quickcheck-state-machine: Test monadic programs using state machine based models

quickcheck-state-machine

quickcheck-state-machine is a Haskell library, based on QuickCheck, for testing stateful programs. The library is different from the Test.QuickCheck.Monadic approach in that it lets the user specify the correctness by means of a state machine based model using pre- and post-conditions. The advantage of the state machine approach is twofold: 1) specifying the correctness of your programs becomes less adhoc, and 2) you get testing for race conditions for free.

The combination of state machine based model specification and property based testing first appeard in Erlang's proprietary QuickCheck. The quickcheck-state-machine library can be seen as an attempt to provide similar functionality to Haskell's QuickCheck library.

Example

As a first example, let's implement and test programs using mutable references. Our implementation will be using IORefs, but let's start with a representation of what actions are possible with program using mutable references. Our mutable references can be created, read from, written to and incremented:

data Action (v :: * -> *) :: * -> * where
  New   ::                                     Action v (Opaque (IORef Int))
  Read  :: Reference v (Opaque (IORef Int)) -> Action v Int
  Write :: Reference v (Opaque (IORef Int)) -> Int -> Action v ()
  Inc   :: Reference v (Opaque (IORef Int)) -> Action v ()

When we generate actions we won't be able to create arbitrary IORefs, that's why all uses of IORefs are wrapped in Reference v, where the parameter v will let us use symbolic references while generating (and concrete ones when executing).

In order to be able to show counterexamples, we need a show instance for our actions. IORefs don't have a show instance, thats why we wrap them in Opaque; which gives a show instance to a type that doesn't have one.

Next, we give the actual implementation of our mutable references. To make things more interesting, we parametrise the semantics by a possible problem.

data Problem = None | Bug | RaceCondition
  deriving Eq

semantics :: Problem -> Action Concrete resp -> IO resp
semantics _   New           = Opaque <$> newIORef 0
semantics _   (Read  ref)   = readIORef  (opaque ref)
semantics prb (Write ref i) = writeIORef (opaque ref) i'
  where
  -- One of the problems is a bug that writes a wrong value to the
  -- reference.
  i' | i `elem` [5..10] = if prb == Bug then i + 1 else i
     | otherwise        = i
semantics prb (Inc   ref)   =
  -- The other problem is that we introduce a possible race condition
  -- when incrementing.
  if prb == RaceCondition
  then do
    i <- readIORef (opaque ref)
    threadDelay =<< randomRIO (0, 5000)
    writeIORef (opaque ref) (i + 1)
  else
    atomicModifyIORef' (opaque ref) (\i -> (i + 1, ()))

Note that above v is instatiated to Concrete, which is essentially the identity type, so while writing the semantics we have access to real IORefs.

We now have an implementation, the next step is to define a model for the implementation to be tested against. We'll use a simple map between references and integers as a model.

newtype Model v = Model [(Reference v (Opaque (IORef Int)), Int)]

initModel :: Model v
initModel = Model []

The pre-condition of an action specifies in what context the action is well-defined. For example, we can always create a new mutuable reference, but we can only read from references that already have been created. The pre-conditions are used while generating programs (lists of actions).

precondition :: Model Symbolic -> Action Symbolic resp -> Bool
precondition _         New           = True
precondition (Model m) (Read  ref)   = ref `elem` map fst m
precondition (Model m) (Write ref _) = ref `elem` map fst m
precondition (Model m) (Inc   ref)   = ref `elem` map fst m

The transition function explains how actions change the model. Note that the transition function is polymorphic in v. The reason for this is that we use the transition function both while generating and executing.

transition :: Model v -> Action v resp -> v resp -> Model v
transition (Model m) New           ref = Model (m ++ [(Reference ref, 0)])
transition m         (Read  _)     _   = m
transition (Model m) (Write ref i) _   = Model (update ref i         m)
transition (Model m) (Inc   ref)   _   = Model (update ref (old + 1) m)
  where
  Just old = lookup ref m

update :: Eq a => a -> b -> [(a, b)] -> [(a, b)]
update ref i m = (ref, i) : filter ((/= ref) . fst) m

