Traditional imperative synchronous programming languages heavily rely on a strict separation between data memory and communication signals. Signals can be shared between computational units but cannot be overwritten within a synchronous reaction cycle. Memory can be destructively updated but cannot be shared between concurrent threads. This incoherence makes traditional imperative synchronous languages cumbersome for the programmer. The recent definition of sequentially constructive synchronous languages offers an improvement. It removes the separation between data memory and communication signals and unifies both through the notion of clock synchronized shared memory . However, it still depends on global causality analyses, which precludes black-box procedural abstraction. This complicates reuse and composition of software components. This article shows how black-box procedural abstraction can be accommodated inside the sequentially constructive model of computation. We present the Sequentially Constructive Procedural Language ( SCoPL ) and its semantic theory of policy-constructive synchronous processes. SCoPL supports black-box procedural abstractions using policy interfaces to ensure that procedure calls are memory-safe and wait-free and their scheduling is determinate and causal. At the same time, a policy interface constrains the level of freedom for the implementation and subsequent refactoring of a procedure. As a result, policies enable separate compilation and composition of procedures. We present our extensions abstractly as a formal semantics for SCoPL and motivate it concretely in the context of the open-source, embedded, real-time language Blech .

Scade is a domain-specific synchronous functional language used to implement safety-critical real-time software for more than twenty years. Two main approaches have been considered for its semantics: (i) an indirect collapsing semantics based on a source-to-source translation of high-level constructs into a data-flow core language whose semantics is precisely specified and is the entry for code generation; a relational synchronous semantics , akin to Esterel, that applies directly to the source. It defines what is a valid synchronous reaction but hides, on purpose, if a semantics exists, is unique and can be computed; hence, it is not executable. This paper presents, for the first time, an executable , state-based semantics for a language that has the key constructs of Scade all together, in particular the arbitrary combination of data-flow equations and hierarchical state machines. It can apply directly to the source language before static checks and compilation steps. It is constructive in the sense that the language in which the semantics is defined is a statically typed functional language with call-by-value and strong normalization, e.g., it is expressible in a proof-assistant where all functions terminate. It leads to a reference, purely functional, interpreter. This semantics is modular and can account for possible errors, allowing to establish what property is ensured by each static verification performed by the compiler. It also clarifies how causality is treated in Scade compared with Esterel. This semantics can serve as an oracle for compiler testing and validation; to prototype novel language constructs before they are implemented, to execute possibly unfinished models or that are correct but rejected by the compiler; to prove the correctness of compilation steps. The semantics given in the paper is implemented as an interpreter in a purely functional style, in OCaml.

Object orientation is a powerful and widely used paradigm for abstraction and structuring in programming. Many languages are designed with this principle or support different degrees of object orientation. In synchronous languages, originally developed to design embedded reactive systems, there are only few object-oriented influences. However, especially in combination with a statechart notation, the modeling process can be improved by facilitating object orientation as we argue here. At the same time the graphical representation can be used to illustrate the object-oriented design of a system. Synchronous statechart dialects, such as the SCCharts language, provide deterministic concurrency for specifying safety-critical systems. Using SCCharts as an example, we illustrate how an object-oriented modeling approach that supports inheritance can be introduced. We further present how external, i.e., host language, objects can be included in the SCCharts language. Specifically, we discuss how the recently developed concepts of scheduling directives and scheduling policies can be used to ensure the determinism of objects while retaining encapsulation.

