The definition is modified somewhat for concurrent execution: an invariant is a condition or relation that is true when the associated lock is being set. Once the lock is set, the invariant can be false. However, the code holding the lock must reestablish the invariant before releasing the lock.
An invariant can also be a condition or relation that is true when a lock is being set. Condition variables can be thought of as having an invariant that is the condition.
mutex_lock(&lock); while((condition)==FALSE) cond_wait(&cv,&lock); assert((condition)==TRUE); . . . mutex_unlock(&lock);
Another example is a module that manages a doubly linked list of elements. For each item on the list a good invariant is the forward pointer of the previous item on the list that should also point to the same thing as the backward pointer of the forward item.
Assume this module uses code-based locking and therefore is protected by a single global mutex lock. When an item is deleted or added the mutex lock is acquired, the correct manipulation of the pointers is made, and the mutex lock is released. Obviously, at some point in the manipulation of the pointers the invariant is false, but the invariant is reestablished before the mutex lock is released.