  Software development is inherently incremental. Nowadays, many software
companies adopt an agile process and a shorter release cycle, where software
needs to be delivered faster with quality assurances. On the other hand, the
majority of existing program analysis tools still target single versions of
programs and are slow and inflexible to handle changes. In the popular version
control systems such as git, the program changes are still presented using
source code diffs. It is hard to understand what program conditions are changed
and which source code lines cause them. In this paper, we propose to compute
"invariant diffs" to specify changes. Similar to source diffs that report
common code and code churns, we define version invariants to represent program
conditions that are common across versions, and invariant churns to show the
changes of program conditions between versions. We designed a static
demand-driven, path-sensitive analysis to compute and compare invariants for
multiple versions of programs using multiversion control flow graphs. We report
invariant diffs at the matched program points where comparing invariants are
meaningful. Importantly, our analysis correlates source diffs with invariant
diffs to explain what source code changes lead to the property changes. We
implemented our algorithms in a tool called $H_2$ and performed experiments on
104 versions of programs. Our results show that we are able to compute
invariant diffs correctly within reasonable amount of time. The version
invariants can capture the common properties of program versions even
constructed by different persons, and the invariant churns can specify the
semantics of changes such as how a patch changed a buggy condition to a correct
condition.
