Verifying Monadic Second-Order Properties of Graph Programs

The core challenge in a Hoare- or Dijkstra-style proof system for graph programs is in defining a weakest liberal precondition construction with respect to a rule and a postcondition. Previous work addressing this has focused on assertion languages for first-order properties, which are unable to express important global properties of graphs such as acyclicity, connectedness, or existence of paths. In this paper, we extend the nested graph conditions of Habel, Pennemann, and Rensink to make them equivalently expressive to monadic second-order logic on graphs. We present a weakest liberal precondition construction for these assertions, and demonstrate its use in verifying non-local correctness specifications of graph programs in the sense of Habel et al.Comment: Extended version of a paper to appear at ICGT 201

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

Machine Assisted Proof of ARMv7 Instruction Level Isolation Properties

In this paper, we formally verify security properties of the ARMv7 Instruction Set Architecture (ISA) for user mode executions. To obtain guarantees that arbitrary (and unknown) user processes are able to run isolated from privileged software and other user processes, instruction level noninterference and integrity properties are provided, along with proofs that transitions to privileged modes can only occur in a controlled manner. This work establishes a main requirement for operating system and hypervisor verification, as demonstrated for the PROSPER separation kernel. The proof is performed in the HOL4 theorem prover, taking the Cambridge model of ARM as basis. To this end, a proof tool has been developed, which assists the verification of relational state predicates semi-automatically

What Does Aspect-Oriented Programming Mean for Functional Programmers?

Aspect-Oriented Programming (AOP) aims at modularising crosscutting concerns that show up in software. The success of AOP has been almost viral and nearly all areas in Software Engineering and Programming Languages have become "infected" by the AOP bug in one way or another. Interestingly the functional programming community (and, in particular, the pure functional programming community) seems to be resistant to the pandemic. The goal of this paper is to debate the possible causes of the functional programming community's resistance and to raise awareness and interest by showcasing the benefits that could be gained from having a functional AOP language. At the same time, we identify the main challenges and explore the possible design-space

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

Modularity in Meta-Languages

A meta-language for semantics has a high degree of modularitywhen descriptions of individual language constructs can be formulated independently using it, and do not require reformulation when new constructs are added to the described language. The quest for modularity in semantic meta-languages has been going on for more than two decades. Here, most of the main meta-languages for operational, denotational, and hybrid styles of semantics are compared regarding their modularity. A simple bench-mark is used: describing the semantics of a pure functional language, then extending the described language with references, exceptions, and concurrency constructs. For each style of semantics, at least one of the considered meta-languages appears to provide a high degree of modularity