Lecture Notes on Formal Program Development

This document was originally produced as lecture notes for the MSc and PG course ``Formal Program Development'' early in 1997. After some initial general considerations on this subject the paper focusses on the way one can use Extended ML (EML) for formal program development, which features EML contains and why, and which pitfalls one has to avoid when formally developing ML programs. Usage, features, and pitfalls are all presented through examples

The variable containment problem

The essentially free variables of a term $t$ in some $\lambda$-calculus, FV $_{\beta}(t)$, form the set ($x$ $_{\mid}^{\mid}$ $\forall u.t=_{\beta}u\Rightarrow x$ $\epsilon$ FV$(u)$}. This set is significant once we consider equivalence classes of $\lambda$-terms rather than $\lambda$-terms themselves, as for instance in higher-order rewriting. An important problem for (generalised) higher-order rewrite systems is the variable containment problem: given two terms $t$ and $u$, do we have for all substitutions $\theta$ and contexts $C$[] that FV$_{\beta}(C[t]^{\theta}) \supseteq$ FV$_{\beta}(C[u^{\theta}])$? This property is important when we want to consider $t \to u$ as a rewrite rule and keep $n$-step rewriting decidable. Variable containment is in general not implied by FV $_{\beta} (t)\supseteq$ FV$_{\beta}(u)$. We give a decision procedure for the variable containment problem of the second-order fragment of $\lambda^{\to}$. For full $\lambda^{\to}$ we show the equivalence of variable containment to an open problem in the theory of PCF; this equivalence also shows that the problem is decidable in the third-order case

Maximum-entropy theory of steady-state quantum transport

We develop a theoretical framework for describing steady-state quantum transport phenomena, based on the general maximum-entropy principle of nonequilibrium statistical mechanics. The general form of the many-body density matrix is derived, which contains the invariant part of the current operator that guarantees the nonequilibrium and steady-state character of the ensemble. Several examples of the theory are given, demonstrating the relationship of the present treatment to the widely used scattering-state occupation schemes at the level of the self-consistent single-particle approximation. The latter schemes are shown not to maximize the entropy, except in certain limits

Investigations on the formation of porous membranes during non-solvent induced phase separation

A common method for the production of membranes is immersion precipitation. For this, a polymer is dissolved in a suitable solvent and then precipitated by immersing it into a precipitation bath consisting of a proper non-solvent. Induced by an exchange between the solvent and the non-solvent phase separation occurs, which leads to the formation of a porous structure. The resulting structure allows the selective separation of a mixture of substances, which is based on a size exclusion mechanism. At the moment, the disadvantage of the commonly used solvents for membrane fabrication is their classification as being hazardous for humans and the environment. This is the reason why there is an increased interest in replacing the conventional solvents by less harmful alternatives. However, the challenge is that despite changing the solvent, the membrane properties must still be controllable. In order to ensure the required control of the resulting membrane properties by adjusting the influencing parameters, it is essential that the membrane fabrication process is well understood. In the first part of this work a method for the characterization of the thermodynamics of polymer solution phase equilibria was developed. In course of the validation of this method, it could be shown that the method provides reliable and reproducible data, which in comparison to the previously established method provides a higher information content. Furthermore, the method was applied for the characterization of a polymer solution system, which is commonly used for membrane preparation, and the results were compared to those of the previously used cloud point titration method. In the second part of this work a comparative study on the influences of polymeric additives on the membrane formation process and the resulting membrane properties was conducted. The focus was particularly laid on the comparison between conventional and alternative solvents in order to allow a substitution of hazardous solvents through less harmful alternatives. It could be shown that there are differences in the observed effects in dependence of the applied solvent. However, it could also be demonstrated that the gained mechanistic understanding can be used for adjusting the membrane preparation process, so that the properties of the fabricated membranes remain controllable. The third part of this work also focused on the influence of variations during the immersion precipitation process using different solvents. In order to obtain an overall picture of the influencing factors on membrane formation, the effects of non-solvent additives in the solution, of variations in the polymer concentration and of altered precipitation conditions were investigated. It could be shown that all three factors have an influence on the characteristics of the fabricated membranes in the investigated solvent systems. In addition, it was repeatedly demonstrated that the choice of the solvent is of high importance for the manifestation of the respective effects

