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.

Sample run (teaser)

Here's a sample output from when we look for race conditions in the mutable reference example:

> quickCheck (MutableReference.prop_parallel RaceCondition)
*** Failed! (after 5 tests and 6 shrinks):

Couldn't linearise:

┌──────────────────────┐
│ New                  │
│                 ⟶ $0 │
└──────────────────────┘
            │ ┌────────┐
            │ │ Inc $0 │
┌─────────┐ │ │        │
│ Inc $0  │ │ │        │
│         │ │ │   ⟶ () │
│         │ │ └────────┘
│    ⟶ () │ │
└─────────┘ │
┌─────────┐ │
│ Read $0 │ │
│     ⟶ 1 │ │
└─────────┘ │

Clearly, if we increment a mutable reference in parallel we can end up with a 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 commands;
• a datatype model;
• pre- and post-conditions of the commands on the model;
• a state transition function that given a model and a command advances the model to its next state;
• a way to generate and shrink commands;
• semantics for executing the commands.

The library then gives back 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 commands;

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

   1. check that the pre-condition holds;
   2. if so, execute the command 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 commands 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 commands 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 commands 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 command;

5. try to find a possible sequential interleaving of command 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.

Examples

To get started it is perhaps easiest to have a look at one of the several examples:

• 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 simpler example where the parallel property is used once again to find a race condition. This is an example used 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].

License

BSD-style (see the file LICENSE).