-- |
-- Module      : Control.Monad.Bayes.Traced.Static
-- Description : Distributions on execution traces of full programs
-- Copyright   : (c) Adam Scibior, 2015-2020
-- License     : MIT
-- Maintainer  : leonhard.markert@tweag.io
-- Stability   : experimental
-- Portability : GHC
module Control.Monad.Bayes.Traced.Static
  ( Traced,
    hoistT,
    marginal,
    mhStep,
    mh,
  )
where

import Control.Applicative (liftA2)
import Control.Monad.Bayes.Class
import Control.Monad.Bayes.Free (FreeSampler)
import Control.Monad.Bayes.Traced.Common
import Control.Monad.Bayes.Weighted (Weighted)
import Control.Monad.Trans (MonadTrans (..))

-- | A tracing monad where only a subset of random choices are traced.
--
-- The random choices that are not to be traced should be lifted from the
-- transformed monad.
data Traced m a
  = Traced
      { model :: Weighted (FreeSampler m) a,
        traceDist :: m (Trace a)
      }

instance Monad m => Functor (Traced m) where
  fmap f (Traced m d) = Traced (fmap f m) (fmap (fmap f) d)

instance Monad m => Applicative (Traced m) where
  pure x = Traced (pure x) (pure (pure x))
  (Traced mf df) <*> (Traced mx dx) = Traced (mf <*> mx) (liftA2 (<*>) df dx)

instance Monad m => Monad (Traced m) where
  (Traced mx dx) >>= f = Traced my dy
    where
      my = mx >>= model . f
      dy = dx `bind` (traceDist . f)

instance MonadTrans Traced where
  lift m = Traced (lift $ lift m) (fmap pure m)

instance MonadSample m => MonadSample (Traced m) where
  random = Traced random (fmap singleton random)

instance MonadCond m => MonadCond (Traced m) where
  score w = Traced (score w) (score w >> pure (scored w))

instance MonadInfer m => MonadInfer (Traced m)

hoistT :: (forall x. m x -> m x) -> Traced m a -> Traced m a
hoistT f (Traced m d) = Traced m (f d)

-- | Discard the trace and supporting infrastructure.
marginal :: Monad m => Traced m a -> m a
marginal (Traced _ d) = fmap output d

-- | A single step of the Trace Metropolis-Hastings algorithm.
mhStep :: MonadSample m => Traced m a -> Traced m a
mhStep (Traced m d) = Traced m d'
  where
    d' = d >>= mhTrans m

-- | Full run of the Trace Metropolis-Hastings algorithm with a specified
-- number of steps.
mh :: MonadSample m => Int -> Traced m a -> m [a]
mh n (Traced m d) = fmap (map output) (f n)
  where
    f 0 = fmap (: []) d
    f k = do
      ~(x : xs) <- f (k -1)
      y <- mhTrans m x
      return (y : x : xs)