{-# LANGUAGE CPP #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE Trustworthy #-}

#if __GLASGOW_HASKELL__ >= 806
{-# LANGUAGE PolyKinds #-}
#else
{-# LANGUAGE TypeInType #-}
#endif

-----------------------------------------------------------------------------

-- |

-- Module      :  Control.Lens.Equality

-- Copyright   :  (C) 2012-16 Edward Kmett

-- License     :  BSD-style (see the file LICENSE)

-- Maintainer  :  Edward Kmett <ekmett@gmail.com>

-- Stability   :  provisional

-- Portability :  Rank2Types

--

----------------------------------------------------------------------------

module Control.Lens.Equality
  (
  -- * Type Equality

    Equality, Equality'
  , AnEquality, AnEquality'
  , (:~:)(..)
  , runEq
  , substEq
  , mapEq
  , fromEq
  , simply
  -- * The Trivial Equality

  , simple
  -- * 'Iso'-like functions

  , equality
  , equality'
  , withEquality
  , underEquality
  , overEquality
  , fromLeibniz
  , fromLeibniz'
  , cloneEquality
  -- * Implementation Details

  , Identical(..)
  ) where

import Control.Lens.Type
import Data.Proxy (Proxy)
import Data.Type.Equality ((:~:)(..))
import GHC.Exts (TYPE)
import Data.Kind (Type)

-- $setup

-- >>> import Control.Lens


#include "lens-common.h"

-----------------------------------------------------------------------------

-- Equality

-----------------------------------------------------------------------------


-- | Provides witness that @(s ~ a, b ~ t)@ holds.

data Identical a b s t where
  Identical :: Identical a b a b

-- | When you see this as an argument to a function, it expects an 'Equality'.

type AnEquality s t a b = Identical a (Proxy b) a (Proxy b) -> Identical a (Proxy b) s (Proxy t)

-- | A 'Simple' 'AnEquality'.

type AnEquality' s a = AnEquality s s a a

-- | Extract a witness of type 'Equality'.

runEq :: AnEquality s t a b -> Identical s t a b
runEq :: forall {k} {k} (s :: k) (t :: k) (a :: k) (b :: k).
AnEquality s t a b -> Identical s t a b
runEq AnEquality s t a b
l = case AnEquality s t a b
l forall {k} {k} (a :: k) (b :: k). Identical a b a b
Identical of Identical a (Proxy b) s (Proxy t)
Identical -> forall {k} {k} (a :: k) (b :: k). Identical a b a b
Identical
{-# INLINE runEq #-}

-- | Substituting types with 'Equality'.

substEq :: forall s t a b rep (r :: TYPE rep).
           AnEquality s t a b -> ((s ~ a, t ~ b) => r) -> r
substEq :: forall {k} {k} (s :: k) (t :: k) (a :: k) (b :: k) r.
AnEquality s t a b -> ((s ~ a, t ~ b) => r) -> r
substEq AnEquality s t a b
l = case forall {k} {k} (s :: k) (t :: k) (a :: k) (b :: k).
AnEquality s t a b -> Identical s t a b
runEq AnEquality s t a b
l of
  Identical s t a b
Identical -> \(s ~ a, t ~ b) => r
r -> (s ~ a, t ~ b) => r
r
{-# INLINE substEq #-}

-- | We can use 'Equality' to do substitution into anything.

mapEq :: forall k1 k2 (s :: k1) (t :: k2) (a :: k1) (b :: k2) (f :: k1 -> Type) . AnEquality s t a b -> f s -> f a
mapEq :: forall k1 k2 (s :: k1) (t :: k2) (a :: k1) (b :: k2)
       (f :: k1 -> *).
AnEquality s t a b -> f s -> f a
mapEq AnEquality s t a b
l f s
r = forall {k} {k} (s :: k) (t :: k) (a :: k) (b :: k) r.
AnEquality s t a b -> ((s ~ a, t ~ b) => r) -> r
substEq AnEquality s t a b
l f s
r
{-# INLINE mapEq #-}

-- | 'Equality' is symmetric.

fromEq :: AnEquality s t a b -> Equality b a t s
fromEq :: forall {k2} {k1} (s :: k2) (t :: k1) (a :: k2) (b :: k1).
AnEquality s t a b -> Equality b a t s
fromEq AnEquality s t a b
l = forall {k} {k} (s :: k) (t :: k) (a :: k) (b :: k) r.
AnEquality s t a b -> ((s ~ a, t ~ b) => r) -> r
substEq AnEquality s t a b
l forall a. a -> a
id
{-# INLINE fromEq #-}

-- | This is an adverb that can be used to modify many other 'Lens' combinators to make them require

-- simple lenses, simple traversals, simple prisms or simple isos as input.

simply :: forall p f s a rep (r :: TYPE rep).
  (Optic' p f s a -> r) -> Optic' p f s a -> r
simply :: forall {k} {k} (p :: k -> k -> *) (f :: k -> k) (s :: k) (a :: k)
       r.
(Optic' p f s a -> r) -> Optic' p f s a -> r
simply = forall a. a -> a
id
{-# INLINE simply #-}

-- | Composition with this isomorphism is occasionally useful when your 'Lens',

-- 'Control.Lens.Traversal.Traversal' or 'Iso' has a constraint on an unused

-- argument to force that argument to agree with the

-- type of a used argument and avoid @ScopedTypeVariables@ or other ugliness.