The concept ‘half’ in Selkup language

The theoretical frame of this article is the field of cognitive linguistics. The past decades have witnessed a progressive increase in writings on cognitive structures. A special focus is laid thereby on concepts, which are considered as mental organisational units reflecting the external world. With the help of concepts, humans organise their perceptions and experiences in order to be able to understand and act. This paper explores a concrete mental organisational unit – the concept ‘half’ – in Selkup language. In the last decades, some works were published concentrating on concepts in Selkup language and culture, like ‘space’ (Polyakova 2006). {PARAGRAPH} The concept ‘half’ is a fundamental cognitive organisational unit, based on dividing, partitioning and subdividing things, like splitting an apple, a fish or a log of wood, with a knife or an axe in two halves. The examined material consists of four words with the meaning ‘half’, extracted from various dictionaries, and approximately 35 sentences, extracted from two Selkup language corpora, in which these words are used. Due to the semantic connotations and the utilization of the word in certain contexts I propose six conceptual domains (division of things into two halves, transversal/horizontal division of things into two halves, longitudinal division of things into two halves, division of locations into two halves, division of time into two halves and division of paired entities), which are analysed in regard of their lexical representation. The paper has the following structure: after a brief introduction, the material and method are presented. The main section deals with the analysis of the six conceptual domains. At the end of each domain, I will analyse the linguistic representation and the main features of the objects belonging to this sphere. The findings are summarized in the final section. The analysis of the concept ‘half’ in Selkup shows that this mental unit of organisation has a complex structure. Some domains are represented linguistically homogenous (e.g. division of things into two halves and division of paired entities), whereas other domains are expressed linguistically by more than one word (e.g. division of location or time in two halves). Sometimes this incoherent linguistic representation is caused by dialect differences or the fact that all word meaning ‘half’ in Selkup are polysemous and the different meanings might eventually interfere

Modularity of Convergence and Strong Convergence in Infinitary Rewriting

Properties of Term Rewriting Systems are called modular iff they are preserved under (and reflected by) disjoint union, i.e. when combining two Term Rewriting Systems with disjoint signatures. Convergence is the property of Infinitary Term Rewriting Systems that all reduction sequences converge to a limit. Strong Convergence requires in addition that redex positions in a reduction sequence move arbitrarily deep. In this paper it is shown that both Convergence and Strong Convergence are modular properties of non-collapsing Infinitary Term Rewriting Systems, provided (for convergence) that the term metrics are granular. This generalises known modularity results beyond metric \infty

Teachers’ views on collaborating in multi-campus course cluster for engineering students

At a European multi-campus university, parallel study programmes offered at every campus (e.g. engineering studies) and appurtenant courses are coordinated, to ensure similar quality and systematic development. In this paper, we present a case from such a multi-campus course, consisting of a cluster of basic courses in physics and chemistry for first-year engineering students. These courses are coordinated through identical syllabus and assessment practice but are taught locally at each campus. The authors had noted some frustration among the teachers involved in these courses, and were interested to investigate the reasons for this frustration, and ultimately to inform the development of these multi-campus courses. This project emerged from a realisation that literature on multi-campus courses is often associated with distance learning, while in this case, the actual teaching is provided locally. Concepts associated with teacher collaboration, such as collaborative culture versus contrived collegiality, collective versus fragmented collaboration, and depth of collaboration seem like a viable way forward in understanding the dynamics between teachers in a context like this. In this paper, we present early results from this ongoing project, which include interviews of teachers involved in these physics/chemistry courses. Preliminary results from these interviews suggest that the expressed frustrations stem from contrived collegiality. Although the teachers experience sufficient freedom in terms of choosing their own teaching methods, several teachers raise concerns about the lack of common aims for this course cluster, which reduces collaboration to coordination of mere practical tasks

Non-omega-overlapping TRSs are UN

This paper solves problem #79 of RTA’s list of open problems [14] — in the positive. If the rules of a TRS do not overlap w.r.t. substitutions of infinite terms then the TRS has unique normal forms. We solve the problem by reducing the problem to one of consistency for “similar” constructor term rewriting systems. For this we introduce a new proof technique. We define a relation ⇓ that is consistent by construction, and which — if transitive — would coincide with the rewrite system’s equivalence relation =R. We then prove the transitivity of ⇓ by coalgebraic reasoning. Any concrete proof for instances of this relation only refers to terms of some finite coalgebra, and we then construct an equivalence relation on that coalgebra which coincides with ⇓