Join-preserving maps on the discrete time scale $\omega^+$, referred to as time warps, have been proposed as graded modalities that can be used to quantify the growth of information in the course of program execution. The set of time warps forms a simple distributive involutive residuated lattice -- called the time warp algebra -- that is equipped with residual operations relevant to potential applications. In this paper, we show that although the time warp algebra generates a variety that lacks the finite model property, it nevertheless has a decidable equational theory. We also describe an implementation of a procedure for deciding equations in this algebra, written in the OCaml programming language, that makes use of the Z3 theorem prover.

Birkedal et al. recently introduced dependent right adjoints as an important class of (non-fibered) modalities in type theory. We observe that several aspects of their calculus are left underdeveloped, and that it cannot serve as an internal language. We resolve these problems by assuming that the modal context operator is a parametric right adjoint. We show that this hitherto unrecognized structure is common. Based on these discoveries we present a new well-behaved Fitch-style multimodal type theory, which can be used as an internal language. Finally, we apply this syntax to guarded recursion and parametricity.

Birkedal et al. recently introduced dependent right adjoints as an important class of (non-fibered) modalities in type theory. We observe that several aspects of their calculus are left underdeveloped and that it cannot serve as an internal language. We resolve these problems by assuming that the modal context operator is a parametric right adjoint. We show that this hitherto unrecognized structure is common. Based on these discoveries we present a new well-behaved Fitch-style multimodal type theory, which can be used as an internal language. Finally, we apply this syntax to guarded recursion and parametricity.

This work is supported by the Emergence project “ReaLiSe” funded by the city of Paris. Abstract Many computer systems are reactive : they execute in continuous interaction with their environment. From the perspective of functional programming, reactive systems can be modeled and programmed as stream functions. Several lines of research have exploited this point of view. Works based on Nakano’s guarded recursion use type-theoretical modalities to guarantee productivity. Works based on synchronous programming use more specialized methods but guarantee incremental processing of stream fragments. In this paper, we contribute to a recent synthesis between the two approaches by describing how a language with a family of type-theoretical modalities can be given an incremental semantics in the synchronous style. We prove that this semantics coincides with a more usual big-step semantics.

Graded modalities have been proposed in recent work on programming languages as a general framework for refining type systems with intensional properties. In particular, continuous endomaps of the discrete time scale, or time warps, can be used to quantify the growth of information in the course of program execution. Time warps form a complete residuated lattice, with the residuals playing an important role in potential programming applications. In this paper, we study the algebraic structure of time warps, and prove that their equational theory is decidable, a necessary condition for their use in real-world compilers. We also describe how our universal-algebraic proof technique lends itself to a constraint-based implementation, establishing a new link between universal algebra and verification technology.

It is well known that modern functional programming languages are naturally amenable to parallel programming. Achieving efficient parallelism using functional languages, however, remains difficult. Perhaps the most important reason for this is their lack of support for efficient in-place updates, i.e., mutation, which is important for the implementation of both parallel algorithms and the run-time system services (e.g., schedulers and synchronization primitives) used to execute them. In this paper, we propose techniques for efficient mutation in parallel functional languages. To this end, we couple the memory manager with the thread scheduler to make reading and updating data allocated by nested threads efficient. We describe the key algorithms behind our technique, implement them in the MLton Standard ML compiler, and present an empirical evaluation. Our experiments show that the approach performs well, significantly improving efficiency over existing functional language implementations.

A classic problem in parallel computing is to take a high-level parallel program written, for example, in nested-parallel style with fork-join constructs and run it efficiently on a real machine. The problem could be considered solved in theory, but not in practice, because the overheads of creating and managing parallel threads can overwhelm their benefits. Developing efficient parallel codes therefore usually requires extensive tuning and optimizations to reduce parallelism just to a point where the overheads become acceptable. In this paper, we present a scheduling technique that delivers provably efficient results for arbitrary nested-parallel programs, without the tuning needed for controlling parallelism overheads. The basic idea behind our technique is to create threads only at a beat (which we refer to as the "heartbeat") and make sure to do useful work in between. We specify our heartbeat scheduler using an abstract-machine semantics and provide mechanized proofs that the scheduler guarantees low overheads for all nested parallel programs. We present a prototype C++ implementation and an evaluation that shows that Heartbeat competes well with manually optimized Cilk Plus codes, without requiring manual tuning.

