Phil wrote: | After some googling it looked like the answer may be Monad Transformers. | Specifically we could add a StateT transform for our Box Muller state to our | VanDerCorput State Monad. | Google didn¹t yield a direct answer here so I¹m not even sure if my | thinking is correct, Ignoring Daniel Fischer's astute observation that you can generalize the idea to directly describe the stream ;) The sample code you're looking for is:
{-# LANGUAGE GeneralizedNewtypeDeriving #-} import Control.Monad.State
newtype VanDerCorput a = VDC (State Int a) deriving Monad
runVDC :: VanDerCorput a -> a runVDC (VDC sa) = evalState sa 1
getVDC :: VanDerCorput Int getVDC = VDC $ do x <- get put (f x) return x where f = (1+)
newtype BoxMuller a = BM (StateT (Maybe Int) VanDerCorput a) deriving Monad
runBM :: BoxMuller a -> a runBM (BM vsa) = runVDC (evalStateT vsa Nothing)
getBM :: BoxMuller Int getBM = BM $ do saved <- get case saved of Just x -> put Nothing >> return x Nothing -> do a <- lift getVDC b <- lift getVDC put (Just (f a b)) return (g a b) where -- or whatever... f = const g = const id
-- Live well, ~wren