TraversalIso.hs

{-# LANGUAGE RankNTypes #-}

module TraversalIso where

import Control.Lens.Traversal
import Control.Monad.State.Lazy
import Data.Traversable (Traversable (..))

{-
type Traversal s t a b = forall f. Applicative f => (a -> f b) -> s -> f t
type Traversal' s a = Traversal s s a a
-}

type SimpleTraversal' s a =
  forall r. r -> (a -> r -> (a,r)) -> s -> (s,r)

iso :: Traversal' s a -> SimpleTraversal' s a
iso trav init step s = runState (trav (state . step) s) init

osi :: SimpleTraversal' s a -> Traversal' s a
osi simpleTrav f s =
  let (_, bs) = simpleTrav [] (\a xs -> (a, f a : xs)) s
  in fmap (\bs' -> fst (simpleTrav bs' (\_ (b:bs) -> (b, bs)) s))
          (sequenceA (reverse bs))