相关论文: Lemma Functions for Frama-C: C Programs as Proofs

Modular deductive verification is a powerful technique capable to show that each function in a program satisfies its contract. However, function contracts do not provide a global view of which high-level (e.g. security-related properties of…

The substitution lemma is a renowned theorem within the realm of lambda-calculus theory and concerns the interactional behaviour of the metasubstitution operation. In this work, we augment the lambda-calculus's grammar with an uninterpreted…

This paper presents an approach to lemma synthesis to support advanced inductive entailment procedures based on separation logic. We first propose a mechanism where lemmas are automatically proven and systematically applied. The lemmas may…

Context-free languages (CFLs) are highly important in computer language processing technology as well as in formal language theory. The Pumping Lemma is a property that is valid for all context-free languages, and is used to show the…

In logical reasoning, it is often the case that only some of a collection of assumptions are needed to reach a conclusion. A strengthening lemma is an assertion that a given conclusion is independent in this sense of a particular…

We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery. The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition…

Worked examples are step-by-step solutions to problems in a specific domain, offered to students to acquire domain-specific problem-solving skills. The effectiveness of worked examples could be enhanced by combining them with…

Auto-active verifiers provide a level of automation intermediate between fully automatic and interactive: users supply code with annotations as input while benefiting from a high level of automation in the back-end. This paper presents…

Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…

We present an experimental, verified clause processor ctv-cp that fits into the framework used at Arm for formal verification of arithmetic hardware designs. This largely automates the ACL2 proof development effort for integer multiplier…

VeriFast is a powerful tool for verification of various correctness properties of C programs using symbolic execution. However, VeriFast itself has not been verified. We present a proof-of-concept extension which generates a correctness…

Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas…

We present \synver{}, a novel synthesis and verification framework for C programs, that deploys a Large Language Model (LLM) to search for a candidate program that satisfies the given specification. Our key idea is to impose syntactic and…

Software testing plays a critical role in ensuring that systems behave as intended. However, existing automated testing approaches struggle to match the capabilities of human engineers due to key limitations such as test locality, lack of…

Although empirical studies have confirmed the effectiveness of spectrum-based fault localization (SBFL) techniques, their performance may be degraded due to presence of some undesired circumstances such as the existence of coincidental…

Search-based testing is widely used to find bugs in models of complex Cyber-Physical Systems. Latest research efforts have improved this approach by casting it as a falsification procedure of formally specified temporal properties,…

Large Language Models (LLMs) have shown potential for solving mathematical tasks. We show that LLMs can be utilized to generate proofs by induction for hardware verification and thereby replace some of the manual work done by Formal…

Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such…

We report on the automation of a technique to prove the correctness of program transformations in higher-order program calculi which may permit recursive let-bindings as they occur in functional programming languages. A program…

This work is concerned with the generation of formal specifications from code, using Large Language Models (LLMs) in combination with symbolic methods. Concretely, in our study, the programming language is C, the specification language is…