A functional approach to heterogeneous computing in embedded systems

Developing programs for embedded systems presents quite a challenge; not only should programs be resource efficient, as they operate under memory and timing constraints, but they should also take full advantage of the hardware to achieve maximum performance. Since performance is such a significant factor in the design of embedded systems, modern systems typically incorporate more than one kind of processing element to benefit from specialized processing capabilities. For such heterogeneous systems the challenge in developing programs is even greater.In this thesis we explore a functional approach to heterogeneous system development as a means to address many of the modularity problems that are typically found in the application of low-level imperative programming for embedded systems. In particular, we explore a staged hardware software co-design language that we name Co-Feldspar and embed in Haskell. The staged approach enables designers to build their applications from reusable components and skeletons while retaining control over much of the generated source code. Furthermore, by embedding the language in Haskell we can exploit its type classes to write not only hardware and software programs, but also generic programs with overloaded instructions and expressions. We demonstrate the usefulness of the functional approach for co-design on a cryptographic example and signal processing filters, and benchmark software and mixed hardware-software implementations. Co-Feldspar currently adopts a monadic interface, which provides an imperative functional programming style that is suitable for explicit memory management and algorithms that rely on a certain evaluation order. For algorithms that are better defined as pure functions operating on immutable values, we provide a signal and array library that extends a monadic language, like Co-Feldspar. These extensions permit a functional style of programming by composing high-level combinators. Our compiler transforms such high-level code into efficient programs with mutating code. In particular, we show how to execute an FFT safely in-place, and how to describe a FIR and IIR filter efficiently as streams. Co-Feldspar’s monadic interface is however quite invasive; not only is the burden of explicit memory management quite heavy on the user, it is also quite easy to shoot on eself in the foot. It is for these reasons that we also explore a dynamic memory management discipline that is based on regions but predictable enough to be of use for embedded systems. Specifically, this thesis introduces a program analysis which annotates values with dynamically allocated memory regions. By limiting our efforts to functional languages that target embedded software, we manage to define a region inference algorithm that is considerably simpler than traditional approaches

How functional programming mattered

In 1989 when functional programming was still considered a niche topic, Hughes wrote a visionary paper arguing convincingly ‘why functional programming matters’. More than two decades have passed. Has functional programming really mattered? Our answer is a resounding ‘Yes!’. Functional programming is now at the forefront of a new generation of programming technologies, and enjoying increasing popularity and influence. In this paper, we review the impact of functional programming, focusing on how it has changed the way we may construct programs, the way we may verify programs, and fundamentally the way we may think about programs

Extensible sparse functional arrays with circuit parallelism

A longstanding open question in algorithms and data structures is the time and space complexity of pure functional arrays. Imperative arrays provide update and lookup operations that require constant time in the RAM theoretical model, but it is conjectured that there does not exist a RAM algorithm that achieves the same complexity for functional arrays, unless restrictions are placed on the operations. The main result of this paper is an algorithm that does achieve optimal unit time and space complexity for update and lookup on functional arrays. This algorithm does not run on a RAM, but instead it exploits the massive parallelism inherent in digital circuits. The algorithm also provides unit time operations that support storage management, as well as sparse and extensible arrays. The main idea behind the algorithm is to replace a RAM memory by a tree circuit that is more powerful than the RAM yet has the same asymptotic complexity in time (gate delays) and size (number of components). The algorithm uses an array representation that allows elements to be shared between many arrays with only a small constant factor penalty in space and time. This system exemplifies circuit parallelism, which exploits very large numbers of transistors per chip in order to speed up key algorithms. Extensible Sparse Functional Arrays (ESFA) can be used with both functional and imperative programming languages. The system comprises a set of algorithms and a circuit specification, and it has been implemented on a GPGPU with good performance

Normalisation by Evaluation in the Compilation of Typed Functional Programming Languages

