-- SPDX-FileCopyrightText: 2021 Tocqueville Group
--
-- SPDX-License-Identifier: LicenseRef-MIT-TQ

module Morley.Util.Sing
  ( eqI
  , eqParamSing
  , eqParamSing2
  , eqParamSing3
  , eqParamMixed3
  , castSing
  , SingI1(..)
  ) where

import Data.Singletons (KindOf, Sing, SingI, sing)
import Data.Singletons.Decide (SDecide, decideEquality)
import Data.Type.Equality (TestEquality(..), (:~:)(..))
import Data.Typeable (eqT)

-- | Version of 'testEquality' that uses 'SingI'
eqI :: forall a b. (SingI a, SingI b, TestEquality (Sing @(KindOf a))) => Maybe (a :~: b)
eqI :: Maybe (a :~: b)
eqI = Sing a -> Sing b -> Maybe (a :~: b)
forall k (f :: k -> *) (a :: k) (b :: k).
TestEquality f =>
f a -> f b -> Maybe (a :~: b)
testEquality (SingI a => Sing a
forall k (a :: k). SingI a => Sing a
sing @a) (SingI b => Sing b
forall k (a :: k). SingI a => Sing a
sing @b)

-- | Suppose you have a data type @X@ with parameter @a@ and you have
-- two values: @x1 :: X a1@ and @x2 :: X a2@. You can't compare them
-- using '==', because they have different types. However, you can
-- compare them using 'eqParamSing' as long as both parameters have
-- SingI instances and their kind is `SDecide`.
eqParamSing ::
  forall a1 a2 t.
  ( SingI a1
  , SingI a2
  , SDecide (KindOf a1)
  , Eq (t a1)
  )
  => t a1
  -> t a2
  -> Bool
eqParamSing :: t a1 -> t a2 -> Bool
eqParamSing t a1
t1 t a2
t2 = Maybe () -> Bool
forall a. Maybe a -> Bool
isJust @() (Maybe () -> Bool) -> Maybe () -> Bool
forall a b. (a -> b) -> a -> b
$ do
  a1 :~: a2
Refl <- SingI a1 => Sing a1
forall k (a :: k). SingI a => Sing a
sing @a1 Sing a1 -> Sing a2 -> Maybe (a1 :~: a2)
forall k (a :: k) (b :: k).
SDecide k =>
Sing a -> Sing b -> Maybe (a :~: b)
`decideEquality` SingI a2 => Sing a2
forall k (a :: k). SingI a => Sing a
sing @a2
  Bool -> Maybe ()
forall (f :: * -> *). Alternative f => Bool -> f ()
guard (t a1
t1 t a1 -> t a1 -> Bool
forall a. Eq a => a -> a -> Bool
== t a1
t a2
t2)

-- | Version of 'eqParamSing' for types with 2 parameters.
eqParamSing2 ::
  forall a1 a2 b1 b2 t.
  ( SingI a1
  , SingI a2
  , SingI b1
  , SingI b2
  , SDecide (KindOf a1)
  , SDecide (KindOf b1)
  , Eq (t a1 b2)
  )
  => t a1 b1
  -> t a2 b2
  -> Bool
eqParamSing2 :: t a1 b1 -> t a2 b2 -> Bool
eqParamSing2 t a1 b1
t1 t a2 b2
t2 = Maybe () -> Bool
forall a. Maybe a -> Bool
isJust @() (Maybe () -> Bool) -> Maybe () -> Bool
forall a b. (a -> b) -> a -> b
$ do
  a1 :~: a2
Refl <- SingI a1 => Sing a1
forall k (a :: k). SingI a => Sing a
sing @a1 Sing a1 -> Sing a2 -> Maybe (a1 :~: a2)
forall k (a :: k) (b :: k).
SDecide k =>
Sing a -> Sing b -> Maybe (a :~: b)
`decideEquality` SingI a2 => Sing a2
forall k (a :: k). SingI a => Sing a
sing @a2
  b1 :~: b2
Refl <- SingI b1 => Sing b1
forall k (a :: k). SingI a => Sing a
sing @b1 Sing b1 -> Sing b2 -> Maybe (b1 :~: b2)
forall k (a :: k) (b :: k).
SDecide k =>
Sing a -> Sing b -> Maybe (a :~: b)
`decideEquality` SingI b2 => Sing b2
forall k (a :: k). SingI a => Sing a
sing @b2
  Bool -> Maybe ()
forall (f :: * -> *). Alternative f => Bool -> f ()
guard (t a1 b1
t1 t a1 b1 -> t a1 b1 -> Bool
forall a. Eq a => a -> a -> Bool
== t a1 b1
t a2 b2
t2)

