{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}

-- The reason why this is a separate module with little in it:
{-# LANGUAGE AllowAmbiguousTypes #-}

module AST.Weaken where


data env :> env' where
  WId :: env :> env
  WSink :: env :> (t : env)
  WCopy :: env :> env' -> (t : env) :> (t : env')
  WPop :: (t : env) :> env' -> env :> env'
  WThen :: env1 :> env2 -> env2 :> env3 -> env1 :> env3
  WClosed :: '[] :> env
deriving instance Show (env :> env')

(.>) :: env2 :> env3 -> env1 :> env2 -> env1 :> env3
(.>) = flip WThen

type family Append a b where
  Append '[] l = l
  Append (x : xs) l = x : Append xs l

data ListSpine list where
  LSNil :: ListSpine '[]
  LSCons :: ListSpine list -> ListSpine (t : list)

class KnownListSpine list where knownListSpine :: ListSpine list
instance KnownListSpine '[] where knownListSpine = LSNil
instance KnownListSpine list => KnownListSpine (t : list) where knownListSpine = LSCons knownListSpine

wSinks :: forall list env. KnownListSpine list => env :> Append list env
wSinks = go (knownListSpine :: ListSpine list)
  where
    go :: forall list'. ListSpine list' -> env :> Append list' env
    go LSNil = WId
    go (LSCons spine) = WSink .> go spine