Welcome to the first part of a tutorial on writing your very own concurrency testing library for Haskell. Before we get into the details, let’s just clarify what I mean by a “concurrency testing library”. The goal is a function which, given some concurrent Haskell like so:

example = do a <- newEmptyMVar forkIO ( putMVar a 1 ) forkIO ( putMVar a 2 ) takeMVar a

Will tell us the possible results of that computation:

λ> test example [1, 2]

We’re going to build this from the ground up, using the concurrency library, as it provides a typeclass abstraction over forking, MVars, STM, and suchlike.

You may have come across my dejafu library before. If not, don’t worry, but you may want to check it out as we’re going to be building something very similar.

Let’s get down to business

Ok, with the preliminaries over, let’s get coding! All the code written in this series is on GitHub, with one tag for each post. The code for this post is under the “post-01” tag.

The goal in this post is to be able to implement a function which can execute simple thread-and-MVar computations (like the example from the beginning) with a stateful scheduler. Firstly, let’s say what we know:

We’re using the MonadConc typeclass from concurrency, rather than IO .

typeclass from concurrency, rather than . We want to be able to examine arbitrary MonadConc computations.

computations. We also want to be able to pause and resume “threads” at will, so we can explore different executions.

That sounds rather like something based on continuations or a free monad. Furthermore, we’re going to need mutable state to implement all of this, as we’re modelling a DSL with mutable references, and doing that purely is a huge pain.

Let’s write down some types. Because we’re writing a mini-dejafu, I’m calling this project “minifu”. So we want a function:

import qualified Control.Concurrent.Classy as C import Data.List.NonEmpty ( NonEmpty ( .. )) newtype ThreadId = ThreadId Int deriving ( Eq , Ord ) type Scheduler s = NonEmpty ThreadId -> s -> ( ThreadId , s ) minifu :: C . MonadConc m => Scheduler s -> s -> MiniFu m a -> m ( Maybe a , s )

For some suitable MiniFu monad transformer. Now we’re going to take the standard way of constructing a free monad, and have a data structure representing our class of interest ( MonadConc ), with one constructor for every function. Because we’re only talking about threads and MVars in this post, it will be a fairly small type:

{-# LANGUAGE GADTs #-} data PrimOp m where Fork :: MiniFu m () -> ( ThreadId -> PrimOp m ) -> PrimOp m NewEmptyMVar :: ( MVar m a -> PrimOp m ) -> PrimOp m PutMVar :: MVar m a -> a -> PrimOp m -> PrimOp m TakeMVar :: MVar m a -> ( a -> PrimOp m ) -> PrimOp m Stop :: m () -> PrimOp m newtype MVarId = MVarId Int deriving ( Eq , Ord ) data MVar m a = MVar { mvarId :: MVarId , mvarRef :: C . CRef m ( Maybe a ) }

The Stop action is what is going to let us communicate the final result out of the computation. I’ve also defined an MVar type. Our MVars are going to be implemented as a CRef (what concurrency calls an IORef ) holding a maybe value, along with an identifier. These identifiers will come into play when we look at threads blocking.

Given this set up, the MiniFu type is very simple:

{-# LANGUAGE GeneralizedNewtypeDeriving #-} import qualified Control.Monad.Cont as K newtype MiniFu m a = MiniFu { runMiniFu :: K . Cont ( PrimOp m ) a } deriving ( Functor , Applicative , Monad )

We’re not actually going to write a MonadConc instance for MiniFu yet, because there are a bunch of constraints which we can’t really satisfy. But we can still define the functions of interest:

fork :: MiniFu m () -> MiniFu m ThreadId fork ma = MiniFu ( K . cont ( Fork ma )) newEmptyMVar :: MiniFu m ( MVar m a ) newEmptyMVar = MiniFu ( K . cont NewEmptyMVar ) putMVar :: MVar m a -> a -> MiniFu m () putMVar v a = MiniFu ( K . cont ( \ k -> PutMVar v a ( k () ))) takeMVar :: MVar m a -> MiniFu m a takeMVar v = MiniFu ( K . cont ( TakeMVar v ))

Hey, not bad! Now we can slap a MiniFu m Int type signature on our example from the start (and rename the forkIO calls) and it compiles!

example :: MiniFu m Int example = do a <- newEmptyMVar fork ( putMVar a 1 ) fork ( putMVar a 2 ) takeMVar a

Take a moment to make sure you’re happy with this section before moving on to the next. MiniFu is going to be a layered application: this is the basic layer which defines the functions we can test; the next layer executes a MiniFu computation; the layers above that will implement the systematic testing behaviour.