-- | Version of 'eqParamSing' for types with 3 parameters.
eqParamSing3 ::
  forall a1 a2 b1 b2 c1 c2 t.
  ( SingI a1
  , SingI a2
  , SingI b1
  , SingI b2
  , SingI c1
  , SingI c2
  , SDecide (KindOf a1)
  , SDecide (KindOf b1)
  , SDecide (KindOf c1)
  , Eq (t a1 b1 c1)
  )
  => t a1 b1 c1
  -> t a2 b2 c2
  -> Bool
eqParamSing3 :: t a1 b1 c1 -> t a2 b2 c2 -> Bool
eqParamSing3 t a1 b1 c1
t1 t a2 b2 c2
t2 = Maybe () -> Bool
forall a. Maybe a -> Bool
isJust @() (Maybe () -> Bool) -> Maybe () -> Bool
forall a b. (a -> b) -> a -> b
$ do
  a1 :~: a2
Refl <- SingI a1 => Sing a1
forall k (a :: k). SingI a => Sing a
sing @a1 Sing a1 -> Sing a2 -> Maybe (a1 :~: a2)
forall k (a :: k) (b :: k).
SDecide k =>
Sing a -> Sing b -> Maybe (a :~: b)
`decideEquality` SingI a2 => Sing a2
forall k (a :: k). SingI a => Sing a
sing @a2
  b1 :~: b2
Refl <- SingI b1 => Sing b1
forall k (a :: k). SingI a => Sing a
sing @b1 Sing b1 -> Sing b2 -> Maybe (b1 :~: b2)
forall k (a :: k) (b :: k).
SDecide k =>
Sing a -> Sing b -> Maybe (a :~: b)
`decideEquality` SingI b2 => Sing b2
forall k (a :: k). SingI a => Sing a
sing @b2
  c1 :~: c2
Refl <- SingI c1 => Sing c1
forall k (a :: k). SingI a => Sing a
sing @c1 Sing c1 -> Sing c2 -> Maybe (c1 :~: c2)
forall k (a :: k) (b :: k).
SDecide k =>
Sing a -> Sing b -> Maybe (a :~: b)
`decideEquality` SingI c2 => Sing c2
forall k (a :: k). SingI a => Sing a
sing @c2
  Bool -> Maybe ()
forall (f :: * -> *). Alternative f => Bool -> f ()
guard (t a1 b1 c1
t1 t a1 b1 c1 -> t a1 b1 c1 -> Bool
forall a. Eq a => a -> a -> Bool
== t a1 b1 c1
t a2 b2 c2
t2)

-- | Version of 'eqParamSing' for types with 3 parameters.
eqParamMixed3 ::
  forall instr1 instr2 a1 a2 b1 b2 t.
  ( Typeable instr1
  , Typeable instr2
  , SingI a1
  , SingI a2
  , SingI b1
  , SingI b2
  , SDecide (KindOf a1)
  , SDecide (KindOf b1)
  , Eq (t instr1 a1 b1)
  )
  => t instr1 a1 b1
  -> t instr2 a2 b2
  -> Bool
eqParamMixed3 :: t instr1 a1 b1 -> t instr2 a2 b2 -> Bool
eqParamMixed3 t instr1 a1 b1
t1 t instr2 a2 b2
t2 = Maybe () -> Bool
forall a. Maybe a -> Bool
isJust @() (Maybe () -> Bool) -> Maybe () -> Bool
forall a b. (a -> b) -> a -> b
$ do
  instr1 :~: instr2
Refl <- (Typeable instr1, Typeable instr2) => Maybe (instr1 :~: instr2)
forall k (a :: k) (b :: k).
(Typeable a, Typeable b) =>
Maybe (a :~: b)
eqT @instr1 @instr2
  a1 :~: a2
Refl <- SingI a1 => Sing a1
forall k (a :: k). SingI a => Sing a
sing @a1 Sing a1 -> Sing a2 -> Maybe (a1 :~: a2)
forall k (a :: k) (b :: k).
SDecide k =>
Sing a -> Sing b -> Maybe (a :~: b)
`decideEquality` SingI a2 => Sing a2
forall k (a :: k). SingI a => Sing a
sing @a2
  b1 :~: b2
Refl <- SingI b1 => Sing b1
forall k (a :: k). SingI a => Sing a
sing @b1 Sing b1 -> Sing b2 -> Maybe (b1 :~: b2)
forall k (a :: k) (b :: k).
SDecide k =>
Sing a -> Sing b -> Maybe (a :~: b)
`decideEquality` SingI b2 => Sing b2
forall k (a :: k). SingI a => Sing a
sing @b2
  Bool -> Maybe ()
forall (f :: * -> *). Alternative f => Bool -> f ()
guard (t instr1 a1 b1
t1 t instr1 a1 b1 -> t instr1 a1 b1 -> Bool
forall a. Eq a => a -> a -> Bool
== t instr1 a1 b1
t instr2 a2 b2
t2)

castSing :: forall a b t.
  (SingI a, SingI b, SDecide (KindOf a))
  => t a
  -> Maybe (t b)
castSing :: t a -> Maybe (t b)
castSing t a
ca = do
  a :~: b
Refl <- SingI a => Sing a
forall k (a :: k). SingI a => Sing a
sing @a Sing a -> Sing b -> Maybe (a :~: b)
forall k (a :: k) (b :: k).
SDecide k =>
Sing a -> Sing b -> Maybe (a :~: b)
`decideEquality` SingI b => Sing b
forall k (a :: k). SingI a => Sing a
sing @b
  t a -> Maybe (t a)
forall (m :: * -> *) a. Monad m => a -> m a
return t a
ca

-- Second-order analogue of 'SingI'
class SingI1 f where
  withSingI1 :: forall x r. SingI x => (SingI (f x) => r) -> r