Verifying Procedural Programs via Constrained Rewriting Induction

Abstract

This paper aims to develop a verification method for procedural programs via a transformation into Logically Constrained Term Rewriting Systems (LCTRSs). To this end, we extend transformation methods based on integer TRSs to handle arbitrary data types, global variables, function calls and arrays, as well as encode safety checks. Then we adapt existing rewriting induction methods to LCTRSs and propose a simple yet effective method to generalize equations. We show that we can automatically verify memory safety and prove correctness of realistic functions. Our approach proves equivalence between two implementations, so in contrast to other works, we do not require an explicit specification in a separate specification language.

On Transforming Functions Accessing Global Variables into Logically Constrained Term Rewriting Systems

“…In this section, we recall LCTRSs, following the definitions in [7,5]. We also recall a small imperative language SIMP + with global variables and function calls.…”

“…To capture the existing approaches for constrained rewriting in one setting, the framework of a logically constrained term rewriting system (an LCTRS, for short) has been proposed [7]. Transformations of C programs with integers, characters, arrays of integers, global variables, and so on into LCTRSs have been discussed in [5].…”

A Coinductive Approach to Proving Reachability Properties in Logically Constrained Term Rewriting Systems

“…We formalize the semantics of LCTRSs as a reduction relation over a particular model that combines order-sorted terms with builtin elements such as integers, booleans, arrays, etc. The new approach, introduced in Section 3, is simpler than the usual semantics for constrained term rewriting systems [18,20,19,13], but it also lifts several technical restrictions that are important for our case studies. 3.…”

Transforming Proof Tableaux of Hoare Logic into Inference Sequences of Rewriting Induction

“…On the other hand, RI-based methods are procedures within RI frameworks to apply inference rules under specified strategies. In recent years, various RI-based methods for constrained rewriting (see, e.g., constrained TRSs [9,19], conditional and constrained TRSs [2], Z-TRSs [6], and logically constrained TRSs [11]) have been developed [2,20,6,12,8]. Constrained systems have built-in semantics for some function and predicate symbols and have been used as a computation model of not only functional but also imperative programs [4,7,9,5,21,12,8].…”

“…Some RI frameworks succeed in proving equivalence of an imperative program and its functional specification such that a proof based on Hoare logic needs a loop invariant (cf. [8]). From such experiences, we are interested in differences between RI frameworks and other verification methods.…”