Traditional imperative synchronous programming languages heavily rely on a strict separation between data memory and communication signals. Signals can be shared between computational units but cannot be overwritten within a synchronous reaction cycle. Memory can be destructively updated but cannot be shared between concurrent threads. This incoherence makes traditional imperative synchronous languages cumbersome for the programmer. The recent definition of sequentially constructive synchronous languages offers an improvement. It removes the separation between data memory and communication signals and unifies both through the notion of clock synchronised shared memory. However, it still depends on global causality analyses which precludes procedural abstraction. This complicates reuse and composition of software components. This paper shows how procedural abstraction can be accommodated inside the sequentially constructive model of computation. We present the Sequentially Constructive Procedural Language (SCPL) and its semantic theory of policy-constructive synchronous processes. SCPL supports procedural abstractions using policy interfaces to ensure that procedure calls are memory safe, wait-free and their scheduling is determinate and causal. At the same time, a policy interface constrains the level of freedom for the implementation and subsequent refactoring of a procedure. As a result, policies enable separate compilation and composition of procedures. We present our extensions abstractly as a formal semantics for SCPL and motivate it concretely in the context of the open-source, embedded, real-time language Blech.

Object orientation is a powerful and widely used paradigm for abstraction and structuring in programming. Many languages are designed with this principle or support different degrees of object orientation. In synchronous languages, originally developed to design embedded reactive systems, there are only few object-oriented influences. However, especially in combination with a statechart notation, the modeling process can be improved by facilitating object orientation as we argue here. At the same time the graphical representation can be used to illustrate the object-oriented design of a system. Synchronous statechart dialects, such as the SCCharts language, provide deterministic concurrency for specifying safety-critical systems. Using SCCharts as an example, we illustrate how an object-oriented modeling approach that supports inheritance, can be introduced. We further present how external, i. e. host language, objects can be included in the SCCharts language. Specifically, we discuss how the recently developed concepts of scheduling directives and scheduling policies can be used to ensure the determinism of objects while retaining encapsulation.

Synchronous Programming ( SP ) is a universal computational principle that provides deterministic concurrency. The same input sequence with the same timing always results in the same externally observable output sequence, even if the internal behaviour generates uncertainty in the scheduling of concurrent memory accesses. Consequently, SP languages have always been strongly founded on mathematical semantics that support formal program analysis. So far, however, communication has been constrained to a set of primitive clock-synchronised shared memory ( csm ) data types, such as data-flow registers, streams and signals with restricted read and write accesses that limit modularity and behavioural abstractions. This paper proposes an extension to the SP theory which retains the advantages of deterministic concurrency, but allows communication to occur at higher levels of abstraction than currently supported by SP data types. Our approach is as follows. To avoid data races, each csm type publishes a policy interface for specifying the admissibility and precedence of its access methods. Each instance of the csm type has to be policy-coherent, meaning it must behave deterministically under its own policy—a natural requirement if the goal is to build deterministic systems that use these types. In a policy-constructive system, all access methods can be scheduled in a policy-conformant way for all the types without deadlocking. In this paper, we show that a policy-constructive program exhibits deterministic concurrency in the sense that all policy-conformant interleavings produce the same input-output behaviour. Policies are conservative and support the csm types existing in current SP languages. Technically, we introduce a kernel SP language that uses arbitrary policy-driven csm types. A big-step fixed-point semantics for this language is developed for which we prove determinism and termination of constructive programs.

The design and analysis of complex distributed systems proceeds along numerous levels of abstractions. One key abstraction step for reducing complexity is the passage from analog transistor electronics to synchronously clocked digital circuits. This significantly simplifies the modelling from continuous differential equations over the real numbers to discrete Mealy automata over two-valued Boolean algebra. Although typically taken for granted, this step is magic. How do we obtain clock synchronization from asynchronous communication of continuous values? How do we decide on the discrete meaning of continuous signals without a synchronization clock? From a logical perspective, the possibility of synchronization is paradoxical and appears "out of thin air." The chicken-or-egg paradox persists at higher levels abstraction for distributed software. We cannot achieve globally consistent state from local communications without synchronization. At the same time we cannot synchronize without access to globally consistent state. From this perspective, distributed algorithms such as for leader election, consensus or mutual exclusion do not strictly solve their task but merely reduce one synchronization problem to another. This talk revisits the logical justification of the synchronous abstraction claiming that correctness arguments, in so far as they are not merely reductions, must intrinsically depend on reasoning in classical logic. This is studied at the circuit level, where all software reductions must end. The well-known result that some synchronization elements cannot be implemented in delay-insensitive circuits is related to Berry's Thesis according to which digital circuits are delay-insensitive if and only if they are provably correct in constructive logic. More technically, the talk will show how non-inertial delays give rise to a constructive modal logic while inertial delays are inherently non-constructive. This gives a logical explanation for why inertial delays can be used to build arbiters, memory-cells and other synchronization elements, while non-inertial delays are not powerful enough. Though these results are tentative, they indicate the importance of logical constructiveness for metastable-free discrete abstractions of physical behavior. This also indicates that metastability is an unavoidable artifact of the digital abstraction in classical logic.

