We saw in a previous post how formal containers can be used in SPARK code. In this post, I describe how to express properties over the content of these containers, using quantified expressions.
SPARK 2014 excludes data structures based on pointers. Instead, one can use the library of formal containers. They are variant of the Ada 2012 bounded containers, specifically designed and annotated to facilitate the proof of programs using them.
In a previous post about pre-call values, I described how the Ada language rules implemented in the compiler prevent surprises when referring to input values in the postcondition, using the Old attribute. Unfortunately, these rules also make it difficult to express some complex postconditions that may be useful when doing formal verification. In this post, I describe how contract cases allow the expression of these complex contracts, while still detecting potential problems with uses of the Old attribute.
Global variables are a common source of programming errors: they may fail to be initialized properly, they can be modified in unexpected ways, sequences of modifications may be illegal, etc. SPARK 2014 provides a way to define abstractly the global state of a unit, so that it can be referred to in subprogram specifications. The associated toolset checks correct access to global variables in the implementation.
Loop variants are the little-known cousins of the loop invariants, used for proving termination of subprograms. Although they may not look very useful at first, they can prove effective as I show with a simple binary search example. And we came up with both an elegant syntax and a slick refinement for loop variants in SPARK 2014, compared to similar constructs in other languages.
Formal verification tools like GNATprove rely on two main inputs from programmers: subprogram contracts (preconditions and postconditions) and loop invariants. While the first ones are easy to understand (based on the "contract" analogy, in which a subprogram and its caller have mutual obligations), the second ones are not so simple to grasp. This post presents loop invariants and the choices we made in SPARK 2014.
Subprogram contracts are commonly presented as special assertions: the precondition is an assertion checked at subprogram entry, while the postcondition is an assertion checked at subprogram exit. A subtlety not covered by this simplified presentation is that postconditions are really two-state assertions: they assert properties over values at subprogram exit and values at subprogram entry. A special attribute Old is defined in Ada 2012 to support these special assertions. A special attribute Loop_Entry is defined in SPARK 2014 to support similar special assertions for loops.
Specifying a program's behavior is seldom expressible in a satisfiable way without the capability of abstraction provided by function calls. Yet, specification functions must obey specific constraints like absence of side-effects and termination, that have led to different solutions in various specification languages. Here is what we did in SPARK 2014.
Besides the usual expression of a subprogram contract as a pair of a precondition and a postcondition, SPARK 2014 provides a way to express such a contract by cases. A little history helps understanding how we came up with this new feature.