A Theory of Tagged Objects

Foundational models of object-oriented constructs typically model objects as records with a structural type. However, many object-oriented languages are class-based; statically-typed formal models of these languages tend to sacrifice the foundational nature of the record-based models, and in addition cannot express dynamic class loading or creation. In this paper, we explore how to model statically-typed object-oriented languages that support dynamic class creation using foundational constructs of type theory. We start with an extensible tag construct motivated by type theory, and adapt it to support static reasoning about class hierarchy and the tags supported by each object. The result is a model that better explains the relationship between object-oriented and functional programming paradigms, suggests a useful enhancement to functional programming languages, and paves the way for more expressive statically typed object-oriented languages. In that vein, we describe the design and implementation of the Wyvern language, which leverages our theory

A Theory of Tagged Objects (Artifact)

A compiler and interpreter for Wyvern programming language written in Java and hosted on http://github.com/wyvernlang/wyvern and some sample programs (.wyv) including the main example from the paper in borderedwindow.wyv. We also include an extract of all the unit tests of which a large number may be designed to fail -- therefore they are best run using JUnit which can be done by checking out the source tree from the GitHub project link above

Location-based and contextual mobile learning. A STELLAR Small-Scale Study

This study starts from several inputs that the partners have collected from previous and current running research projects and a workshop organised at the STELLAR Alpine Rendevous 2010. In the study, several steps have been taken, firstly a literature review and analysis of existing systems; secondly, mobile learning experts have been involved in a concept mapping study to identify the main challenges that can be solved via mobile learning; and thirdly, an identification of educational patterns based on these examples has been done. Out of this study the partners aim to develop an educational framework for contextual learning as a unifying approach in the field. Therefore one of our central research questions is: how can we investigate, theorise, model and support contextual learning

Ice quivers with potential arising from once-punctured polygons and Cohen-Macaulay modules

Given a tagged triangulation of a once-punctured polygon $P^*$ with $n$ vertices, we associate an ice quiver with potential such that the frozen part of the associated frozen Jacobian algebra has the structure of a Gorenstein $K[X]$-order $\Lambda$. Then we show that the stable category of the category of Cohen-Macaulay $\Lambda$-modules is equivalent to the cluster category $\mathcal{C}$ of type $D_n$. It gives a natural interpretation of the usual indexation of cluster tilting objects of $\mathcal{C}$ by tagged triangulations of $P^*$. Moreover, it extends naturally the triangulated categorification by $\mathcal{C}$ of the cluster algebra of type $D_n$ to an exact categorification by adding coefficients corresponding to the sides of $P$. Finally, we lift the previous equivalence of categories to an equivalence between the stable category of graded Cohen-Macaulay $\Lambda$-modules and the bounded derived category of modules over a path algebra of type $D_n$.Comment: 50 pages. Several improvements after refereeing. arXiv admin note: text overlap with arXiv:1307.067