The synchronous language Esterel provides determinate concurrency for reactive systems. Determinacy is ensured by the signal coherence rule , which demands that signals have a stable value throughout one reaction cycle. This is natural for the original application domains of Esterel, such as controller design and hardware development; however, it is unnecessarily restrictive for software development. Sequentially Constructive Esterel (SCEst) overcomes this restriction by allowing values to change instantaneously, as long as determinacy is still guaranteed, adopting the recently proposed Sequentially Constructive model of computation. SCEst is grounded in the minimal Sequentially Constructive Language ( scl ), which also provides a novel semantic definition and compilation approach for Esterel.

In this paper we propose a WCRT analysis technique for synchronous programs, executed as sequential or multi-threaded code, based on formal power series in min-max-plus algebra. The algebraic model constitutes the first fully declarative timing-aware semantics of synchronous programs with arbitrary hierarchical control-flow structure. Under signal abstraction this model permits efficient compositional WCRT analyses based on structural boxes as the unit of composition. The algebraic model leads to a sound methodology to deal with the state space explosion arising from tick alignment of parallel composition by reduction to the maximum weighted clique problem.

Hybrid systems combine discrete controllers with adjoining physical processes. While many approaches exist for simulating hybrid systems, there are few approaches for their emulation, especially when the actual physical plant is not available. This paper develops the first formal framework for emulation along with a new compiler that enables large-scale (1000+ components) simulation. We propose a formal model called Synchronous Emulation Automaton (SEA) specifically for modular compilation and parallel execution. SEA combines Linear Time Invariant (LTI) systems with discrete mode switches and has the following semantic differences with Hybrid Automata: ➀ the Ordinary Differential Equations are solved analytically and the solutions are sampled at the Worst-Case Reaction Time of the model and ➁ we develop a new composition semantics, which allows individual SEAs to execute in parallel with each other. The proposed semantics eliminates: ⓐ the need for dynamic numerical solvers, and ⓑ the Zeno-phenomenon by construction. Experimental results show that process models designed using our tool (Piha) give a 3.6 times execution speedup over Simulink®, and upto 26 times speedup on manycore architectures.

Synchronous languages are ideal for designing safety-critical systems. Static Worst-Case Reaction Time (WCRT) analysis is an essential component in the design flow that ensures the real-time requirements are met. There are a few approaches for WCRT analysis, and the most versatile of all is explicit path enumeration. However, as synchronous programs are highly concurrent, techniques based on this approach, such as model checking, suffer from state explosion as the number of threads increases. One observation on this problem is that these existing techniques analyse the program by enumerating a functionally equivalent automaton while WCRT is a non-functional property. This mismatch potentially causes algorithm-induced state explosion. In this paper, we propose a WCRT analysis technique based on the notion of timing equivalence, expressed using WCRT algebra. WCRT algebra can effectively capture the timing behaviour of a synchronous program by converting its intermediate representation Timed Concurrent Control Flow Graph (TCCFG) into a Tick Cost Automaton (TCA), a minimal automaton that is timing equivalent to the original program. Then the WCRT is computed over the TCA. We have implemented our approach and benchmarked it against state-of-the-art WCRT analysis techniques. The results show that the WCRT algebra is 3.5 times faster on average than the fastest published technique.