simple :: Equality' a a
simple :: forall {k2} (a :: k2). Equality' a a
simple = forall a. a -> a
id
{-# INLINE simple #-}

cloneEquality :: AnEquality s t a b -> Equality s t a b
cloneEquality :: forall {k1} {k2} (s :: k1) (t :: k2) (a :: k1) (b :: k2).
AnEquality s t a b -> Equality s t a b
cloneEquality AnEquality s t a b
an = forall {k} {k} (s :: k) (t :: k) (a :: k) (b :: k) r.
AnEquality s t a b -> ((s ~ a, t ~ b) => r) -> r
substEq AnEquality s t a b
an forall a. a -> a
id
{-# INLINE cloneEquality #-}

-- | Construct an 'Equality' from explicit equality evidence.

equality :: s :~: a -> b :~: t -> Equality s t a b
equality :: forall {k1} {k2} (s :: k1) (a :: k1) (b :: k2) (t :: k2).
(s :~: a) -> (b :~: t) -> Equality s t a b
equality s :~: a
Refl b :~: t
Refl = forall a. a -> a
id
{-# INLINE equality #-}

-- | A 'Simple' version of 'equality'

equality' :: a :~: b -> Equality' a b
equality' :: forall {k2} (a :: k2) (b :: k2). (a :~: b) -> Equality' a b
equality' a :~: b
Refl = forall a. a -> a
id
{-# INLINE equality' #-}

-- | Recover a "profunctor lens" form of equality. Reverses 'fromLeibniz'.

overEquality :: AnEquality s t a b -> p a b -> p s t
overEquality :: forall {k} {k} (s :: k) (t :: k) (a :: k) (b :: k)
       (p :: k -> k -> *).
AnEquality s t a b -> p a b -> p s t
overEquality AnEquality s t a b
an = forall {k} {k} (s :: k) (t :: k) (a :: k) (b :: k) r.
AnEquality s t a b -> ((s ~ a, t ~ b) => r) -> r
substEq AnEquality s t a b
an forall a. a -> a
id
{-# INLINE overEquality #-}

-- | The opposite of working 'overEquality' is working 'underEquality'.

underEquality :: AnEquality s t a b -> p t s -> p b a
underEquality :: forall {k} {k} (s :: k) (t :: k) (a :: k) (b :: k)
       (p :: k -> k -> *).
AnEquality s t a b -> p t s -> p b a
underEquality AnEquality s t a b
an = forall {k} {k} (s :: k) (t :: k) (a :: k) (b :: k) r.
AnEquality s t a b -> ((s ~ a, t ~ b) => r) -> r
substEq AnEquality s t a b
an forall a. a -> a
id
{-# INLINE underEquality #-}

-- | Convert a "profunctor lens" form of equality to an equality. Reverses

-- 'overEquality'.

--

-- The type should be understood as

--

-- @fromLeibniz :: (forall p. p a b -> p s t) -> Equality s t a b@

fromLeibniz :: (Identical a b a b -> Identical a b s t) -> Equality s t a b
fromLeibniz :: forall {k1} {k2} (a :: k1) (b :: k2) (s :: k1) (t :: k2).
(Identical a b a b -> Identical a b s t) -> Equality s t a b
fromLeibniz Identical a b a b -> Identical a b s t
f = case Identical a b a b -> Identical a b s t
f forall {k} {k} (a :: k) (b :: k). Identical a b a b
Identical of Identical a b s t
Identical -> forall a. a -> a
id
{-# INLINE fromLeibniz #-}

-- | Convert Leibniz equality to equality. Reverses 'mapEq' in 'Simple' cases.

--

-- The type should be understood as

--

-- @fromLeibniz' :: (forall f. f s -> f a) -> Equality' s a@

fromLeibniz' :: (s :~: s -> s :~: a) -> Equality' s a
fromLeibniz' :: forall {k2} (s :: k2) (a :: k2).
((s :~: s) -> s :~: a) -> Equality' s a
fromLeibniz' (s :~: s) -> s :~: a
f = case (s :~: s) -> s :~: a
f forall {k} (a :: k). a :~: a
Refl of s :~: a
Refl -> forall a. a -> a
id
{-# INLINE fromLeibniz' #-}

-- | A version of 'substEq' that provides explicit, rather than implicit,

-- equality evidence.

withEquality :: forall s t a b rep (r :: TYPE rep).
   AnEquality s t a b -> (s :~: a -> b :~: t -> r) -> r
withEquality :: forall {k} {k} (s :: k) (t :: k) (a :: k) (b :: k) r.
AnEquality s t a b -> ((s :~: a) -> (b :~: t) -> r) -> r
withEquality AnEquality s t a b
an = forall {k} {k} (s :: k) (t :: k) (a :: k) (b :: k) r.
AnEquality s t a b -> ((s ~ a, t ~ b) => r) -> r
substEq AnEquality s t a b
an (\(s :~: a) -> (b :~: t) -> r
f -> (s :~: a) -> (b :~: t) -> r
f forall {k} (a :: k). a :~: a
Refl forall {k} (a :: k). a :~: a
Refl)
{-# INLINE withEquality #-}