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Blog Archive for / 2020 / 03 /

Invariants and Preconditions

Thursday, 05 March 2020

I tend to think about invariants and preconditions a lot. Pretty much every class has invariants, and most functions have preconditions. I don't think they are complicated concepts, but somehow they seem to confuse people anyway, so I decided it was time to write down some of my thoughts.

Invariants

A class invariant is something that is always true for every instance of that class. Users of objects of that class never see an object for which the invariant is not true; it is true for all states of all objects of that class at all times. This is what makes it invariant.

In order to perform the required operations, class member functions may temporarily break invariants, and then restore them afterwards. Unless you allow concurrent invocations of member functions on the same object, or deliberately pass the object to another function from inside a member function, this is OK, as the outside world will not be able to interact with the object when it is in such a state. It does mean you need to be especially careful when calling other functions from inside a member function, to ensure that the invariants still hold.

Invariants are important. If you writing a function that operates on an object, the only thing that is guaranteed to be true about it is that the class invariants hold, unless you choose to impose additional preconditions.

Preconditions

Preconditions are those that must be true when a function is called. Every operation on a class has the implicit precondition that the class invariants hold, but operations can add additional preconditions. For example, you always call v.empty() to check if a vector is empty, but you only call v.front() to retrieve the first element if the vector is not empty. v[i] and v.at(i) differ only in their preconditions; v[i] requires the vector to have more than i elements, whereas v.at(i) is specified to work for any vector, throwing if i is out of range.

Some people like to write classes with two-stage construction — first you default-construct the object, then you call x.init() or similar to "finish off" the initialization, and you can't call any other function on that object until after the initialization is complete. Though I don't like this pattern it is valid code; every member function has a precondition that x.init() has been called.

Some people like to say that such a class can have "invariants" that do not hold until after initialization is complete. I think this is a misuse of the term; invariants must always hold for every object of a class, outside the internals of its member functions. As I just stated above, what such a class really has is a precondition on every function, not an invariant.

If I write a function

void do_stuff(X& x){
  // my code here
}

then I can rely on the invariants of X holding, but cannot rely on anything else unless I add preconditions to do_stuff.

Likewise, it should not be possible to do anything to an object that breaks its invariants. If you can then either you gave a bug, or they are not really invariants, just preconditions for most operations.

Some people like to write classes that have operations to transfer the internals from one object to another, leaving the source in a special "emptier than empty" state. This can be good for efficiency, especially when doing otherwise would require allocating resources to return the source to the plain "empty" state, and it is likely that the source will be destroyed immediately anyway.

Again, this is a perfectly reasonable thing to do, particularly when the resources are expensive to allocate and performance of the code is important. The problem comes when people then want to say that the class invariants don't hold for this state. Just as with the pre-initialization state above, I think this is a misuse of the term; they are not invariants, it is just that most operations have a precondition that the object is not "emptier than empty".

Move semantics

Since C++11, C++ has had the concept of "moving" objects, transferring resources from the source to the destination. This is an important facility for expressiveness of code and efficiency. Objects that own resources such as std::unique_ptr, std::thread or std::fstream can now be moved, transferring ownership of the resource from the source to the destination. This allows such objects to be put in containers, and transferred between scopes, which can greatly simplify code. Likewise, containers like std::vector can be moved, transferring the entire set of contained objects from one vector to another without reallocation. These facilities are of great importance for writing clean, efficient code.

One thing all these operations have in common is that after a move, the class invariants still hold for the source object. This should go without saying: the source is still an object of its type, so of course the invariants hold.

The issue is with things like std::list, where some implementations allocate a sentinel node for the head/tail of the list in the default constructor, which is thus transferred during move operations, so the move constructor has to allocate a new sentinel node for the source, in order to ensure the class invariants still hold. A similar thing occurs with anything that uses the pimpl idiom: if the implementation pointer is transferred then either the class invariants must allow for there to be a null implementation pointer, or a new implementation object must be allocated.

Some people therefore argue that move operations should allow the source to be left with broken invariants, as a hollow shell of an object, in an "emptier than empty" state. I think this is misuse of the term "invariants". By all means, steal the internals and leave the source with a null pointer to the internals, or whatever. However, you now need to change the invariants of your class to allow this, or they are not invariants, because they would no longer apply to all objects of that class. There is no need to update any of the functions on your class to handle this new state, but if you do not do so, then any functions that don't work for objects in this "emptier than empty" state now have an additional precondition that the object is not in that state.

This is all perfectly fine, objects with such states are plentiful, and have legitimate reasons for existing, but it is important to accept that their functions now have preconditions. My do_stuff function above can only call member functions that are safe to use in such a state unless it too has a precondition that the object x is not in such a state.

From a user perspective, it would be nice to be able to query such a state, so I could know what operations are permitted. For example, std::future provides a member function valid so you can call f.valid() before trying to do anything with it, and std::thread provides the joinable member function, which can be used to see if the object holds a thread handle. My do_stuff function can then call x.is_emptier_than_empty() in order to check for the special state and take appropriate action. That said, this is a "nice to have": the absence of such a function doesn't mean that the state can't exist, just that it's potentially harder to deal with.

Interaction with other code

If you pass an object to a function or class, then you need to know what that function requires of your object and ensure that those expectations are met. If the function expects your object to be a container with at least one element and you pass an empty container, then you've broken the expectations and your code has a bug. Likewise, if the function expects to be able to call x.foo() on your object, but foo cannot be called on an "emptier than empty" object, and you passed such an object to the function, your code has a bug.

The difficulty comes when such a state arises as a consequence of other actions. If x.foo() can leave x in an "emptier than empty" state, then do_stuff had better be prepared to handle the scenario, otherwise there is a bug somewhere. Where the bug is depends on the documentation: if do_stuff requires that you can always perform certain actions on the object it is passed as a parameter, and those actions require that the object is not "emptier than empty", then the bug is in the caller, or maybe the implementation of class X. If there is no such documentation, the bug is in do_stuff.

Note that requiring that x.foo() can only be called with objects that are not "emptier than empty" is a precondition. It should be perfectly acceptable for do_stuff to call any functions on x that do not have preconditions, even if x ends up in an "emptier than empty" state.

This is the exactly the same scenario we get with other code. For example if you pass a vector to a function that requires that the vector isn't empty, the function can erase the last element without a problem. If it wishes to erase the last element again, thus removing two elements in total, then it needs to check for and handle the case that the first erasure left the vector empty. Calling v.clear() or v.empty() or v.push_back(y) would be fine without checking, as those functions have no preconditions.

If x.foo() is instead spelled y=std::move(x), then nothing changes: it is perfectly fine for x to end up in an "emptier than empty" state if do_stuff knows how to handle such a state, or doesn't care, because it doesn't touch x again.

One option is for do_stuff to say that after a move-assignment like this, it can't rely on x having any particular value, but it is still an instance of class X, so its invariants must hold, and therefore any operation without a precondition can be used. It can therefore call x.is_emptier_than_empty() and behave appropriately.

The other option is for do_stuff to place stronger requirements on x, such as requiring that it does not end up "emptier than empty" after a move, or even requiring that it has a specific state.

Valid but unspecified states

The standard library has chosen option 1: after move, objects must be valid - i.e. still actually be objects of the expected type, and not destroyed - but they have an unspecified state, so the function cannot rely on any specific value, and can therefore only perform operations without preconditions, until it has verified that the preconditions for other operations hold.

This holds both for standard library types such as std::string or std::vector<int>, but also for user defined types that you use with the standard library. If you write

std::string s="hello";
std::string s2=std::move(s);

then s was the source of a move operation, and thus is in a valid, but unspecified state. For implementations that use the Small String Optimization, such that short strings are stored entirely within the string object itself, without requiring dynamic allocation, this might mean that s still has the value hello after the move, because then it doesn't have to store an empty string value in s as well as copying the contents to s2. It is also possible that the implementation might clear s, for consistency with longer strings. Both are valid choices, as in either case s is still a std::string object, and the exact details of the state are unspecified.

Likewise, if you write

std::vector<MyWidget> v=create_some_widgets();
v.insert(v.begin(),MyWidget());

then that call to v.insert is going to have to move the widgets around in order to make room at the beginning for the extra one. The library requires that moving widgets leaves them in a valid, but unspecified, state. In this case, that means that having moved a widget from one position to another, it is OK to move another widget on top of the first one, as that is the only operation the vector will perform anyway. If you pass your object to a standard library function that does something other than move things around (such as std::sort or std::remove_if), then you need to check that the other operations the function might do can still be done on a moved-from object. By calling the library function you are stating that your objects meet (and will continue to meet) any preconditions you have imposed on the operations that the library function specification says it might perform.

