No abstract

The Verified Software Toolchain builds foundational machine-checked proofs of the functional correctness of C programs. Its program logic, Verifiable C, is a shallowly embedded higher-order separation Hoare logic which is proved sound in Coq with respect to the operational semantics of CompCert C light. This paper introduces VST-Floyd, a verification assistant which offers a set of semiautomatic tactics helping users build functional correctness proofs for C programs using Verifiable C.

We develop powerful and general techniques to mechanically verify realistic programs that manipulate heaprepresented graphs. These graphs can exhibit well-known organization principles, such as being a directed acyclic graph or a disjoint-forest; alternatively, these graphs can be totally unstructured. The common thread for such structures is that they exhibit deep intrinsic sharing and can be expressed using the language of graph theory. We construct a modular and general setup for reasoning about abstract mathematical graphs and use separation logic to define how such abstract graphs are represented concretely in the heap. We develop a Localize rule that enables modular reasoning about such programs, and show how this rule can support existential quantifiers in postconditions and smoothly handle modified program variables. We demonstrate the generality and power of our techniques by integrating them into the Verified Software Toolchain and certifying the correctness of seven graph-manipulating programs written in CompCert C, including a 400-line generational garbage collector for the CertiCoq project. While doing so, we identify two places where the semantics of C is too weak to define generational garbage collectors of the sort used in the OCaml runtime. Our proofs are entirely machine-checked in Coq.

A quantum circuit is a computational unit that transforms an input quantum state to an output state. A natural way to reason about its behavior is to compute explicitly the unitary matrix implemented by it. However, when the number of qubits increases, the matrix dimension grows exponentially and the computation becomes intractable. In this paper, we propose a symbolic approach to reasoning about quantum circuits. It is based on a small set of laws involving some basic manipulations on vectors and matrices. This symbolic reasoning scales better than the explicit one and is well suited to be automated in Coq, as demonstrated with some typical examples.

Program representation, which aims at converting program source code into vectors with automatically extracted features, is a fundamental problem in programming language processing (PLP). Recent work tries to represent programs with neural networks based on source code structures. However, such methods often focus on the syntax and consider only one single perspective of programs, limiting the representation power of models. This paper proposes a multi-view graph (MVG) program representation method. MVG pays more attention to code semantics and simultaneously includes both data flow and control flow as multiple views. These views are then combined and processed by a graph neural network (GNN) to obtain a comprehensive program representation that covers various aspects. We thoroughly evaluate our proposed MVG approach in the context of algorithm detection, an important and challenging subfield of PLP. Specifically, we use a public dataset POJ-104 and also construct a new challenging dataset ALG-109 to test our method. In experiments, MVG outperforms previous methods significantly, demonstrating our model's strong capability of representing source code.

No abstract

No abstract

Separation logic adds two connectives to assertion languages: separating conjunction * ("star") and its adjoint, separating implication − * ("magic wand"). Comparatively, separating implication is less widely used.This paper demonstrates that by using magic wand to express frames that relate mutable local portions of data structures to global portions, we can exploit its power while proofs are still easily understandable. Many useful separation logic theorems about partial data structures can now be proved by simple automated tactics, which were usually proved by induction. This magic-wand-as-frame technique is especially useful when formalizing the proofs by a high order logic. We verify binary search tree insert in Coq as an example to demonstrate this proof technique.