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@nicuveo
Last active Sep 30, 2019
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{-# LANGUAGE ConstraintKinds #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE ParallelListComp #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UndecidableInstances #-}
{-
Inspired by:
https://www.reddit.com/r/haskellquestions/comments/db18yc/trying_to_index_a_ndimensional_list/
Disclaimer: I have no idea what I'm doing.
-}
module Indexable ( Indexable
, Indexed
, indexN
, index1
, index2
, index3
, index4
, index5
) where
-- import
import Data.Proxy
import GHC.TypeLits
-- peano numbers
data PN = PZ | PS PN
-- conversion from nats to peano
type family ToPN (n :: Nat) where
ToPN 0 = 'PZ
ToPN n = 'PS (ToPN (n-1))
-- indexation recursion
class PNIndexable (n :: PN) a where
type PNIndexed n a
indexify :: [Int] -> Proxy n -> a -> PNIndexed n a
instance PNIndexable 'PZ a where
type PNIndexed 'PZ a = ([Int], a)
indexify c _ x = (reverse c, x)
instance PNIndexable n a => PNIndexable ('PS n) [a] where
type PNIndexed ('PS n) [a] = [PNIndexed n a]
indexify c n v = [indexify (i:c) (prevNat n) p | i <- [0..] | p <- v]
where prevNat :: Proxy ('PS n) -> Proxy n
prevNat = const Proxy
-- aliases for natural numbers
type Indexable (n :: Nat) a = PNIndexable (ToPN n) a
type Indexed (n :: Nat) a = PNIndexed (ToPN n) a
-- index functions
indexN :: Indexable n a => Proxy n -> a -> Indexed n a
indexN = indexify [] . toPN
where toPN :: Proxy n -> Proxy (ToPN n)
toPN = const Proxy
index1 :: Indexable 1 a => a -> Indexed 1 a
index1 = indexN (Proxy :: Proxy 1)
index2 :: Indexable 2 a => a -> Indexed 2 a
index2 = indexN (Proxy :: Proxy 2)
index3 :: Indexable 3 a => a -> Indexed 3 a
index3 = indexN (Proxy :: Proxy 3)
index4 :: Indexable 4 a => a -> Indexed 4 a
index4 = indexN (Proxy :: Proxy 4)
index5 :: Indexable 5 a => a -> Indexed 5 a
index5 = indexN (Proxy :: Proxy 5)
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