Invariants and Concurrency

Right back at the beginning of this article I stated that "Users of objects of that class never see an object for which the invariant is not true", but also that "class member functions may temporarily break invariants, and then restore them afterwards". These two things don't work together very well if an object can be accessed concurrently from multiple threads, and this is one aspect that makes writing concurrent code hard, especially if you try to use fine-grained locks or atomic operations.

Consider a simple class Names which holds two vectors, one for first names and one for last names:

class Names{
  std::vector<std::string> firstNames,lastNames;
};

I want the invariant of this class to be that the number of elements in firstNames and lastNames is always the same, so that I can add operations to this class knowing that is always true. There is a strong argument that this ought to be a std::vector<std::pair<std::string,std::string>> rather than two vectors, but assume that the class author has a legitimate reason for the separate vectors.

At first glance, a member function to add an entry is quite simple:

void Names::addEntry(std::string const& first,std::string const& last){
    firstNames.push_back(first);
    lastNames.push_back(last);
}

However, even for the single-threaded case, this isn't good: if lastNames.push_back(last) throws an exception, then our invariant is broken, as we successfully added an element to firstNames but not to lastNames. We therefore need to handle that case:

void Names::addEntry(std::string const& first,std::string const& last){
  firstNames.push_back(first);
  try{
    lastNames.push_back(last);
  } catch(...){
    firstNames.resize(lastNames.size());
    throw;
  }
}

Now, if lastNames.push_back(last) throws, then std::vector guarantees that lastNames is unchanged, so we can ensure our invariant holds again by shrinking firstNames back to the same size, and the single-threaded case is now sorted. If our Names object is only ever accessed by a single thread, then the invariant holds at all times outside the internals of a member function.

What about the concurrent case? If we call Names::addEntry from multiple threads, then everything is broken: std::vector is not safe for concurrent access from multiple threads, so we have data races and undefined behaviour. Using a ThreadSafeVector class instead which provides the operations we need but is safe for concurrent access removes these data races and the undefined behaviour, but doesn't fix the overall problem. Thread safety is not composable. In this case, the invariants are still broken during the call to Names::addEntry, so a concurrent call will see an object with broken invariants: the thread safety of the two vectors doesn't matter if the second thread can see firstNames and lastNames with different sizes.

We can fix the problem by using a mutex: the mutex lock prevents the second thread from accessing the internals of the object until the first thread has finished, so the second thread cannot see the state with a broken invariant. It also allows us to revert back to std::vector rather than ThreadSafeVector since the individual vectors are only ever accessed by one thread at a time:

class Names{
  std::mutex mutex;
  std::vector<std::string> firstNames,lastNames;

public:
  void addEntry(std::string const& first,std::string const& last){
    std::lock_guard guard(mutex);
    firstNames.push_back(first);
    try{
      lastNames.push_back(last);
    } catch(...){
      firstNames.resize(lastNames.size());
      throw;
    }
  }
};

This is one of the big reasons why lock-free data structures are so hard to write: we cannot just stick a mutex lock on the outside to ensure other threads never see broken invariants. Instead, we must ensure that the invariants hold at all times, even during the operation of member functions. For this reason, lock-free data structures are often designed so that as much as possible is done off to the side, without modifying the core data structures, and then either the entire change is committed with a single atomic operation, or care is taken to ensure that the invariants still hold after each incremental step.

End note

Invariants are important. They are vital to working with objects, and without them it is much harder to write correct code. However, you have to choose your invariants carefully: invariants that make the rest of your code easier to reason about can have a cost, so you have to be aware of the trade-offs. Like everything in programming it is up to you what trade-off you choose: simplicitly vs performance is a common choice, but it can also be a choice of which operations are fast and which are slow. Whatever you choose, there will be cases where the other choice was more appropriate.

Whatever you choose, you must be honest with yourself, and the users of your class. Don't claim something is an invariant just because it holds most of the time; it must hold all of the time. Obviously, you can make it so a precondition of a function that objects it operates on are only in certain states, and then write your program logic to ensure that the conditions are met, but don't confuse the two.

Posted by Anthony Williams
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