{-# LANGUAGE PatternSynonyms #-}
{-# LANGUAGE ConstraintKinds #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE GADTs #-}
-----------------------------------------------------------------------------
-- |
-- Module : Data.Type.Index
-- Copyright : Copyright (C) 2015 Kyle Carter
-- License : BSD3
--
-- Maintainer : Kyle Carter <kylcarte@indiana.edu>
-- Stability : experimental
-- Portability : RankNTypes
--
-- A @singleton@-esque type for representing indices in a type-level list.
--
-----------------------------------------------------------------------------
module Data.Type.Index where
import Type.Class.HFunctor
import Type.Class.Known
import Type.Family.List
import Type.Family.Nat
data Index :: [k] -> k -> * where
IZ :: Index (a :< as) a
IS :: !(Index as a) -> Index (b :< as) a
deriving instance Eq (Index as a)
deriving instance Ord (Index as a)
deriving instance Show (Index as a)
type a ∈ as = Elem as a
infix 6 ∈
class Elem (as :: [k]) (a :: k) where
elemIndex :: Index as a
instance {-# OVERLAPPING #-} Elem (a :< as) a where
elemIndex = IZ
instance {-# OVERLAPPABLE #-} Elem as a => Elem (b :< as) a where
elemIndex = IS elemIndex
instance {-# OVERLAPPING #-} Known (Index (a :< as)) a where
known = IZ
instance {-# OVERLAPPABLE #-} Known (Index as) a => Known (Index (b :< as)) a where
known = IS known