The Static Argument Transformation (SAT)

This page summarises progress on the Static Argument Transformation.

See:

• Andre Sansos's thesis which has a whole chapter.
• Danvy's lambda-dropping paper

In comment:10 of #5059, Max notes that SAT provides 20-30% wins in nofib, wow!

I think we really want to be able to perform value specialization of recursive functions without SAT. The performance trade-off of SAT when it comes to code generation doesn't look so hot in many cases. BTW, I noticed that the lack of SAT or argument specialization can prevent good optimization of derived code. For example, data Tree a = Branch (Tree a) (Tree a) | Leaf a deriving Foldable yields a very mediocre-looking foldl' that would be fixed by a foldr that could inline. It also produces a very boxing length, but that smells like a trickier higher-order demand issue. --dfeuer

Tickets

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Matt's Notes

The primary value of performing SAT is to enable the function to be inlined and hence simplified.

The decision about whether to run SAT is currently predicated on the number of static value arguments. If there is more than one static argument then the transformation is run, otherwise it is not. I am unsure why this decision has been made, there are useful situations where running the transformation with one argument (see test2 below). I don't think it has been scrutinised much as 1. Not many people use this optimisation and 2. Usually there is more than one static argument. (For example, a dictionary and a function which uses that dictionary).

Interaction with specialisation

One very useful time to run SAT is after specialisation and SpecConstr. Specialisation especially can create situations where static dictionaries are passed to functions using RankNTypes which are then not eliminated leading to slow dictionary lookups.

However, we also have the be careful as sometimes these passes produce recursive groups which are later broken up. SAT only works for recursive groups which contain exactly one definition due to the possibility of blow-up.

test and test2 are only optimised well with an additional late pass of SAT.

{-# LANGUAGE RankNTypes, BangPatterns  #-}
module Standalone where

import qualified Control.Monad.State as S

times :: Monad m => Int -> m a -> m ()
times n ma = go n where
  go 0 = pure ()
  go n = ma >> go (n - 1)
{-# inline times #-}


newtype VSM s a = VSM { runVSM :: forall m. Monad m => m s -> (s -> m ()) -> m a}

instance Functor (VSM s) where
  fmap f (VSM g) = VSM $ \get put ->
    g get put >>= \a -> pure (f a)
  {-# inline fmap #-}

instance Applicative (VSM s) where
  pure a = VSM $ \get put -> pure a
  VSM mf <*> VSM ma = VSM $ \get put ->
    mf get put >>= \f ->
    ma get put >>= \a -> pure (f a)
  {-# inline pure #-}
  {-# inline (<*>) #-}

instance Monad (VSM s) where
  return a = VSM $ \get put -> pure a
  VSM ma >>= f = VSM $ \get put ->
    ma get put >>= \a -> runVSM (f a) get put
  {-# inline return #-}

vmmodify :: (s -> s) -> VSM s ()
vmmodify f = VSM $ \get put ->
  get >>= \s ->
  let !s' = f s in
  put s'
{-# inline vmmodify #-}

vmrunState :: VSM s a -> s -> (a, s)
vmrunState (VSM ma) = S.runState (ma S.get S.put)
{-# inline vmrunState #-}

test :: Int -> ((), Int)
test n = vmrunState (times n $ vmmodify (+1)) n


newtype CS s a = CS {runCS ::
     forall r.
     (a -> r)          -- pure
  -> ((s -> r) -> r)   -- get
  -> (s -> r -> r)     -- put
  -> r
  }

instance Functor (CS s) where
  fmap f (CS g) = CS $ \pure get put -> g (pure . f) get put
  {-# inline fmap #-}

instance Applicative (CS s) where
  pure a = CS $ \pure get put -> pure a
  {-# inline pure #-}
  CS mf <*> CS ma = CS $ \pure get put ->
    mf (\f -> ma (pure . f) get put) get put
  {-# inline (<*>) #-}

instance Monad (CS s) where
  return a = CS $ \pure get put -> pure a
  {-# inline return #-}
  CS ma >>= f = CS $ \pure get put ->
    ma (\a -> runCS (f a) pure get put) get put
  {-# inline (>>=) #-}
  CS ma >> CS mb = CS $ \pure get put -> ma (\_ -> mb pure get put) get put
  {-# inline (>>) #-}

cmodify :: (s -> s) -> CS s ()
cmodify f = CS $ \pure get put ->
  get $ \s -> let !s' = f s in
  put s' $
  pure ()
{-# inline cmodify #-}

crunState :: CS s a -> s -> (a, s)
crunState (CS f) = f
  (\a s -> (a, s))
  (\got s -> got s s)
  (\s' put s -> put s')
{-# inline crunState #-}

test2 :: Int -> ((), Int)
test2 n = crunState (times n (cmodify (+1))) 0

# Interaction with Join Points

In section 5 of "compiling without continuations" it is noted that join points enable fusion but in order to do so you have to write your programs in a particular style.

module Join where

find :: (a -> Bool) -> [a] -> Maybe a
find p xs = go xs
  where
    go [] = Nothing
    go (x:xs) = if p x then Just x else go xs

any :: (a -> Bool) -> [a] -> Bool
any p xs  = case find p xs of
              Just _ -> True
              Nothing -> False

The core for any is then nicely fused as go is identified as a join point which means that it can be inlined even though find is recursive.

This particular style is exactly the kind of code which the static argument transformation produces. Currently it is not enough to turn on -fstatic-argument-transformation as the order the transformations are run seems wrong.