{-# LANGUAGE DeriveGeneric       #-}
{-# LANGUAGE TypeOperators       #-}
{-# LANGUAGE TypeFamilies        #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE GADTs               #-}
{-# LANGUAGE FlexibleInstances   #-}
{-# LANGUAGE StandaloneDeriving  #-}
{-# LANGUAGE NoImplicitPrelude   #-}
{-# LANGUAGE PolyKinds           #-}

-----------------------------------------------------------------------------
-- |
-- Module      :  Data.Type.Coercion
-- License     :  BSD-style (see the LICENSE file in the distribution)
--
-- Maintainer  :  libraries@haskell.org
-- Stability   :  experimental
-- Portability :  not portable
--
-- Definition of representational equality ('Coercion').
--
-- @since 4.7.0.0
-----------------------------------------------------------------------------

module Data.Type.Coercion
  ( Coercion(..)
  , coerceWith
  , sym
  , trans
  , repr
  , TestCoercion(..)
  ) where

import qualified Data.Type.Equality as Eq
import Data.Maybe
import GHC.Enum
import GHC.Show
import GHC.Read
import GHC.Base

-- | Representational equality. If @Coercion a b@ is inhabited by some terminating
-- value, then the type @a@ has the same underlying representation as the type @b@.
--
-- To use this equality in practice, pattern-match on the @Coercion a b@ to get out
-- the @Coercible a b@ instance, and then use 'coerce' to apply it.
--
-- @since 4.7.0.0
data Coercion a b where
  Coercion :: Coercible a b => Coercion a b

-- with credit to Conal Elliott for 'ty', Erik Hesselink & Martijn van
-- Steenbergen for 'type-equality', Edward Kmett for 'eq', and Gabor Greif
-- for 'type-eq'

newtype Sym a b = Sym { unsym :: Coercion b a }

-- | Type-safe cast, using representational equality
coerceWith :: Coercion a b -> a -> b
coerceWith Coercion x = coerce x

-- | Symmetry of representational equality
sym :: forall a b. Coercion a b -> Coercion b a
sym Coercion = unsym (coerce (Sym Coercion :: Sym a a))

-- | Transitivity of representational equality
trans :: Coercion a b -> Coercion b c -> Coercion a c
trans c Coercion = coerce c

-- | Convert propositional (nominal) equality to representational equality
repr :: (a Eq.:~: b) -> Coercion a b
repr Eq.Refl = Coercion

deriving instance Eq   (Coercion a b)
deriving instance Show (Coercion a b)
deriving instance Ord  (Coercion a b)

instance Coercible a b => Read (Coercion a b) where
  readsPrec d = readParen (d > 10) (\r -> [(Coercion, s) | ("Coercion",s) <- lex r ])

instance Coercible a b => Enum (Coercion a b) where
  toEnum 0 = Coercion
  toEnum _ = error "Data.Type.Coercion.toEnum: bad argument"

  fromEnum Coercion = 0

instance Coercible a b => Bounded (Coercion a b) where
  minBound = Coercion
  maxBound = Coercion

-- | This class contains types where you can learn the equality of two types
-- from information contained in /terms/. Typically, only singleton types should
-- inhabit this class.
class TestCoercion f where
  -- | Conditionally prove the representational equality of @a@ and @b@.
  testCoercion :: f a -> f b -> Maybe (Coercion a b)

instance TestCoercion ((Eq.:~:) a) where
  testCoercion Eq.Refl Eq.Refl = Just Coercion

instance TestCoercion (Coercion a) where
  testCoercion c Coercion = Just $ coerce (sym c)
