Symbolic Manipulators Affect Mathematical Mindsets

Symbolic calculators like Mathematica are becoming more commonplace among upper level physics students. The presence of such a powerful calculator can couple strongly to the type of mathematical reasoning students employ. It does not merely offer a convenient way to perform the computations students would have otherwise wanted to do by hand. This paper presents examples from the work of upper level physics majors where Mathematica plays an active role in focusing and sustaining their thought around calculation. These students still engage in powerful mathematical reasoning while they calculate but struggle because of the narrowed breadth of their thinking. Their reasoning is drawn into local attractors where they look to calculation schemes to resolve questions instead of, for example, mapping the mathematics to the physical system at hand. We model the influence of Mathematica as an integral part of the constant feedback that occurs in how students frame, and hence focus, their work

Structural Separation Logic

This thesis presents structural separation logic, a novel program reasoning approach for software that manipulates both standard heaps and structured data such as lists and trees. Structural separation logic builds upon existing work in both separation logic and context logic. It considers data abstractly, much as it is exposed by library interfaces, ignoring implementation details. We provide a programming language that works over structural heaps, which are similar to standard heaps but allow data to be stored in an abstract form. We introduce abstract heaps, which extend structural heaps to enable local reasoning about abstract data. Such data can be split up with structural addresses. Structural addresses allow sub-data (e.g. a sub-tree within a tree) to be abstractly allocated, promoting the sub-data to an abstract heap cell. This cell can be analysed in isolation, then re-joined with the original data. We show how the tight footprints this allows can be refined further with promises, which enable abstract heap cells to retain information about the context from which they were allocated. We prove that our approach is sound with respect to a standard Hoare logic. We study two large examples. Firstly, we present an axiomatic semantics for the Docu- ment Object Model in structural separation logic. We demonstrate how structural separa- tion logic allows abstract reasoning about the DOM tree using tighter footprints than were possible in previous work. Secondly, we give a novel presentation of the POSIX file system library. We identify a subset of the large POSIX standard that focuses on the file system, including commands that manipulate both the file heap and the directory structure. Axioms for this system are given using structural separation logic. As file system resources are typically identified by paths, we use promises to give tight footprints to commands, so that that they do not require all the resource needed to explain paths being used. We demonstrate our reasoning using a software installer example.Open Acces

Responsibility and the modern corporation

Corporate governance crises as well as human rights issues in global value chains have pushed notions of Corporate Social Responsibility (CSR), Corporate Citizenship (CC), Triple P (People, Planet, Profit) and sustainable development onto the agenda of corporations and into the discussion of corporate governance. However, it has been argued that the CSR debate tends to rest on rather underspecified conceptions of the public corporation and corporate governance

Of Discipline and Civilization: a Roundtable Discussion on the Legacies of Norbert Elias and Michel Foucault

When one considers the proximity of their concerns, it is perhaps surprising that the works of Norbert Elias and Michel Foucault have not been more systematically compared and discussed. However, the differentiation of disciplinary knowledge (particularly the boundary that separates philosophy from social theory), com-pounded by parochialisms fostered by the cult of the intellectual, have delayed this process far past its due. This conversation, which began in 2008 at a conference on the works of Elias and Foucault at the University of Hamburg, is, in this regard, an effort to make up for lost time. Fashioned from hours of discussion recorded on an afternoon at the University of Amsterdam in June 2009, (enriched and clarified by the editor and participants in several rounds of polishing and revision), the discus-sion that follows seeks to draw out conflicts and convergences between the trajecto-ries of thought we know as Eliasian and Foucauldian

The Planned and the Unplanned: A Roundtable Discussion on the Legacies of Michel Foucault and Norbert Elias

When one considers the proximity of their concerns, it is perhaps surprising that the works of Norbert Elias and Michel Foucault have not been more systematically compared and discussed. However, the differentiation of disciplinary knowledge (particularly the boundary that separates philosophy from social theory), com-pounded by parochialisms fostered by the cult of the intellectual, have delayed this process far past its due. This conversation, which began in 2008 at a conference on the works of Elias and Foucault at the University of Hamburg, is, in this regard, an effort to make up for lost time. Fashioned from hours of discussion recorded on an afternoon at the University of Amsterdam in June 2009, (enriched and clarified by the editor and participants in several rounds of polishing and revision), the discus-sion that follows seeks to draw out conflicts and convergences between the trajecto-ries of thought we know as Eliasian and Foucauldian

Staged generic programming

Generic programming libraries such as Scrap Your Boilerplate eliminate the need to write repetitive code, but typically introduce significant performance overheads. This leaves programmers with the regrettable choice between writing succinct but slow programs and writing tedious but efficient programs. Applying structured multi-stage programming techniques transforms Scrap Your Boilerplate from an inefficient library into a typed optimising code generator, bringing its performance in line with hand-written code, and so combining high-level programming with uncompromised performance.</jats:p

The use of data-mining for the automatic formation of tactics

This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques