module Hyper.Type.AST.NamelessScope.InvDeBruijn
    ( InvDeBruijnIndex(..), inverseDeBruijnIndex, scope, scopeVar
    ) where

import Control.Lens (Prism', iso)
import Control.Lens.Operators
import Data.Proxy (Proxy(..))
import Hyper.Type (type (#))
import Hyper.Type.AST.NamelessScope (DeBruijnIndex(..), EmptyScope, Scope(..), ScopeVar(..))

class DeBruijnIndex a => InvDeBruijnIndex a where
    deBruijnIndexMax :: Proxy a -> Int

instance InvDeBruijnIndex EmptyScope where
    deBruijnIndexMax _ = -1

instance InvDeBruijnIndex a => InvDeBruijnIndex (Maybe a) where
    deBruijnIndexMax _ = 1 + deBruijnIndexMax (Proxy @a)

inverseDeBruijnIndex :: forall a. InvDeBruijnIndex a => Prism' Int a
inverseDeBruijnIndex =
    iso (l -) (l -) . deBruijnIndex
    where
        l = deBruijnIndexMax (Proxy @a)

scope ::
    forall expr a f.
    InvDeBruijnIndex a =>
    (Int -> f # expr (Maybe a)) ->
    Scope expr a # f
scope f = Scope (f (inverseDeBruijnIndex # (Nothing :: Maybe a)))

scopeVar :: InvDeBruijnIndex a => Int -> ScopeVar expr a f
scopeVar x = ScopeVar (x ^?! inverseDeBruijnIndex)