Post-conditions are checked after we executed an action and got access to the result.

postcondition :: Model Concrete -> Action Concrete resp -> resp -> Property
postcondition _         New         _    = property True
postcondition (Model m) (Read ref)  resp = lookup ref m === Just resp
postcondition _         (Write _ _) _    = property True
postcondition _         (Inc _)     _    = property True

Finally, we have to explain how to generate and shrink actions.

generator :: Model Symbolic -> Gen (Untyped Action)
generator (Model m)
  | null m    = pure (Untyped New)
  | otherwise = frequency
      [ (1, pure (Untyped New))
      , (8, Untyped .    Read  <$> elements (map fst m))
      , (8, Untyped <$> (Write <$> elements (map fst m) <*> arbitrary))
      , (8, Untyped .    Inc   <$> elements (map fst m))
      ]

shrinker :: Action v resp -> [Action v resp]
shrinker (Write ref i) = [ Write ref i' | i' <- shrink i ]
shrinker _             = []

We can now define a sequential property as follows.

prop_references :: Problem -> Property
prop_references prb = forAllProgram
  generator
  shrinker
  precondition
  transition
  initModel $ \prog ->
    runAndCheckProgram
      precondition
      transition
      postcondition
      initModel
      (semantics prb)
      ioProperty
      prog

If we run the sequential property without introducing any problems to the semantics function, i.e. quickCheck (prop_references None), then the property passes. If we however introduce the bug problem, then it will fail with the minimal counterexample:

> quickCheck (prop_references Bug)
*** Failed! Falsifiable (after 16 tests and 4 shrinks):
[New (Var 0),Write (Var 0) 5 (Var 2),Read (Var 0) (Var 3)]
Just 5 /= Just 6

Recall that the bug problem causes the write of values i `elem` [5..10] to actually write i + 1.

Running the sequential property with the race condition problem will not uncover the race condition.

If we however define a parallel property as follows.

prop_referencesParallel :: Problem -> Property
prop_referencesParallel prb = forAllParallelProgram
  generator
  shrinker
  precondition
  transition
  initModel $ \parallel ->
    runParallelProgram (semantics prb) parallel $ \hist ->
      checkParallelProgram
        transition
        postcondition
        initModel
        parallel
        hist

And run it using the race condition problem, then we'll find the race condition:

> quickCheck (prop_referencesParallel RaceCondition)
*** Failed! (after 8 tests and 6 shrinks):

Couldn't linearise:

┌────────────────────────────────┐
│ Var 0 ← New                    │
│                       ⟶ Opaque │
└────────────────────────────────┘
┌─────────────┐ │
│ Inc (Var 0) │ │
│             │ │ ┌──────────────┐
│             │ │ │ Inc (Var 0)  │
│        ⟶ () │ │ │              │
└─────────────┘ │ │              │
                │ │         ⟶ () │
                │ └──────────────┘
                │ ┌──────────────┐
                │ │ Read (Var 0) │
                │ │          ⟶ 1 │
                │ └──────────────┘
Just 2 /= Just 1

As we can see above, a mutable reference is first created, and then in parallel (concurrently) we do two increments of said reference, and finally we read the value 1 while the model expects 2.

Recall that incrementing is implemented by first reading the reference and then writing it, if two such actions are interleaved then one of the writes might end up overwriting the other ones -- creating the race condition.

We shall come back to this example below, but if your are impatient you can find the full source code here.

How it works

The rought idea is that the user of the library is asked to provide:

• a datatype of actions;
• a datatype model;
• pre- and post-conditions of the actions on the model;
• a state transition function that given a model and a action advances the model to its next state;
• a way to generate and shrink actions;
• semantics for executing the actions.

The library then gives back a bunch of combinators that let you define a sequential and a parallel property.

Sequential property

The sequential property checks if the model is consistent with respect to the semantics. The way this is done is:

1. generate a list of actions;

2. starting from the initial model, for each action do the the following:

   1. check that the pre-condition holds;
   2. if so, execute the action using the semantics;
   3. check if the the post-condition holds;
   4. advance the model using the transition function.

