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{-# LANGUAGE DataKinds #-}
{-# LANGUAGE EmptyCase #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE StandaloneKindSignatures #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
module CHAD.EnvDescr where

import Data.Kind (Type)
import Data.Some
import GHC.TypeLits (Symbol)

import Analysis.Identity (ValId(..))
import AST.Env
import AST.Types
import AST.Weaken
import CHAD.Types
import Data


type Storage :: Symbol -> Type
data Storage s where
  SAccum :: Storage "accum"  -- ^ in the monad state as a mutable accumulator
  SMerge :: Storage "merge"  -- ^ just return and merge
  SDiscr :: Storage "discr"  -- ^ we happen to know this is a discrete type and won't need any contributions
deriving instance Show (Storage s)

-- | Environment description
data Descr env sto where
  DTop :: Descr '[] '[]
  DPush :: Descr env sto -> (STy t, Maybe (ValId t), Storage s) -> Descr (t : env) (s : sto)
deriving instance Show (Descr env sto)

descrList :: Descr env sto -> SList STy env
descrList DTop = SNil
descrList (des `DPush` (t, _, _)) = t `SCons` descrList des

descrPrj :: Descr env sto -> Idx env t -> (STy t, Maybe (ValId t), Some Storage)
descrPrj (_ `DPush` (ty, vid, sto)) IZ = (ty, vid, Some sto)
descrPrj (des `DPush` _) (IS i) = descrPrj des i
descrPrj DTop i = case i of {}

-- | This could have more precise typing on the output storage.
subDescr :: Descr env sto -> Subenv env env'
         -> (forall sto'. Descr env' sto'
                       -> Subenv (Select env sto "merge") (Select env' sto' "merge")
                       -> Subenv (D2AcE (Select env sto "accum")) (D2AcE (Select env' sto' "accum"))
                       -> Subenv (D1E env) (D1E env')
                       -> r)
         -> r
subDescr DTop SETop k = k DTop SETop SETop SETop
subDescr (des `DPush` (t, vid, sto)) (SEYes sub) k =
  subDescr des sub $ \des' submerge subaccum subd1e ->
    case sto of
      SMerge -> k (des' `DPush` (t, vid, sto)) (SEYes submerge) subaccum (SEYes subd1e)
      SAccum -> k (des' `DPush` (t, vid, sto)) submerge (SEYes subaccum) (SEYes subd1e)
      SDiscr -> k (des' `DPush` (t, vid, sto)) submerge subaccum (SEYes subd1e)
subDescr (des `DPush` (_, _, sto)) (SENo sub) k =
  subDescr des sub $ \des' submerge subaccum subd1e ->
    case sto of
      SMerge -> k des' (SENo submerge) subaccum (SENo subd1e)
      SAccum -> k des' submerge (SENo subaccum) (SENo subd1e)
      SDiscr -> k des' submerge subaccum (SENo subd1e)

-- | Select only the types from the environment that have the specified storage
type family Select env sto s where
  Select '[] '[] _ = '[]
  Select (t : ts) (s : sto) s = t : Select ts sto s
  Select (_ : ts) (_ : sto) s = Select ts sto s

select :: Storage s -> Descr env sto -> SList STy (Select env sto s)
select _ DTop = SNil
select s@SAccum (DPush des (t, _, SAccum)) = SCons t (select s des)
select s@SMerge (DPush des (_, _, SAccum)) = select s des
select s@SDiscr (DPush des (_, _, SAccum)) = select s des
select s@SAccum (DPush des (_, _, SMerge)) = select s des
select s@SMerge (DPush des (t, _, SMerge)) = SCons t (select s des)
select s@SDiscr (DPush des (_, _, SMerge)) = select s des
select s@SAccum (DPush des (_, _, SDiscr)) = select s des
select s@SMerge (DPush des (_, _, SDiscr)) = select s des
select s@SDiscr (DPush des (t, _, SDiscr)) = SCons t (select s des)