A FOOLish Encoding of the Next State Relations of Imperative Programs

Abstract

Abstract. Automated theorem provers are routinely used in program analysis and verification for checking program properties. These properties are translated from program fragments to formulas expressed in the logic supported by the theorem prover. Such translations can be complex and require deep knowledge of how theorem provers work in order for the prover to succeed on the translated formulas. Our previous work introduced FOOL, a modification of first-order logic that extends it with syntactical constructs resembling features of programming languages. One can express program properties directly in FOOL and leave translations to plain first-order logic to the theorem prover. In this paper we present a FOOL encoding of the next state relations of imperative programs. Based on this encoding we implement a translation of imperative programs annotated with their pre-and post-conditions to partial correctness properties of these programs. We present experimental results that demonstrate that program properties translated using our method can be efficiently checked by the first-order theorem prover Vampire.

Automated Reasoning in Non-classical Logics in the TPTP World

“…Since the introduction of TFF and THF there have been some features that have received little attention: tuples, conditional expressions (if-then-else), and let expressions (let-defn-in). Recently conditional expressions and let expressions have become more important because of their use in software verification [27]. In a separate development, Evgeny Kotelnikov et al [26] introduced the FOOL logic that extends TFF so that (i) formulae of type $o can be used as terms, (ii) variables of type $o can be used as formulae, (iii) tuple terms and tuple types are available as first-class citizens, and (iv) conditional and let expressions are supported.…”

Interactive Visualization of Saturation Attempts in Vampire

“…Over the past years, saturation-based theorem proving has been extended to first-order logic with theories, such as arithmetic, theory of arrays and algebraic datatypes [8]. Further, first-class boolean sorts and if-then-else and let-in constructs have also been introduced as extensions to the input syntax of first-order theorem provers [7]. Thanks to these recent developments, first-order theorem provers became better suited in applications of formal methods, being for example a competitive alternative to SMT-solvers [1,5] in software verification and program analysis.…”