The synchronous language Esterel provides determinate concurrency for reactive systems. Determinacy is ensured by the “signal coherence rule,” which demands that signals have a stable value throughout one reaction cycle. This is natural for the original application domains of Esterel, such as controller design and hardware development; however, it is unnecessarily restrictive for software development. Sequentially Constructive Esterel (SCEst) overcomes this restriction by allowing values to change instantaneously, as long as determinacy is still guaranteed, adopting the recently proposed Sequentially Constructive model of computation. SCEst is grounded in the minimal Sequentially Constructive Language, which also provides a novel semantic definition and compilation approach for Esterel.

We present a new visual language, SCCharts, designed for specifying safety-critical reactive systems. SCCharts use a statechart notation and provide determinate concurrency based on a synchronous model of computation (MoC), without restrictions common to previous synchronous MoCs. Specifically, we lift earlier limitations on sequential accesses to shared variables, by leveraging the sequentially constructive MoC. The semantics and key features of SCCharts are defined by a very small set of elements, the Core SCCharts, consisting of state machines plus fork/join concurrency. We also present a compilation chain that allows efficient synthesis of software and hardware.

We aim to establish the multi-modal logic CK n as a baseline for a constructive correspondence theory of constructive modal logics. Just like many classical multi-modal logics may be studied as theories of the basic system K obtained by model-theoretic specialisation, we envisage constructive modal logics to be derived as proof-theoretic enrichments of CK n . The system CK n would then act as a core system for constructive contextual reasoning with controlled information flow. In this paper, as a first step towards this goal, we study CK n as a type theory and introduce its computational λ-calculus, λCK n . Extending previous work on CK n , we present a cut-free contextual sequent system in the spirit of Masini's two-dimensional generalisation of natural deduction and Brünnler's nested sequents and give a computational interpretation for CK n following the Curry-Howard Correspondence. The associated modal type theory λCK n permits an interpretation for both the modalities □ and ◊ of CK n as type operators with simple and independent constructors and destructors, which has been missing in the literature. It is shown that the calculus satisfies subject reduction, strong normalisation and confluence. Since normal forms can be characterised by way of a Gentzen-style typing system with sub-formula property, λCK n is suitable for proof search in CK n . At the same time, λCK n enjoys natural deduction style typing which is important for programming applications. In contrast to most existing modal type theories, which are obtained as theories of the constructive modal logic S4, CK n is not bound to a particular contextual interpretation. Thus, λCK n constitutes the core of a functional language which provides static type checking of information processing to support safe contextual navigation in relational structures like those treated by description logics. We review some existing work on modal type theories and discuss their relation to λCK n .

Synchronous languages ensure determinate concurrency but at the price of restrictions on what programs are considered valid, or constructive . Meanwhile, sequential languages such as C and Java offer an intuitive, familiar programming paradigm but provide no guarantees with regard to determinate concurrency. The sequentially constructive (SC) model of computation (MoC) presented here harnesses the synchronous execution model to achieve determinate concurrency while taking advantage of familiar, convenient programming paradigms from sequential languages. In essence, the SC MoC extends the classical synchronous MoC by allowing variables to be read and written in any order and multiple times, as long as the sequentiality expressed in the program provides sufficient scheduling information to rule out race conditions. This allows to use programming patterns familiar from sequential programming, such as testing and later setting the value of a variable, which are forbidden in the standard synchronous MoC. The SC MoC is a conservative extension in that programs considered constructive in the common synchronous MoC are also SC and retain the same semantics. In this article, we investigate classes of shared variable accesses, define SC-admissible scheduling as a restriction of “free scheduling,” derive the concept of sequential constructiveness, and present a priority-based scheduling algorithm for analyzing and compiling SC programs efficiently.

