Language Definitions as Rewrite Theories

Abstract

K is a formal framework for defining the operational semantics of programming languages. It includes software tools for compiling K language definitions to Maude rewrite theories, for executing programs in the defined languages based on the Maude rewriting engine, and for analyzing programs by adapting various Maude analysis tools. A recent extension to the K tool suite is an automatic transformation of language definitions that enables the symbolic execution of programs, i.e., the execution of programs with symbolic inputs. In this paper we investigate the theoretical relationships between K language definitions and their translations to Maude, between symbolic extensions of K definitions and their Maude encodings, and how the relations between K definitions and their symbolic extensions are reflected on their respective representations in Maude. These results show, in particular, how analyses performed with Maude tools can be formally lifted up to the original language definitions.

Verifying Reachability-Logic Properties on Rewriting-Logic Specifications

“…In [22] it is shown how rl specifications can be encoded as rwl theories. Here, we take an alternative approach, which consists in using rl as a property language for rwl.…”

Symbolic execution based on language transformation

“…For instance, checking the program int x; x = read(); x = x + 1; against ♦ Ltl odd (x) and the symbolic input a returns a counterexample because the prover cannot deduce that one of a or a + Int 1 satises odd (x), which holds whenever the value of the program variable x given as argument is odd. Another issue with the LTL model-checking is given by the fact that the K tool usually implements only an approximation of the language denition, see [4] for a detailed discussion on this aspect. This approximation is propagated to the symbolic version and therefore the results of an LTL model-checking must be interpreted with respect this approximation.…”

“…In this case it behaves like the concrete semantics. The theoretical relationships between K language denitions int n, s; n = read(); s = 0; while (n > 0) { s = s + n; n = n -1; } print("Sum = ", s, "\n"); [4].…”

“…Our prototype is based on several transformations which are encoded as compilation steps in the K denition compiler. The relationships between K language denitions and their compilation into Maude, and between the transformed K denitions and their Maude encodings are investigated in [4]. In this paper we briey describe our implementation as a language-engineering tool, and demonstrate its genericity by instantiating it on nontrivial languages dened in K. We emphasise that the tool uses the K language-denitions as they are, without requiring modications, and automatically harnesses them for symbolic execution.…”

Automatic Inference of Specifications in the K Framework

“…These formulas, called patterns, specify those concrete configurations that match the pattern algebraic structure and satisfy its constraints. Since patterns allow logical variables and constraints over them, by using patterns, K rewriting becomes symbolic execution with the semantic rules of the language [3]. The SMT solver Z3 [19] is used in K for checking the satisfiability of the path constraints.…”