{-# LANGUAGE DataKinds #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE QuantifiedConstraints #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
module CHAD where

import Data.Functor.Const

import AST


type Ex = Expr (Const ())

data Bindings f env env' where
  BTop :: Bindings f env env
  BPush :: Bindings f env env' -> f env' t -> Bindings f env (t : env')
deriving instance (forall e t. Show (f e t)) => Show (Bindings f env env')

weakenBindings :: (forall e1 e2 t. e1 :> e2 -> f e1 t -> f e2 t)
               -> env1 :> env2 -> Bindings f env1 env'
               -> (forall env2'. Bindings f env2 env2' -> env' :> env2' -> r) -> r
weakenBindings _ w BTop k = k BTop w
weakenBindings wf w (BPush b x) k =
  weakenBindings wf w b $ \b' w' -> k (BPush b' (wf w' x)) (WCopy w')

sinkWithBindings :: Bindings f env env' -> env :> env'
sinkWithBindings BTop = WId
sinkWithBindings (BPush b _) = WSink .> sinkWithBindings b

bconcat :: Bindings f env1 env2 -> Bindings f env2 env3 -> Bindings f env1 env3
bconcat b1 BTop = b1
bconcat b1 (BPush b2 x) = BPush (bconcat b1 b2) x

bconcat' :: (forall e1 e2 t. e1 :> e2 -> f e1 t -> f e2 t)
         -> Bindings f env env1 -> Bindings f env env2
         -> (forall env12. Bindings f env env12 -> r) -> r
bconcat' wf b1 b2 k = weakenBindings wf (sinkWithBindings b1) b2 $ \b2' _ -> k (bconcat b1 b2')

type family D1 t where
  D1 TNil = TNil
  D1 (TPair a b) = TPair (D1 a) (D1 b)
  D1 (TArr n t) = TArr n (D1 t)
  D1 (TScal t) = TScal t

type family D2 t where
  D2 TNil = TNil
  D2 (TPair a b) = TPair (D2 a) (D2 b)
  -- D2 (TArr n t) = _
  D2 (TScal t) = D2s t

type family D2s t where
  D2s TI32 = TNil
  D2s TI64 = TNil
  D2s TF32 = TScal TF32
  D2s TF64 = TScal TF64
  D2s TBool = TNil

type family D1E env where
  D1E '[] = '[]
  D1E (t : env) = D1 t : D1E env

type family D2E env where
  D2E '[] = '[]
  D2E (t : env) = D2 t : D2E env

d1 :: STy t -> STy (D1 t)
d1 STNil = STNil
d1 (STPair a b) = STPair (d1 a) (d1 b)
d1 (STArr n t) = STArr n (d1 t)
d1 (STScal t) = STScal t
d1 STEVM{} = error "EVM not allowed in input program"

d2 :: STy t -> STy (D2 t)
d2 STNil = STNil
d2 (STPair a b) = STPair (d2 a) (d2 b)
d2 STArr{} = error "TODO arrays"
d2 (STScal t) = case t of
  STI32 -> STNil
  STI64 -> STNil
  STF32 -> STScal STF32
  STF64 -> STScal STF64
  STBool -> STNil
d2 STEVM{} = error "EVM not allowed in input program"

d2list :: SList STy env -> SList STy (D2E env)
d2list SNil = SNil
d2list (SCons x l) = SCons (d2 x) (d2list l)

conv1Idx :: Idx env t -> Idx (D1E env) (D1 t)
conv1Idx IZ = IZ
conv1Idx (IS i) = IS (conv1Idx i)

conv2Idx :: Idx env t -> Idx (D2E env) (D2 t)
conv2Idx IZ = IZ
conv2Idx (IS i) = IS (conv2Idx i)

data Ret env t =
  forall env'.
    Ret (Bindings Ex (D1E env) env')
        (Ex env' (D1 t))
        (Ex (D2 t : env') (TEVM (D2E env) TNil))
deriving instance Show (Ret env t)

drev :: SList STy env -> Ex env t -> Ret env t
drev senv = \case
  EVar _ t i ->
    Ret BTop
        (EVar ext (d1 t) (conv1Idx i))
        (EMOne (d2list senv) (conv2Idx i) (EVar ext (d2 t) IZ))
  ELet _ rhs body
    | Ret rhs0 rhs1 rhs2 <- drev senv rhs
    , Ret body0 body1 body2 <- drev (SCons (typeOf rhs) senv) body ->
    weakenBindings weakenExpr (WCopy (sinkWithBindings rhs0)) body0 $ \body0' wbody0' ->
    Ret (bconcat (BPush rhs0 rhs1) body0')
        (weakenExpr wbody0' body1)
        (EMBind (EMScope (weakenExpr (WCopy wbody0') body2))
                (ELet ext (ESnd ext STNil (EVar ext (STPair STNil (d2 (typeOf rhs))) IZ)) $
                  weakenExpr (WCopy (WSink .> WSink .> WPop (sinkWithBindings body0'))) rhs2))
  _ -> undefined
  where
    ext = Const ()