Synchronous languages ensure deterministic concurrency, but at the price of heavy restrictions on what programs are considered valid, or constructive. Meanwhile, sequential languages such as C and Java offer an intuitive, familiar programming paradigm but provide no guarantees with regard to deterministic concurrency. The sequentially constructive model of computation (SC MoC) presented here harnesses the synchronous execution model to achieve deterministic concurrency while addressing concerns that synchronous languages are unnecessarily restrictive and difficult to adopt. In essence, the SC MoC extends the classical synchronous MoC by allowing variables to be read and written in any order as long as sequentiality expressed in the program provides sufficient scheduling information to rule out race conditions. The SC MoC is a conservative extension in that programs considered constructive in the common synchronous MoC are also SC and retain the same semantics. In this paper, we identify classes of variable accesses, define sequential constructiveness based on the concept of SC-admissible scheduling, and present a priority-based scheduling algorithm for analyzing and compiling SC programs.

The synchronous model of computation together with a suitable execution platform facilitates system-level timing predictability. This paper introduces an algebraic framework for precisely capturing worst case reaction time (WCRT) characteristics for Esterel-style reactive processors with hardware-supported multithreading. This framework provides a formal grounding for the WCRT problem, and allows to improve upon earlier heuristics by accurately and modularly characterizing timing interfaces.

No abstract available.

1PARC, CA, USA 2ANU, Australia 3University of Bamberg, Germany

Valeria de Paiva, Rajeev Goré, Michael Mendler; Forthcoming Papers, Journal of Logic and Computation, Volume 14, Issue 4, 1 August 2004, Pages 621–622, https://

No abstract available.

The semantics of Statecharts macro steps, as introduced by Pnueli and Shalev [1991], lacks compositionality. This article first analyzes the compositionality problem and traces it back to the invalidity of the Law of the Excluded Middle. It then characterizes the semantics via a particular class of linear intuitionistic Kripke models. This yields, for the first time in the literature, a simple fully abstract semantics that interprets Pnueli and Shalev's concept of failure naturally. The results not only give insight into the semantic subtleties of Statecharts, but also provide a basis for an implementation, for developing algebraic theories for macro steps, and for comparing different Statecharts variants.

This special issue reports on some recent advances in the area of intuitionistic modal type theories and their application to Computer Science. It collects a selection of papers presented at the Logic in Computer Science (LICS'99) satellite workshop on Intuitionistic Modal Logics and Applications (IMLA'99) held at Trento, Italy in July 1999. All of the contributors to this one day workshop, which was widely attended, were invited to submit a full and revised version of their papers to this special issue of MSCS. The selection was based on a second round of peer reviewing.

Abstrlld.Computing hardware is designed by refining an abstract specification through various lower levels of abstraction to arme ar a tranmtor Jayout implCJ11en1ed in a physic:al medium.Fomalizing the reftnements-one taslc of the mathematical aemantics of computation-involves proving that the dc:vioe described at eadr Jevel of abstraction does indeed bohave as prescribed by thc dcscriptlon at lhe nm higher lcvcl.Onc obstacle to this goal that has long been recognized is thal certain dasses of behaviors can bc physic:a!lyrealizcd only approximately.Thc notorious prob!em of metastable operation predudes, for example, lhe rcalization on classical principlcs of fllpftops that react in bounded time to arbitrary input signals.The litcrature suggests that lbe dißicully lies ultimatcly in thc specification 's requiring that thc realizing device react propcrly in bounded time.We show, howcver, that a simplc•time""llboundod synchronization problcm, namely, mutual exc!usion by means of an arbitcr, cannot bc solved with perfect reliabilily using oontinllOUs, i.e~ Newtonian, physica!phenomena.In particular, for any physic:al device operating on Ncwtonian principles !hat satisfics specific assumptions c:onceming an arbitcr's input-output bchavior, therc always cxist compcting requcsts to which il re8Cl5 by granting them all.