Liquid Clocks - Refinement Types for Time-Dependent Stream Functions

The concept of liquid clocks introduced in this paper is a significant step towards a more precise compile-time framework for the analysis of synchronous and polychromous languages. Compiling languages such as Lustre or SIGNAL indeed involves a number of static analyses of programs before they can be synthesized into executable code, e.g., synchronicity class characterization, clock assignment, static scheduling or causality analysis. These analyses are often equivalent to undecidable problems, necessitating abstracting such programs to provide sound yet incomplete analyses. Such abstractions unfortunately often lead to the rejection of programs that could very well be synthesized into deterministic code, provided abstraction refinement steps could be applied for more accurate analysis. To reduce the false negatives occurring during the compilation process, we leverage recent advances in type theory -- with the definition of decidable classes of value-dependent type systems -- and formal verification, linked to the development of efficient SAT/SMT solvers, to provide a type-theoretic approach that considers all the above analyses as type inference problems. In order to simplify the exposition of our new approach in this paper, we define a refinement type system for a minimalistic, synchronous, stream-processing language to concisely represent, analyse, and verify logical and quantitative properties of programs expressed as stream-processing data-flow networks. Our type system provides a new framework to represent logical time (clocks) and scheduling properties, and to describe their relations with stream values and, possibly, other quantas. We show how to analyze synchronous stream processing programs (à la Lustre, Signal) to enable previously described analyzes involved in compiling such programs. We also prove the soundness of our type system and elaborate on the adaptability of this core framework by outlining its extensibility to specific models of computations and other quantas

Static Trace-Based Deadlock Analysis for Synchronous Mini-Go

We consider the problem of static deadlock detection for programs in the Go programming language which make use of synchronous channel communications. In our analysis, regular expressions extended with a fork operator capture the communication behavior of a program. Starting from a simple criterion that characterizes traces of deadlock-free programs, we develop automata-based methods to check for deadlock-freedom. The approach is implemented and evaluated with a series of examples

Implementing Multi-Periodic Critical Systems: from Design to Code Generation

This article presents a complete scheme for the development of Critical Embedded Systems with Multiple Real-Time Constraints. The system is programmed with a language that extends the synchronous approach with high-level real-time primitives. It enables to assemble in a modular and hierarchical manner several locally mono-periodic synchronous systems into a globally multi-periodic synchronous system. It also allows to specify flow latency constraints. A program is translated into a set of real-time tasks. The generated code (\C\ code) can be executed on a simple real-time platform with a dynamic-priority scheduler (EDF). The compilation process (each algorithm of the process, not the compiler itself) is formally proved correct, meaning that the generated code respects the real-time semantics of the original program (respect of periods, deadlines, release dates and precedences) as well as its functional semantics (respect of variable consumption).Comment: 15 pages, published in Workshop on Formal Methods for Aerospace (FMA'09), part of Formal Methods Week 2009

Semantic-Preserving Transformations for Stream Program Orchestration on Multicore Architectures

Because the demand for high performance with big data processing and distributed computing is increasing, the stream programming paradigm has been revisited for its abundance of parallelism in virtue of independent actors that communicate via data channels. The synchronous data-flow (SDF) programming model is frequently adopted with stream programming languages for its convenience to express stream programs as a set of nodes connected by data channels. Static data-rates of SDF programming model enable program transformations that greatly improve the performance of SDF programs on multicore architectures. The major application domain is for SDF programs are digital signal processing, audio, video, graphics kernels, networking, and security. This thesis makes the following three contributions that improve the performance of SDF programs: First, a new intermediate representation (IR) called LaminarIR is introduced. LaminarIR replaces FIFO queues with direct memory accesses to reduce the data communication overhead and explicates data dependencies between producer and consumer nodes. We provide transformations and their formal semantics to convert conventional, FIFO-queue based program representations to LaminarIR. Second, a compiler framework to perform sound and semantics-preserving program transformations from FIFO semantics to LaminarIR. We employ static program analysis to resolve token positions in FIFO queues and replace them by direct memory accesses. Third, a communication-cost-aware program orchestration method to establish a foundation of LaminarIR parallelization on multicore architectures. The LaminarIR framework, which consists of the aforementioned contributions together with the benchmarks that we used with the experimental evaluation, has been open-sourced to advocate further research on improving the performance of stream programming languages

Resource Control for Synchronous Cooperative Threads

We develop new methods to statically bound the resources needed for the execution of systems of concurrent, interactive threads. Our study is concerned with a \emph{synchronous} model of interaction based on cooperative threads whose execution proceeds in synchronous rounds called instants. Our contribution is a system of compositional static analyses to guarantee that each instant terminates and to bound the size of the values computed by the system as a function of the size of its parameters at the beginning of the instant. Our method generalises an approach designed for first-order functional languages that relies on a combination of standard termination techniques for term rewriting systems and an analysis of the size of the computed values based on the notion of quasi-interpretation. We show that these two methods can be combined to obtain an explicit polynomial bound on the resources needed for the execution of the system during an instant. As a second contribution, we introduce a virtual machine and a related bytecode thus producing a precise description of the resources needed for the execution of a system. In this context, we present a suitable control flow analysis that allows to formulte the static analyses for resource control at byte code level

Automatic modular abstractions for template numerical constraints

We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and containing linear assignments and tests. In addition to loop-free code, the same method also applies for obtaining least fixed points as functions of the precondition, which permits the analysis of loops and recursive functions. Our algorithms are based on new quantifier elimination and symbolic manipulation techniques. Given the specification of an abstract domain, and a program block, our method automatically outputs an implementation of the corresponding abstract transformer. It is thus a form of program transformation. The motivation of our work is data-flow synchronous programming languages, used for building control-command embedded systems, but it also applies to imperative and functional programming

A Static Analyzer for Large Safety-Critical Software

We show that abstract interpretation-based static program analysis can be made efficient and precise enough to formally verify a class of properties for a family of large programs with few or no false alarms. This is achieved by refinement of a general purpose static analyzer and later adaptation to particular programs of the family by the end-user through parametrization. This is applied to the proof of soundness of data manipulation operations at the machine level for periodic synchronous safety critical embedded software. The main novelties are the design principle of static analyzers by refinement and adaptation through parametrization, the symbolic manipulation of expressions to improve the precision of abstract transfer functions, the octagon, ellipsoid, and decision tree abstract domains, all with sound handling of rounding errors in floating point computations, widening strategies (with thresholds, delayed) and the automatic determination of the parameters (parametrized packing)