João F. Ferreira

JaSkel: a Java skeleton-based framework for structured cluster and grid computing

This paper presents JaSkel, a skeleton-based framework to develop parallel and grid applications. The framework provides a set of Java abstract classes as a skeleton catalogue, which implements recurring parallel interaction paradigms. This approach aims to improve code efficiency and portability. It also helps to structure scalable applications through the refinement and composition of skeletons. Evaluation results show that using the provided skeletons do contribute to improve both application development time and execution performance.

Automated verification of the FreeRTOS scheduler in Hip/Sleek

Automated verification of operating system kernels is a challenging problem, partly due to the use of shared mutable data structures. In this paper, we show how we can automatically verify memory safety and functional correctness properties of the task scheduler component of the FreeRTOS kernel using the verification system Hip/Sleek. We show how some of Hip/Sleek features such as user-defined predicates and lemmas make the specifications highly expressive and the verification process viable. To the best of our knowledge, this is the first code-level verification of memory safety and functional correctness properties of the FreeRTOS scheduler. The outcome of our experiment confirms that Hip/Sleek can indeed be used to verify code that is used in production. Moreover, since the properties that we verify are quite general, we envisage that the same approach can be adopted to verify components of other operating systems.

On Euclid's algorithm and elementary number theory

Algorithms can be used to prove and to discover new theorems. This paper shows how algorithmic skills in general, and the notion of invariance in particular, can be used to derive many results from Euclids algorithm. We illustrate how to use the algorithm as a verification interface (i.e., how to verify theorems) and as a construction interface (i.e., how to investigate and derive new theorems). The theorems that we verify are well-known and most of them are included in standard number-theory books. The new results concern distributivity properties of the greatest common divisor and a new algorithm for efficiently enumerating the positive rationals in two different ways. One way is known and is due to Moshe Newman. The second is new and corresponds to a deforestation of the Stern-Brocot tree of rationals. We show that both enumerations stem from the same simple algorithm. In this way, we construct a Stern-Brocot enumeration algorithm with the same time and space complexity as Newmans algorithm. A short review of the original papers by Stern and Brocot is also included.

Logic training through algorithmic problem solving

Although much of mathematics is algorithmic in nature, the skills needed to formulate and solve algorithmic problems do not form an integral part of mathematics education. In particular, logic, which is central to algorithm development, is rarely taught explicitly at preuniversity level, under the justification that it is implicit in mathematics and therefore does not need to be taught as an independent topic. This paper argues in the opposite direction, describing a one-week workshop done at the University of Minho, in Portugal, whose goal was to introduce to high-school students calculational principles and techniques of algorithmic problem solving supported by calculational logic. The workshop resorted to recreational problems to convey the principles and to software tools, the Alloy Analyzer and Netlogo, to animate models.

Which Mathematics for the Information Society

MathIS is a new project that aims to reinvigorate secondary-school mathematics by exploiting insights of the dynamics of algorithmic problem solving. This paper describes the main ideas that underpin the project. In summary, we propose a central role for formal logic, the development of a calculational style of reasoning, the emphasis on the algorithmic nature of mathematics, and the promotion of self-discovery by the students. These ideas are discussed and the case is made, through a number of examples that show the teaching style that we want to introduce, for their relevance in shaping mathematics training for the years to come. In our opinion, the education of software engineers that work effectively with formal methods and mathematical abstractions should start before university and would benefit from the ideas discussed here.

Reasoning about Fences and Relaxed Atomics

For efficiency reasons, weak (or relaxed) memory is now the norm on modern architectures. To cater for this trend, modern programming languages are adapting their memory models. The new C11 memory model [1] allows several levels of memory weakening, including non-atomics, relaxed atomics, release-acquire atomics, and sequentially consistent atomics. Under such weak memory models, multithreaded programs exhibit more behaviours, some of which would have been inconsistent under the traditional strong (i.e. sequentially consistent) memory model. This makes the task of reasoning about concurrent programs even more challenging. The GPS framework, recently developed by Turon et al.[22], has made a step forward towards tackling this challenge. By integrating ghost states, per-location protocols and separation logic, GPS can successfully verify programs with release-acquire atomics. In this paper, we present a program logic, an enhancement of the GPS framework, that can support the verification of a bigger class of C11 programs, that is, programs with release-acquire atomics, relaxed atomics and release-acquire fences. Key elements of our proposed logic include two new types of assertions, a more expressive resource model and a set of newly-designed verification rules.

Recounting the Rationals: Twice!

We derive an algorithm that enables the rationals to be efficiently enumerated in two different ways. One way is known and is credited to Moshe Newman; it corresponds to a deforestation of the so-called Calkin-Wilf tree of rationals. The second is new and corresponds to a deforestation of the Stern-Brocot tree of rationals. We show that both enumerations stem from the same simple algorithm. In this way, we construct a Stern-Brocot enumeration algorithm with the same time and space complexity as Newmans algorithm.

Structure Editing of Handwritten Mathematics: Improving the Computer Support for the Calculational Method

We present a structure editor that aims to facilitate the presentation and manipulation of handwritten mathematical expressions. The editor is oriented to the calculational mathematics involved in algorithmic problem solving and it provides features that allow reliable structure manipulation of mathematical formulae, as well as flexible and interactive presentations. We describe some of its most important features, including the use of gestures to manipulate algebraic formulae, the structured selection of expressions, definition and redefinition of operators in runtime, gestures editor, and handwritten templates. The editor is made available in the form of a C# class library which can be easily used to extend existing tools. For example, we have extended Classroom Presenter, a tool for ink-based teaching presentations and classroom interaction. We have tested and evaluated the editor with target users. The results obtained seem to indicate that the software is usable, suitable for its purpose and a valuable contribution to teaching and learning algorithmic problem solving.

Linear Logic Programming for Narrative Generation

In this paper, we explore the use of Linear Logic programming for story generation. We use the language Celf to represent narrative knowledge, and its own querying mechanism to generate story instances, through a number of proof terms. Each proof term obtained is used, through a resource-flow analysis, to build a directed graph where nodes are narrative actions and edges represent inferred causality relationships. Such graphs represent narrative plots structured by narrative causality. This approach is a candidate technique for narrative generation which unifies declarative representations and generation via query and deduction mechanisms.

Automated Verification of the FreeRTOS Scheduler in HIP/SLEEK

Automated verification of operating system kernels is a challenging problem, partly due to the use of shared mutable data structures. In this paper, we show how we can automatically verify memory safety and functional correctness of the task scheduler component of the Free RTOS kernel using the verification system Hip Sleek. We show how some of Hip Sleek features like user-defined predicates and lemmas make the specifications highly expressive and the verification process viable. To the best of our knowledge, this is the first code-level verification of memory safety and functional correctness properties of the Free RTOS scheduler. The outcome of our experiment confirms that Hip Sleek can indeed be used to verify code that is used in production. Moreover, since the properties that we verify are quite general, we envisage that the same approach can be adopted to verify the scheduler of other operating systems.