Implementing minifu

Recall the type of minifu :

minifu :: C . MonadConc m => Scheduler s -> s -> MiniFu m a -> m ( Maybe a , s )

So, what does it need to do? It needs to set up the execution environment: in this case that’s specifying that the provided computation is the main thread, and then it needs to repeatedly call the scheduler, executing one PrimOp of the chosen thread at a time, until either the main thread terminates or everything is blocked.

In the best functional programming practice, minifu is going to do the minimum it can and call another function to do the rest. So what minifu is actually going to do is to extract the continuation and set up the mechanism to communicate the final result back:

minifu sched s ( MiniFu ma ) = do out <- C . newCRef Nothing s' <- run sched s ( K . runCont ma ( Stop . C . writeCRef out . Just )) a <- C . readCRef out pure ( a , s' )

Before we move on to the implementation of run , let’s first look at two concerns we’ll have along the way: getting unique names (for threads and MVars) and representing threads.

Names

Each thread gets a unique ThreadId , and each MVar gets a unique MVarId . As these are just an Int , we can use the same source for both:

type IdSource = Int initialIdSource :: IdSource initialIdSource = 0 nextThreadId :: IdSource -> ( ThreadId , IdSource ) nextThreadId n = ( ThreadId n , n + 1 ) nextMVarId :: IdSource -> ( MVarId , IdSource ) nextMVarId n = ( MVarId n , n + 1 )

This is as simple as it gets, but it’s good enough for now.

Threads

What is a thread? Well, it has a continuation, which is some value of type PrimOp m , and it might be blocked. We want to know if a thread is blocked for two reasons: we don’t want the scheduler to schedule a blocked thread, and we want to be able to tell if the computation is deadlocked. Threads can only block on reading from or writing to MVars (currently), so let’s use a Maybe MVarId to indicate whether the thread is blocked:

data Thread m = Thread { threadK :: PrimOp m , threadBlock :: Maybe MVarId }

When we create a thread, it’s initially unblocked:

thread :: PrimOp m -> Thread m thread k = Thread { threadK = k , threadBlock = Nothing }

And finally we need a way to construct our initial collection of threads:

import Data.Map ( Map ) import qualified Data.Map as M type Threads m = Map ThreadId ( Thread m ) initialise :: PrimOp m -> ( Threads m , IdSource ) initialise k = let ( tid , idsrc ) = nextThreadId initialIdSource in ( M . singleton tid ( thread k ), idsrc )

And now back to the implementation of minifu .

Implementing run

The run function is responsible for taking the first continuation, creating the collection of threads, and repeatedly calling the scheduler and stepping the chosen thread, until the computation is done.

It has this type:

run :: C . MonadConc m => Scheduler s -> s -> PrimOp m -> m s

As with minifu , we shall keep it simple, and delegate most of the work to yet another function:

import Data.List.NonEmpty ( nonEmpty ) import Data.Maybe ( isNothing ) run sched s0 = go s0 . initialise where go s ( threads , ids ) | initialThreadId ` M . member ` threads = case runnable threads of Just tids -> let ( chosen , s' ) = sched tids s in go s' =<< stepThread chosen ( threads , ids ) Nothing -> pure s | otherwise = pure s runnable = nonEmpty . M . keys . M . filter ( isNothing . threadBlock ) initialThreadId = fst ( nextThreadId initialIdSource )

Let’s break down that go function a bit:

We check if the initial thread still exists. If not, we return. We check if the collection of runnable threads is nonempty. If not, we return. We call the scheduler to pick a thread from the runnable ones. We call the (not yet defined) stepThread function to execute one step of that thread. We go around the loop again.

Not too bad, hey? Finally (really finally) we just have one function to go, stepThread . Can you see what the type will be?

It’s going to start like this:

stepThread :: C . MonadConc m => ThreadId -> ( Threads m , IdSource ) -> m ( Threads m , IdSource ) stepThread tid ( threads , idsrc ) = case M . lookup tid threads of Just thrd -> go ( threadK thrd ) Nothing -> pure ( threads , idsrc ) where adjust :: ( Thread m -> Thread m ) -> Threads m -> Threads m adjust f = M . adjust f tid goto :: PrimOp m -> Threads m -> Threads m goto k = adjust ( \ thrd -> thrd { threadK = k }) block :: Maybe MVarId -> Threads m -> Threads m block mv = adjust ( \ thrd -> thrd { threadBlock = mv }) unblock :: MVarId -> Threads m -> Threads m unblock v = fmap ( \ thrd -> if threadBlock thrd == Just v then thrd { threadBlock = Nothing } else thrd ) go :: PrimOp m -> m ( Threads m , IdSource ) -- go ...

