Trustworthy Refactoring via Decomposition and Schemes: A Complex Case Study

Widely used complex code refactoring tools lack a solid reasoning about the correctness of the transformations they implement, whilst interest in proven correct refactoring is ever increasing as only formal verification can provide true confidence in applying tool-automated refactoring to industrial-scale code. By using our strategic rewriting based refactoring specification language, we present the decomposition of a complex transformation into smaller steps that can be expressed as instances of refactoring schemes, then we demonstrate the semi-automatic formal verification of the components based on a theoretical understanding of the semantics of the programming language. The extensible and verifiable refactoring definitions can be executed in our interpreter built on top of a static analyser framework.Comment: In Proceedings VPT 2017, arXiv:1708.0688

Invariant Generation through Strategy Iteration in Succinctly Represented Control Flow Graphs

We consider the problem of computing numerical invariants of programs, for instance bounds on the values of numerical program variables. More specifically, we study the problem of performing static analysis by abstract interpretation using template linear constraint domains. Such invariants can be obtained by Kleene iterations that are, in order to guarantee termination, accelerated by widening operators. In many cases, however, applying this form of extrapolation leads to invariants that are weaker than the strongest inductive invariant that can be expressed within the abstract domain in use. Another well-known source of imprecision of traditional abstract interpretation techniques stems from their use of join operators at merge nodes in the control flow graph. The mentioned weaknesses may prevent these methods from proving safety properties. The technique we develop in this article addresses both of these issues: contrary to Kleene iterations accelerated by widening operators, it is guaranteed to yield the strongest inductive invariant that can be expressed within the template linear constraint domain in use. It also eschews join operators by distinguishing all paths of loop-free code segments. Formally speaking, our technique computes the least fixpoint within a given template linear constraint domain of a transition relation that is succinctly expressed as an existentially quantified linear real arithmetic formula. In contrast to previously published techniques that rely on quantifier elimination, our algorithm is proved to have optimal complexity: we prove that the decision problem associated with our fixpoint problem is in the second level of the polynomial-time hierarchy.Comment: 35 pages, conference version published at ESOP 2011, this version is a CoRR version of our submission to Logical Methods in Computer Scienc

CFA2: a Context-Free Approach to Control-Flow Analysis

In a functional language, the dominant control-flow mechanism is function call and return. Most higher-order flow analyses, including k-CFA, do not handle call and return well: they remember only a bounded number of pending calls because they approximate programs with control-flow graphs. Call/return mismatch introduces precision-degrading spurious control-flow paths and increases the analysis time. We describe CFA2, the first flow analysis with precise call/return matching in the presence of higher-order functions and tail calls. We formulate CFA2 as an abstract interpretation of programs in continuation-passing style and describe a sound and complete summarization algorithm for our abstract semantics. A preliminary evaluation shows that CFA2 gives more accurate data-flow information than 0CFA and 1CFA.Comment: LMCS 7 (2:3) 201

A formal semantics for control and data flow in the gannet service-based system-on-chip architecture

There is a growing demand for solutions which allow the design of large and complex reconfigurable Systems-on- Chip (SoC) at high abstraction levels. The Gannet project proposes a functional programming approach for high-abstraction design of very large SoCs. Gannet is a distributed service-based SoC architecture, i.e. a network of services offered by hardware or software cores. The Gannet SoC is task-level reconfigurable: it performs tasks by executing functional task description programs using a demand-driven dataflow mechanism. The Gannet architecture combines the flexible connectivity offered by a Networkon- Chip with the functional language paradigm to create a fully concurrent distributed SoC with the option to completely separate data flows from control flows. This feature is essential to avoid a bottleneck at he controller for run-time control of multiple high-throughput data flows. In this paper we present the Gannet architecture and language and introduce an operational semantics to formally describe the mechanism to separate control and data flows