This thesis addresses the design and implementationof a programming language for real-time streaming applications,such as video decoding. The model of Kahnprocess networks is a natural fit for this area and hasbeen used extensively. In this model, a program consistsin a set of parallel processes communicating via singlereader, single writer queues. The strength of the modellies in its determinism.Synchronous functional languages such as Lustre arededicated to critical embedded systems. A Lustre programdefines a synchronous Kahn process network, thatis, which can be executed using finite queues and withoutdeadlocks. This is enforced by a dedicated type system,the clock calculus, which establishes a global timescale throughout a program. The global time scale isused to define clocks: per-queue boolean sequences indicating,for each time step, whether a process producesor consumes a token in the queue. This information isused both for enforcing synchrony and for generatingfinite-state software or hardware.We propose and study integer clocks, a generalizationof boolean clocks featuring arbitrarily big natural numbers.Integer clocks model the production or consumptionof several values from the same queue in the courseof a time step. We then rely on integer clocks to definethe local time scale construction, which may hide timesteps performed by a sub-program from the surroundingcontext.These principles are integrated into a clock calculus fora higher-order functional language. We study its properties,proving among other results that well-typed programsdo not deadlock. We adjust the clock-directedcode generation scheme of Lustre to generate finite-statedigital synchronous circuits from typed programs. Thetyping information controls certain trade-offs betweentime and space in the generated circuits.

Multicore architectures are increasingly used in embedded systems to achieve higher throughput with lower energy consumption. This trend accentuates the need to convert existing sequential code to effectively exploit the resources of these architectures. We present a parallelization flow and toolset for legacy C code that includes a performance estimation tool, a parallelization tool, and a streaming-oriented parallelization framework. These are part of the work-in-progress EU FP7 PHARAON project that aims to develop a complete set of techniques and tools to guide and assist software development for heterogeneous parallel architectures. We demonstrate the effectiveness of the use of the toolset in an experiment where we measure the parallelization quality and time for inexperienced users, and the parallelization flow and performance results for the parallelization of a practical example of a stereo vision application.

Les langages flot de donnees synchrones a la Lustre proposent un formalisme equationnel de haut niveau dedie a la conception et l'implantation de systemes temps reel. Ils sont traditionnellement restreints aux systemes critiques ne necessitant pas de calcul intensif ; en particulier, le code imperatif genere ne contient pas naturellement de boucles. Lucy-n est une variante recente de Lustre plus adaptee aux traitements multimedias. Dans cet article, nous proposons une extension de la semantique de Lucy-n ou les flots transportent des rafales de valeurs plutot que de simples scalaires, ainsi qu'un systeme de types qui caracterise la taille de ces rafales. L'ambition est d'adapter les techniques de generation de code usuelles pour produire des boucles imbriquees.

Bounded single-producer single-consumer FIFO queues are one of the simplest concurrent data-structure, and they do not require more than sequential consistency for correct operation. Still, sequential consistency is an unrealistic hypothesis on shared-memory multiprocessors, and enforcing it through memory barriers induces significant performance and energy overhead. This paper revisits the optimization and correctness proof of bounded FIFO queues in the context of weak memory consistency, building upon the recent axiomatic formalization of the C11 memory model. We validate the portability and performance of our proven implementation over 3 processor architectures with diverse hardware memory models, including ARM and PowerPC. Comparison with state-of-the-art implementations demonstrate consistent improvements for a wide range of buffer and batch sizes.

In this article, we present the work-in-progress of the EU FP7 PHARAON project, started in September 2011. The first objective of the project is the development of new techniques and tools capable to assist the designer in the development of parallel embedded systems, from executable specifications to target-specific implementation and debugging on a multicore platform. This tool chain will offer and implement several parallelization strategies, reflecting the functional and non-functional constraints of the system, and driving the designer into incremental parallelization and adaptation steps. The second objective of the project is to develop monitoring and control techniques in the middleware of the system capable to automatically adapt platform services to application requirements and therefore reduce power consumption transparently.

Bounded single-producer single-consumer FIFO queues are one of the simplest concurrent data-structure, and they do not require more than sequential consistency for correct operation. Still, sequential consistency is an unrealistic hypothesis on shared-memory multiprocessors, and enforcing it through memory barriers induces significant performance and energy overhead. This paper revisits the optimization and correctness proof of bounded FIFO queues in the context of weak memory consistency, building upon the recent axiomatic formalization of the C11 memory model. We validate the portability and performance of our proven implementation over 3 processor architectures with diverse hardware memory models, including ARM and PowerPC. Comparison with state-of-the-art implementations demonstrate consistent improvements for a wide range of buffer and batch sizes.

The generation of efficient sequential code for synchronous data-flow languages raises two intertwined issues: control and memory optimization. While the former has been extensively studied, for instance in the compilation of Lustre and Signal, the latter has only been addressed in a restricted manner. Yet, memory optimization becomes a pressing issue when arrays are added to such languages. This article presents a two-level solution to the memory optimization problem. It combines a compile-time optimization algorithm, reminiscent of register allocation, paired with language annotations on the source given by the designer. Annotations express in-place modifications and control where allocation is performed. Moreover, they allow external functions performing in-place modifications to be safely imported. Soundness of annotations is guaranteed by a semilinear type system and additional scheduling constraints. A key feature is that annotations for well-typed programs do not change the semantics of the language: removing them may lead to less efficient code but will not alter the semantics. The method has been implemented in a new compiler for a LUSTRE-like synchronous language extended with hierarchical automata and arrays. Experiments show that the proposed approach removes most of the unnecessary array copies, resulting in faster code that uses less memory.