Test monadic programs using state machine based models
|Version on this page:||0.3.0|
|LTS Haskell 14.27:||0.6.0|
|Stackage Nightly 2019-09-21:||0.6.0|
|Latest on Hackage:||0.7.0|
Module documentation for 0.3.0
quickcheck-state-machine is a Haskell library, based
on QuickCheck, for testing
stateful programs. The library is different from
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.
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 programs using mutable
references. Our mutable references can be created, read from, written to and
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
why all uses of
IORefs are wrapped in
Reference v, where the parameter
will let us use symbolic references while generating (and concrete ones when
In order to be able to show counterexamples, we need a show instance for our
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 instantiated to
Concrete, which is essentially the
identity type, so while writing the semantics we have access to real
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 mutable 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 -> Bool postcondition _ New _ = True postcondition (Model m) (Read ref) resp = lookup ref m == Just resp postcondition _ (Write _ _) _ = True postcondition _ (Inc _) _ = 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 _ = 
To be able to fit the code on a line we pack up all of them above into a record.
sm :: Problem -> StateMachine Model Action IO sm prb = stateMachine generator shrinker precondition transition postcondition initModel (semantics prb) id
We can now define a sequential property as follows.
prop_references :: Problem -> PropertyOf (Program Action) prop_references prb = monadicSequentialC sm' $ \prog -> do (hist, _, res) <- runProgram sm' prog prettyProgram sm' hist $ checkActionNames prog (res === Ok) where sm' = sm prb
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
> quickCheck (prop_references Bug) *** Failed! Falsifiable (after 19 tests and 3 shrinks): Model  New --> Opaque Model [(Reference Concrete Opaque,0)] Write (Reference (Symbolic (Var 0))) 5 --> () Model [(Reference Concrete Opaque,5)] Read (Reference (Symbolic (Var 0))) --> 6 Model [(Reference Concrete Opaque,5)] PostconditionFailed /= Ok
Recall that the bug problem causes the write of values
i `elem` [5..10] to
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 = monadicParallel (sm prb) $ \prog -> prettyParallelProgram prog =<< runParallelProgram (sm prb) prog
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
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 one – 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 rough 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 an 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.
The sequential property checks if the model is consistent with respect to the semantics. The way this is done is:
generate a list of actions;
starting from the initial model, for each action do the the following:
- check that the pre-condition holds;
- if so, execute the action using the semantics;
- check if the the post-condition holds;
- advance the model using the transition function.
If something goes wrong, shrink the initial list of actions and present a minimal counterexample.
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:
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);
generate two lists of actions that will act as parallel suffixes;
execute the prefix sequentially;
execute the suffixes in parallel and gather the a trace (or history) of invocations and responses of each action;
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.
Here are some more examples to get you started:
The water jug problem from Die Hard 3 – this is a simple example of a specification where we use the sequential property to find a solution (counterexample) 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 the
Test.QuickCheck.Monadicmodule 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 counterexamples are minimal, are specified in a separate module;
Circular buffer example – another example that shows how the sequential property can find help find different kind of bugs. This example is borrowed from the paper Testing the Hard Stuff and Staying Sane [PDF, video];
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 cleaned up. 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;
CRUD webserver where create returns unique ids example – create, read, update and delete users in a sqlite database on a webserver using an API written using Servant. Creating a user will return a unique id, which subsequent reads, updates, and deletes need to use. In this example, unlike in the last one, the server is setup and torn down once per property rather than generate program.
To get a better feel for the examples it might be helpful to
git clone this
cd into the
example/ directory and fire up
stack ghci and run the
different properties interactively.
How to contribute
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!
The QuickCheck bugtrack issue – where the initial discussion about how how to add state machine based testing to QuickCheck started;
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:
The use of state machines to model and verify properties about programs is quite well-established, as witnessed by several books on the subject:
Modeling in Event-B: System and Software Engineering. Parts of this book are covered in the following (video) course given at Microsoft Research by the author, Jean-Raymond Abrial, himself:
Lecture 1: introduction to modeling and Event-B (chapter 1 of the book) and start of “controlling cars on bridge” example (chapter 2);
Lecture 2: refining the “controlling cars on a bridge” example (sections 2.6 and 2.7);
Lecture 3: design patterns and the “mechanical press controller” example (chapter 3);
Lecture 4: sorting algorithm example (chapter 15);
Lecture 5: designing sequential programs (chapter 15);
Lecture 6: status report of the hypervisor that Microsoft Research are developing using Event-B.
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:
Other similar libraries:
Erlang QuickCheck, eqc, the first property based testing library to have support for state machines (closed source);
The Haskell library Hedgehog, also has support for state machine based testing;
BSD-style (see the file LICENSE).
A propositional logic module was added to help provide better counterexamples when pre- and post-conditions don’t hold;
Generation of parallel programs was improved (base on a comment by Hans Svensson about how Erlang QuickCheck does it);
Support for semantics that might fail was added;
Pretty printing of counterexamples was improved.
Z-inspired definition of relations and associated operations were added to help defining concise and showable models;
Template Haskell derivation of
shrinkand type classes:
New and more flexible combinators for building sequential and parallel properties replaced the old clunky ones;
Circular buffer example was added;
Two examples of how to test CRUD web applications were added.
- The API was simplified, thanks to ideas stolen from Hedgehog.
- Initial release.