RightF f g a)
readPrec :: ReadPrec (RightF f g a)
$creadListPrec :: forall k (f :: k) k (g :: k -> *) (a :: k).
Read (g a) =>
ReadPrec [RightF f g a]
readListPrec :: ReadPrec [RightF f g a]
Read, RightF f g a -> RightF f g a -> Bool
(RightF f g a -> RightF f g a -> Bool)
-> (RightF f g a -> RightF f g a -> Bool) -> Eq (RightF f g a)
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
forall k (f :: k) k (g :: k -> *) (a :: k).
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RightF f g a -> RightF f g a -> Bool
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RightF f g a -> RightF f g a -> Bool
/= :: RightF f g a -> RightF f g a -> Bool
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RightF f g a -> RightF f g a -> Ordering
forall k (f :: k) k (g :: k -> *) (a :: k).
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RightF f g a -> RightF f g a -> RightF f g a
$ccompare :: forall k (f :: k) k (g :: k -> *) (a :: k).
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$cmax :: forall k (f :: k) k (g :: k -> *) (a :: k).
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RightF f g a -> RightF f g a -> RightF f g a
max :: RightF f g a -> RightF f g a -> RightF f g a
$cmin :: forall k (f :: k) k (g :: k -> *) (a :: k).
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min :: RightF f g a -> RightF f g a -> RightF f g a
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 Data (g a)) =>
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> RightF f g a -> r
gmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> RightF f g a -> r
$cgmapQ :: forall k (f :: k) k (g :: k -> *) (a :: k) u.
(Typeable f, Typeable a, Typeable g, Typeable k, Typeable k,
 Data (g a)) =>
(forall d. Data d => d -> u) -> RightF f g a -> [u]
gmapQ :: forall u. (forall d. Data d => d -> u) -> RightF f g a -> [u]
$cgmapQi :: forall k (f :: k) k (g :: k -> *) (a :: k) u.
(Typeable f, Typeable a, Typeable g, Typeable k, Typeable k,
 Data (g a)) =>
Int -> (forall d. Data d => d -> u) -> RightF f g a -> u
gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> RightF f g a -> u
$cgmapM :: forall k (f :: k) k (g :: k -> *) (a :: k) (m :: * -> *).
(Typeable f, Typeable a, Typeable g, Typeable k, Typeable k,
 Data (g a), Monad m) =>
(forall d. Data d => d -> m d) -> RightF f g a -> m (RightF f g a)
gmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> RightF f g a -> m (RightF f g a)
$cgmapMp :: forall k (f :: k) k (g :: k -> *) (a :: k) (m :: * -> *).
(Typeable f, Typeable a, Typeable g, Typeable k, Typeable k,
 Data (g a), MonadPlus m) =>
(forall d. Data d => d -> m d) -> RightF f g a -> m (RightF f g a)
gmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> RightF f g a -> m (RightF f g a)
$cgmapMo :: forall k (f :: k) k (g :: k -> *) (a :: k) (m :: * -> *).
(Typeable f, Typeable a, Typeable g, Typeable k, Typeable k,
 Data (g a), MonadPlus m) =>
(forall d. Data d => d -> m d) -> RightF f g a -> m (RightF f g a)
gmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> RightF f g a -> m (RightF f g a)
Data)

deriveShow1 ''RightF
deriveRead1 ''RightF
deriveEq1 ''RightF
deriveOrd1 ''RightF

instance HBifunctor RightF where
    hbimap :: forall (f :: k -> *) (j :: k -> *) (g :: k -> *) (l :: k -> *).
(f ~> j) -> (g ~> l) -> RightF f g ~> RightF j l
hbimap f ~> j
_ g ~> l
g (RightF g x
x) = l x -> RightF j l x
forall {k} {k} (f :: k) (g :: k -> *) (a :: k). g a -> RightF f g a
RightF (g x -> l x
g ~> l
g g x
x)

instance HFunctor (RightF g) where
    hmap :: forall (f :: k1 -> *) (g :: k1 -> *).
(f ~> g) -> RightF g f ~> RightF g g
hmap f ~> g
f (RightF f x
x) = g x -> RightF g g x
forall {k} {k} (f :: k) (g :: k -> *) (a :: k). g a -> RightF f g a
RightF (f x -> g x
f ~> g
f f x
x)

instance Inject (RightF g) where
    inject :: forall (f :: k -> *). f ~> RightF g f
inject = f x -> RightF g f x
forall {k} {k} (f :: k) (g :: k -> *) (a :: k). g a -> RightF f g a
RightF

instance HTraversable (RightF g) where
    htraverse :: forall (h :: * -> *) (f :: k1 -> *) (g :: k1 -> *) (a :: k1).
Applicative h =>
(forall (x :: k1). f x -> h (g x))
-> RightF g f a -> h (RightF g g a)
htraverse forall (x :: k1). f x -> h (g x)
f (RightF f a
x) = g a -> RightF g g a
forall {k} {k} (f :: k) (g :: k -> *) (a :: k). g a -> RightF f g a
RightF (g a -> RightF g g a) -> h (g a) -> h (RightF g g a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> f a -> h (g a)
forall (x :: k1). f x -> h (g x)
f f a
x

instance HBind (RightF g) where
    hbind :: forall (f :: k -> *) (g :: k -> *).
(f ~> RightF g g) -> RightF g f ~> RightF g g
hbind f ~> RightF g g
f (RightF f x
x) = f x -> RightF g g x
f ~> RightF g g
f f x
x

instance Interpret (RightF g) f where
    retract :: RightF g f ~> f
retract (RightF f x
x) = f x
x
    interpret :: forall (g :: k -> *). (g ~> f) -> RightF g g ~> f
interpret g ~> f
f (RightF g x
x) = g x -> f x
g ~> f
f g x
x