I’ve introduced a few helper functions, which will crop up a lot. That go function will have a case for every constructor of PrimOp m , and it’s going to look a bit hairy, so we’ll take it one constructor at a time. Let’s do the constructors in order.

First, we can fork threads:

go ( Fork ( MiniFu ma ) k ) = let ( tid' , idsrc' ) = nextThreadId idsrc thrd' = thread ( K . runCont ma ( \ _ -> Stop ( pure () ))) in pure ( goto ( k tid' ) ( M . insert tid' thrd' threads ), idsrc' )

Forking is pretty straightforward. We simply get the next available ThreadId from the IdSource , create a thread with the provided continuation, and insert it into the Threads m map.

Next up is NewEmptyMVar :

go ( NewEmptyMVar k ) = do ref <- C . newCRef Nothing let ( mvid , idsrc' ) = nextMVarId idsrc pure ( goto ( k ( MVar mvid ref )) threads , idsrc' )

Remember that we’re implementing our MVar type using the CRef type of the underlying MonadConc . As the MVar starts out empty, the CRef starts out holding Nothing .

The PutMVar and TakeMVar actions are almost the same, so let’s tackle them together:

go ( PutMVar ( MVar mvid ref ) a k ) = do old <- C . readCRef ref case old of Just _ -> pure ( block ( Just mvid ) threads , idsrc ) Nothing -> do C . writeCRef ref ( Just a ) pure ( goto k ( unblock mvid threads ), idsrc ) go ( TakeMVar ( MVar mvid ref ) k ) = do old <- C . readCRef ref case old of Just a -> do C . writeCRef ref Nothing pure ( goto ( k a ) ( unblock mvid threads ), idsrc ) Nothing -> pure ( block ( Just mvid ) threads , idsrc )

In both cases, we start out by reading the value of the reference. Remember that Nothing indicates emptiness, and Just indicates the presence of a value. So, for PutMVar if there already is a value (and for TakeMVar if there isn’t a value), we block the thread. In the other case, we update the value in the reference, putting in the new value (or taking out the old), unblock all the relevant threads, and go to the continuation.

These implementations are not atomic. But that’s fine: despite MiniFu testing concurrent programs, there’s no concurrency going on within MiniFu itself. We can do as much or as little as we want during one atomic “step” of our program. This will turn out to be very useful when we implement STM in a few posts time.

Finally, we have Stop :

go ( Stop mx ) = do mx pure ( M . delete tid threads , idsrc )

And we’re done! That’s it! All we need now is a scheduler, and we can execute our example!

A Simple Scheduler

Our example is nondeterministic, so we want a scheduler which will let us see that. It would be no good us implementing something which always made the same decisions, as we’d only see one result! So until we implement the systematic testing behaviour, let’s just use a simple random scheduler.

import qualified System.Random as R randomSched :: R . RandomGen g => Scheduler g randomSched ( t :| ts ) g = let ( i , g' ) = R . randomR ( 0 , length ts ) g in (( t : ts ) !! i , g' )

There’s no deep magic here, we’re just picking a random value from a nonempty list. Finally, we can construct a little demo:

demo :: IO () demo = do g <- R . newStdGen print . fst =<< minifu randomSched g example

Which we can run in ghci like so:

λ> demo Just 1 λ> demo Just 1 λ> demo Just 1 λ> demo Just 2 λ> demo Just 1

Success!

A random scheduler is fine for demonstration purposes, but not so great for testing. Different seeds may lead to the same execution, which makes it hard to know how many executions of a test is enough. It can be a useful technique, but for us this is only the beginning.

Next time…

Next time we’ll look at implementing exceptions, both synchronous and asynchronous.

I hope you enjoyed this post, any feedback is welcome. As I mentioned at the start, this is on GitHub, you can get the code we ended up with at the “post-01” tag.

Before next time, I have some homework for you! You have seen how to implement MVars, so now try implementing CRefs! Here are the functions should you have a go at writing:

data CRef m a = -- ... newCRef :: a -> MiniFu m ( CRef m a ) readCRef :: CRef m a -> MiniFu m a writeCRef :: CRef m a -> a -> MiniFu m () atomicModifyCRef :: CRef m a -> ( a -> ( a , b )) -> MiniFu m b

Don’t worry about any of the relaxed memory stuff implemented in dejafu, just do sequential consistency (and if you don’t know what that means: it means to do the obvious). I’ll put up a solution (and maybe do a little refactoring) before the next post.

Thanks to José Manuel Calderón Trilla for reading an earlier draft of this post.