This thesis presents a critical analysis of normalisation by evaluation as a technique for speeding up compilation of typed functional programming languages. Our investigation focuses on the SML.NET compiler and its typed intermediate language MIL. We implement and measure the performance of normalisation by evaluation for MIL across a range of benchmarks. Taking a different approach, we also implement and measure the performance of a graph-based shrinking reductions algorithm for SML.NET. MIL is based on Moggi’s computational metalanguage. As a stepping stone to normalisation by evaluation, we investigate strong normalisation of the computational metalanguage by introducing an extension of Girard-Tait reducibility. Inspired by previous work on local state and parametric polymorphism, we define reducibility for continuations and more generally reducibility for frame stacks. First we prove strong normalistion for the computational metalanguage. Then we extend that proof to include features of MIL such as sums and exceptions. Taking an incremental approach, we construct a collection of increasingly sophisticated normalisation by evaluation algorithms, culminating in a range of normalisation algorithms for MIL. Congruence rules and alpha-rules are captured by a compositional parameterised semantics. Defunctionalisation is used to eliminate eta-rules. Normalisation by evaluation for the computational metalanguage is introduced using a monadic semantics. Variants in which the monadic effects are made explicit, using either state or control operators, are also considered. Previous implementations of normalisation by evaluation with sums have relied on continuation-passing-syle or control operators. We present a new algorithm which instead uses a single reference cell and a zipper structure. This suggests a possible alternative way of implementing Filinski’s monadic reflection operations. In order to obtain benchmark results without having to take into account all of the features of MIL, we implement two different techniques for eliding language constructs. The first is not semantics-preserving, but is effective for assessing the efficiency of normalisation by evaluation algorithms. The second is semantics-preserving, but less flexible. In common with many intermediate languages, but unlike the computational metalanguage, MIL requires all non-atomic values to be named. We use either control operators or state to ensure each non-atomic value is named. We assess our normalisation by evaluation algorithms by comparing them with a spectrum of progressively more optimised, rewriting-based normalisation algorithms. The SML.NET front-end is used to generate MIL code from ML programs, including the SML.NET compiler itself. Each algorithm is then applied to the generated MIL code. Normalisation by evaluation always performs faster than the most naıve algorithms— often by orders of magnitude. Some of the algorithms are slightly faster than normalisation by evaluation. Closer inspection reveals that these algorithms are in fact defunctionalised versions of normalisation by evaluation algorithms. Our normalisation by evaluation algorithms perform unrestricted inlining of functions. Unrestricted inlining can lead to a super-exponential blow-up in the size of target code with respect to the source. Furthermore, the worst-case complexity of compilation with unrestricted inlining is non-elementary in the size of the source code. SML.NET alleviates both problems by using a restricted form of normalisation based on Appel and Jim’s shrinking reductions. The original algorithm is quadratic in the worst case. Using a graph-based representation for terms we implement a compositional linear algorithm. This speeds up the time taken to perform shrinking reductions by up to a factor of fourteen, which leads to an improvement of up to forty percent in total compile time

System Synthesis from a Monadic Functional Language

Embedded systems typically combine a mixture of heterogeneous components, some that are software executing on general purpose CPUs, some that are off-the-shelf hardware components, and some that are application specific circuitry. A major challenge when designing and implementing such systems is the dissimilar models of computation exhibited by hardware and software targets. To successfully navigate this challenge, components must be implemented in a way that does not unnecessarily bias the implementation towards either computational model, allowing the components to be retargeted as application requirements change. This dissertation presents an approach to this problem using a functional programming language extended with monadic imperative and concurrency effects. We argue that these language features allow components to be implemented and compiled to either hardware or software targets. To demonstrate this claim, we detail the design of such a language, Oread. Moreover, we describe the compilation of Oread to both hardware, via VHDL, and software, via C. Using these compilation techniques, we describe the development of a digital processing component in Oread and the integration of that component into a larger system

Effects as Sessions, Sessions as Effects

Effect and session type systems are two expressive behavioural type systems. The former is usually developed in the context of the lambda-calculus and its variants, the latter for the ?-calculus. In this paper we explore their relative expressive power. Firstly, we give an embedding from PCF, augmented with a parameterised effect system, into a session-typed pi-calculus (session calculus), showing that session types are powerful enough to express effects. Secondly, we give a reverse embedding, from the session calculus back into PCF, by instantiating PCF with concurrency primitives and its effect system with a session-like effect algebra; effect systems are powerful enough to express sessions. The embedding of session types into an effect system is leveraged to give a new implementation of session types in Haskell, via an effect system encoding. The correctness of this implementation follows from the second embedding result. We also discuss various extensions to our embeddings

Functional Programming for Embedded Systems

Embedded Systems application development has traditionally been carried out in low-level machine-oriented programming languages like C or Assembler that can result in unsafe, error-prone and difficult-to-maintain code. Functional programming with features such as higher-order functions, algebraic data types, polymorphism, strong static typing and automatic memory management appears to be an ideal candidate to address the issues with low-level languages plaguing embedded systems. However, embedded systems usually run on heavily memory-constrained devices with memory in the order of hundreds of kilobytes and applications running on such devices embody the general characteristics of being (i) I/O- bound, (ii) concurrent and (iii) timing-aware. Popular functional language compilers and runtimes either do not fare well with such scarce memory resources or do not provide high-level abstractions that address all the three listed characteristics. This work attempts to address this gap by investigating and proposing high-level abstractions specialised for I/O-bound, concurrent and timing-aware embedded-systems programs. We implement the proposed abstractions on eagerly-evaluated, statically-typed functional languages running natively on microcontrollers. Our contributions are divided into two parts - Part 1 presents a functional reactive programming language - Hailstorm - that tracks side effects like I/O in its type system using a feature called resource types. Hailstorm’s programming model is illustrated on the GRiSP microcontroller board.Part 2 comprises two papers that describe the design and implementation of Synchron, a runtime API that provides a uniform message-passing framework for the handling of software messages as well as hardware interrupts. Additionally, the Synchron API supports a novel timing operator to capture the notion of time, common in embedded applications. The Synchron API is implemented as a virtual machine - SynchronVM - that is run on the NRF52 and STM32 microcontroller boards. We present programming examples that illustrate the concurrency, I/O and timing capabilities of the VM and provide various benchmarks on the response time, memory and power usage of SynchronVM