相关论文: Automated Lemma Synthesis in Symbolic-Heap Separat…

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…

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…

Separation Logic (SL) with inductive definitions is a natural formalism for specifying complex recursive data structures, used in compositional verification of programs manipulating such structures. The key ingredient of any automated…

We present an approach to automatically synthesise recursive predicates in Separation Logic (SL) from concrete data structure instances using Inductive Logic Programming (ILP) techniques. The main challenges to make such synthesis effective…

The entailment between separation logic formulae with inductive predicates, also known as symbolic heaps, has been shown to be decidable for a large class of inductive definitions. Recently, a 2-EXPTIME algorithm was proposed and an…

Proving equivalence between functional programs is a fundamental problem in program verification, which often amounts to reasoning about algebraic data types (ADTs) and compositions of structural recursions. Modern theorem provers address…

Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates…

We introduce heap automata, a formalism for automatic reasoning about robustness properties of the symbolic heap fragment of separation logic with user-defined inductive predicates. Robustness properties, such as satisfiability,…

We define a class of Separation Logic formulae, whose entailment problem: given formulae $\phi, \psi_1, \ldots, \psi_n$, is every model of $\phi$ a model of some $\psi_i$? is 2EXPTIME-complete. The formulae in this class are existentially…

Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…

Real-world arguments in text and dialogues are normally enthymemes (i.e. some of their premises and/or claims are implicit). Natural language processing (NLP) methods for handling enthymemes can potentially identify enthymemes in text but…

This paper describes a deductive approach to synthesizing imperative programs with pointers from declarative specifications expressed in Separation Logic. Our synthesis algorithm takes as input a pair of assertions---a pre- and a…

We establish various complexity results for the entailment problem between formulas in Separation Logic with user-defined predicates denoting recursive data structures. The considered fragments are characterized by syntactic conditions on…

We consider the problem of automated reasoning about dynamically manipulated data structures. The state-of-the-art methods are limited to the unfold-and-match (U+M) paradigm, where predicates are transformed via (un)folding operations…

Automatically generating formal specifications including loop invariants, preconditions, and postconditions for legacy code is critical for program understanding, reuse and verification. However, the inherent complexity of control and data…

Mathematical theorem proving is an important testbed for large language models' deep and abstract reasoning capability. This paper focuses on improving LLMs' ability to write proofs in formal languages that permit automated proof…

Humans tame the complexity of mathematical reasoning by developing hierarchies of abstractions. With proper abstractions, solutions to hard problems can be expressed concisely, thus making them more likely to be found. In this paper, we…

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 develop a doubly-exponential decision procedure for the satisfiability problem of guarded separation logic -- a novel fragment of separation logic featuring user-supplied inductive predicates, Boolean connectives, and separating…

Recursively defined linked data structures embedded in a pointer-based heap and their properties are naturally expressed in pure first-order logic with least fixpoint definitions (FO+lfp) with background theories. Such logics, unlike pure…