Monday, February 15, 2016

Fixing a space leak by copying thunks.

After my last blog post about FRP I got feedback that my approach makes it easy to accidentally introduce space leaks. I also got helpful pointers to resources. In this post I give an example program with a space leak and discuss how to fix it.

The Behavior type

We work with the following Behavior type:

data Behavior next a =
  AndThen a (next (Behavior next a))

now :: Behavior next a -> a
now (AndThen a _) = a

future :: Behavior next a -> next (Behavior next a)
future (AndThen _ nextBehavior) = nextBehavior

A behavior is a stream of values. It has a current value that we can extract with now and a future behavior that we can extract with future. The Behavior type constructor has two type parameters. The first type parameter called next lets us decide which effects we want to allow when we advance to the next iteration. The second type parameter called a is the type of values this behavior carries. The behavior type is the same (up to renaming) as Cofree.

We can instantiate next with different types. We have instances of Functor and Applicative for Behavior as long as we instantiate next with types that have instances of Functor and Applicative:

instance (Functor next) => Functor (Behavior next) where

  fmap f (a `AndThen` nextAs) =
    (f a) `AndThen` (fmap (fmap f) nextAs)

instance (Applicative next) => Applicative (Behavior next) where

  pure a = a `AndThen` (pure (pure a))

  (f `AndThen` nextFs) <*> (x `AndThen` nextXs) =
    (f x) `AndThen` (liftA2 (<*>) nextFs nextXs)

Just a note: this Applicative instance is different to the one for Cofree.

In the last post next was IO which allows arbitrary side-effects and is hard to reason about. But we can for example instantiate next to Identity which means we get ordinary pure lists. Because behaviors over Identity are like lists we have correspondences between fmap and map, now and head and liftA2 and zipWith.

To test behaviors where next is Identity we use a function that writes its elements to the console:

runList :: (Show a) => Behavior Identity a -> IO ()
runList (a `AndThen` as) = do
  print a
  runList (runIdentity as)

We use runIdentity to get the next behavior to run.

A leaky program

Let’s create a program with a space leak! We will take inspiration from programs on lists. We use two functions that correspond to enumFrom and repeat called countFrom and always. countFrom takes an Int and starts counting from that number. always lets us transport any value indefinitely far into the future. They work for behaviors with all sorts of instantiations for next as long as they are Applicative because they use pure.

countFrom :: (Applicative next) => Int -> Behavior next Int
countFrom i = i `AndThen` pure (countFrom (i + 1))

always :: (Applicative next) => a -> Behavior next a
always a = a `AndThen` pure (always a)

We will use countFrom to create a behavior called numbers. We will pair it with a behavior that is always zero. When we run the final program (for historical reasons named animations) the output looks like this:

> animations

The trick is that the second element of the printed pairs will require a reference to numbers. This means that numbers cannot be garbage collected. As numbers expands it will take up more and more heap space. The program looks like this:

main :: IO ()
main = do

  let numbers = countFrom 0

  let alwaysNumbers = fmap now (always numbers)

  let pairs = liftA2 (,) numbers alwaysNumbers

  runList pairs

We transport numbers into the future using always. This would be a behavior of behaviors. At each point in time we extract the current value to get a behavior of Int using fmap now. We call the resulting behavior alwaysNumbers. Then we zip numbers and alwaysNumbers together using liftA2. Finally we run the behavior (which means to keep iterating and printing).

Here is a heap profile created by invoking the program with animations +RTS -h. We invoked hp2pretty on animations.hp to produce the following picture:

list heap profile

Space usage grows linearly with time.

The problem pictorially

The following shows a sketch of the heap after the program printed (3,0):

list heap sketch

The chain of cells represents the numbers value. The two arrows coming from the top are two references: one to the original numbers value and one to the current element. The little cloud represents the unevaluated thunk that is the future behavior.

Now, what if we didn’t have a single chain of cells? What if we copied all future behavior thunks and did not replace them? We would get a picture like this:

copying heap sketch

The garbage collector will reclaim the cells for 1 and 2 because there are no references to them.

Copying thunks

Let me demonstrate what I mean with “copying thunks” with a small ghci session. On a high level we bind exampleThunk to the pure value True and evaluate it three times. To observe the evaluation we use trace from Debug.Trace to print "thunk evaluated" upon evaluation.

> import Debug.Trace
> let exampleThunk = trace "thunk evaluated" True
> exampleThunk
thunk evaluated
> exampleThunk
> exampleThunk

The string "thunk evaluated" appears only once. Later evaluations reuse the previously computed value. Usually this is a good thing because the thunk might have been costly to evaluate.

But now what we’d like to have are two functions with the following signatures:

copy :: a -> Copy a
getCopy :: Copy a -> a

This time we use functions copy and getCopy to make the evaluation of exampleThunk happen multiple times.

> import Debug.Trace
> let exampleThunk = trace "thunk evaluated" True
> let copyOfExampleThunk = copy exampleThunk
> getCopy copyOfExampleThunk
thunk evaluated
> getCopy copyOfExampleThunk
thunk evaluated
> getCopy copyOfExampleThunk
thunk evaluated

Whenever we force the result of getCopy the thunk is evaluated. We do not replace the original thunk by the result.

The Copy Applicative

I don’t think it is possible to get the desired behavior of Copy with current GHC. But luckily Joachim Breitner has published an experiment in the form of the ghc-dup package a few years ago. It works (as a prototype) for GHC 7.4 and GHC 7.6. It provides a function dup that allows us to create the desired Copy type and make it an Applicative:

data Copy a = Copy a

copy :: a -> Copy a
copy a = Copy a

getCopy :: Copy a -> a
getCopy (Copy a) = case dup a of Box a' -> a'

instance Functor Copy where
  fmap f a = copy (f (getCopy a))

instance Applicative Copy where
  pure a = copy a
  f <*> a = copy ((getCopy f) (getCopy a))

We are careful to never directly use the thunk inside Copy. Instead we copy it with getCopy.

Heap profile with copying

Now we can instantiate our behavior with Copy instead of with Identity and still run it like so:

runCopying :: (Show a) => Behavior Copy a -> IO ()
runCopying (a `AndThen` copyAs) = do
  print a
  runCopying (getCopy copyAs)

We use getCopy instead of runIdentity to get the next behavior. This allows us to change the previously leaky program to use Copy instead of Identity by using runCopying instead of runList:

main :: IO ()
main = do

  let numbers = countFrom 0

  let alwaysNumbers = fmap now (always numbers)

  let pairs = liftA2 (,) numbers alwaysNumbers

  runCopying pairs

We get the same output but the following heap profile:

enter image description here

The space leak is gone.


GHC uses call-by-need by default. It allows for call-by-value via seq and deepseq. Sometimes we want call-by-name. I believe that if ghc-dup was a feature supported by GHC we would see it used.

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