3. If something goes wrong, shrink the initial list of actions and present a minimal counter example.

Parallel property

The parallel property checks if parallel execution of the semantics can be explained in terms of the sequential model. This is useful for trying to find race conditions -- which normally can be tricky to test for. It works as follows:

1. generate a list of actions that will act as a sequential prefix for the parallel program (think of this as an initialisation bit that setups up some state);

2. generate two lists of actions that will act as parallel suffixes;

3. execute the prefix sequentially;

4. execute the suffixes in parallel and gather the a trace (or history) of invocations and responses of each action;

5. try to find a possible sequential interleaving of action invocations and responses that respects the post-conditions.

The last step basically tries to find a linearisation of calls that could have happend on a single thread.

More examples

Here are some more examples to get you started:

• The water jug problem from Die Hard 2 -- this is a simple example of a specification where we use the sequential property to find a solution (counter example) to a puzzle from an action movie. Note that this example has no meaningful semantics, we merely model-check. It might be helpful to compare the solution to the Hedgehog solution and the TLA+ solution;

• The union-find example -- another use of the sequential property, this time with a useful semantics (imperative implementation of the union-find algorithm). It could be useful to compare the solution to the one that appears in the paper Testing Monadic Code with QuickCheck [PS], which is the Test.QuickCheck.Monadic module is based on;

• Mutable reference example -- this is a bigger example that shows both how the sequential property can find normal bugs, and how the parallel property can find race conditions. Several metaproperties, that for example check if the counter examples are minimal, are specified in a separate module;

• Ticket dispenser example -- a simple example where the parallel property is used once again to find a race condition. The semantics in this example uses a simple database file that needs to be setup and teared down. This example also appears in the Testing a Database for Race Conditions with QuickCheck and Testing the Hard Stuff and Staying Sane [PDF, video] papers.

All examples have an associated Spec module located in the example/test directory. These make use of the properties in the examples, and get tested as part of Travis CI.

To get a better feel for the examples it might be helpful to git clone this repo, cd into the example/ directory and fire up stack ghci and run the different properties interactively.

How to contribute

The quickcheck-state-machine library is still very experimental.

We would like to encourage users to try it out, and join the discussion of how we can improve it on the issue tracker!

See also

• The QuickCheck bugtrack issue -- where the initial discussion about how how to add state machine based testing to QuickCheck started;

• Finding Race Conditions in Erlang with QuickCheck and PULSE [PDF, video] -- this is the first paper to describe how Erlang's QuickCheck works (including the parallel testing);

• Linearizability: a correctness condition for concurrent objects [PDF], this is a classic paper that describes the main technique of the parallel property;

• Aphyr's blogposts about Jepsen, which also uses the linearisability technique, and has found bugs in many distributed systems:

  • Knossos: Redis and linearizability;
  • Strong consistency models;
  • Computational techniques in Knossos;
  • Serializability, linearizability, and locality.

• The use of state machines to model and verify properties about programs is quite well-established, as witnessed by several books on the subject:

  • Specifying Systems: The TLA+ Language and Tools for Hardware and Software Engineers;
  • Modeling in Event-B: System and Software Engineering;
  • Abstract State Machines: A Method for High-Level System Design and Analysis.

  The books contain general advice how to model systems using state machines, and are hence relevant to us. For shorter texts on why state machines are important for modeling, see:

  • Lamport's Computation and State Machines;

  • Gurevich's Evolving Algebras 1993: Lipari Guide and Sequential Abstract State Machines Capture Sequential Algorithms [PDF].

• Other similar libraries:

  • Erlang QuickCheck, eqc, the first property based testing library to have support for state machines (closed source);

  • The Erlang library PropEr is eqc-inspired, open source, and has support for state machine testing;

  • The Haskell library Hedgehog, also has support for state machine based testing (no parallel property yet though);

  • ScalaCheck, likewise has support for state machine based testing (no parallel property);

  • The Python library Hypothesis, also has support for state machine based testing (no parallel property).

License

BSD-style (see the file LICENSE).