Term Rewriting with Logical Constraints

Rewriting modulo SMT and open system analysis

“…This difference is understandable by observing that the goal in [29] is to prove universal formulas about equational specifications by inductive theorem proving, whereas our goal is very different, namely, to prove existential reachability formulas about a concurrent system specified by a rewrite theory. More recently, C. Kop and N. Nishida [40] have proposed a way to unify the ideas regarding equational rewriting with logical constraints and have proposed in [41] an inductive method of proving properties of programs in an imperative language by their notion of symbolic rewriting modulo decidable constraints. The main difference with our approach is that, as in [29], their notion of symbolic rewriting is universal, and therefore completely different from our existential notion in Definition 7; furthermore, in [41] termination of the rewrite theory is required for inductive reasoning, whereas no termination is required at all in our setting.…”

“…One similarity between the work in [41] and our work is that, to handle input-output in an imperative language, they allow, as we do, extra variables in the righthand sides of rewrite rules. In general, while approaches such as in [5,12,[27][28][29][38][39][40] address symbolic reasoning for equational theorem proving purposes, or apply these techniques to imperative program analysis and verification, even allowing sometimes extra variables in the right-hand sides of equations, e.g., [41,63,64], theses approaches are quite different from ours because of their predominant focus on equational reasoning for proving, often inductively, universal formulas, and/or on applications to, typically sequential, programming languages.…”

“…Rewriting modulo SMT techniques can then be applied to increase the power of rewrite-based equational reasoning for (Σ, E) such as, for instance, inductive theorem proving [29,39,40], termination checking [28,61], and procedural verification [41]. However, the full power of rewriting modulo SMT, including its model checking capabilities, can be better exploited when applied to concurrent open systems.…”

Intelligent Computer Mathematics

“…In the context of rewrite systems, a similar idea was realized in [KN13]. There, sorted first-order rewrite theories consist of an interpreted and a free part, and computation on the interpreted part is relegated to an arbitrary model.…”

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

“…In particular, constrained rewriting systems are popular for these transformations, since logical constraints used for modeling the control flow can be separated from terms expressing intermediate states [2,3,6,9,13]. 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].…”