{-# LANGUAGE DataKinds #-}
{-# LANGUAGE EmptyCase #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE TypeOperators #-}
module AST.Env where

import AST.Weaken
import Data


-- | @env'@ is a subset of @env@: each element of @env@ is either included in
-- @env'@ ('SEYes') or not included in @env'@ ('SENo').
data Subenv env env' where
  SETop :: Subenv '[] '[]
  SEYes :: Subenv env env' -> Subenv (t : env) (t : env')
  SENo  :: Subenv env env' -> Subenv (t : env) env'
deriving instance Show (Subenv env env')

subList :: SList f env -> Subenv env env' -> SList f env'
subList SNil SETop = SNil
subList (SCons x xs) (SEYes sub) = SCons x (subList xs sub)
subList (SCons _ xs) (SENo sub) = subList xs sub

subenvAll :: SList f env -> Subenv env env
subenvAll SNil = SETop
subenvAll (SCons _ env) = SEYes (subenvAll env)

subenvNone :: SList f env -> Subenv env '[]
subenvNone SNil = SETop
subenvNone (SCons _ env) = SENo (subenvNone env)

subenvOnehot :: SList f env -> Idx env t -> Subenv env '[t]
subenvOnehot (SCons _ env) IZ = SEYes (subenvNone env)
subenvOnehot (SCons _ env) (IS i) = SENo (subenvOnehot env i)
subenvOnehot SNil i = case i of {}

subenvCompose :: Subenv env1 env2 -> Subenv env2 env3 -> Subenv env1 env3
subenvCompose SETop SETop = SETop
subenvCompose (SEYes sub1) (SEYes sub2) = SEYes (subenvCompose sub1 sub2)
subenvCompose (SEYes sub1) (SENo sub2) = SENo (subenvCompose sub1 sub2)
subenvCompose (SENo sub1) sub2 = SENo (subenvCompose sub1 sub2)