Theory and Practice of Higher-type Computation (Tutorial)

In higher-type computation, established by Kleene and Kreisel in the late 1950\u27s (independently), one works with the data types obtained from the discrete natural numbers by closing under finite products and function spaces. For the theory of higher-type programming languages, it is natural to work with a corresponding hierarchy, or type structure, of domains, identified by Ershov and Scott in the late 1960\u27s (again independently). The Kleene-Kreisel and Ershov-Scott hierarchies account for total and partial computation respectively. In this tutorial I\u27ll explain the theory and practice of higher-type computation and programming languages, and develop old and new applications. From a theoretical point of view, I\u27ll present Kleene-Kreisel spaces and Ershov-Scott domains, and relate the two. Moreover, I\u27ll discuss common generalizations, chiefly QCB spaces and equilogical spaces, which admit further useful closure properties, and their relationship to TTE (Schroeder, Simpson. Scott, Bauer, Weihrauch and many others). I\u27ll also present a natural higher-type model of computation/programming language, namely PCF (Platek, Scott, Plotkin). From a practical point of view, I\u27ll introduce a fragment of the language Haskell as a faithful implementation of PCF. Moreover, I\u27ll develop and run several examples (and prove theorems about them), pertaining to (i) exhaustive search of infinite sets in finite time in particular Ulrich Berger\u27s algorithm and generalizations), and (ii) computation with real numbers (in particular Alex Simpson\u27s integration algorithm and generalizations)

Logic programming in the context of multiparadigm programming: the Oz experience

Oz is a multiparadigm language that supports logic programming as one of its major paradigms. A multiparadigm language is designed to support different programming paradigms (logic, functional, constraint, object-oriented, sequential, concurrent, etc.) with equal ease. This article has two goals: to give a tutorial of logic programming in Oz and to show how logic programming fits naturally into the wider context of multiparadigm programming. Our experience shows that there are two classes of problems, which we call algorithmic and search problems, for which logic programming can help formulate practical solutions. Algorithmic problems have known efficient algorithms. Search problems do not have known efficient algorithms but can be solved with search. The Oz support for logic programming targets these two problem classes specifically, using the concepts needed for each. This is in contrast to the Prolog approach, which targets both classes with one set of concepts, which results in less than optimal support for each class. To explain the essential difference between algorithmic and search programs, we define the Oz execution model. This model subsumes both concurrent logic programming (committed-choice-style) and search-based logic programming (Prolog-style). Instead of Horn clause syntax, Oz has a simple, fully compositional, higher-order syntax that accommodates the abilities of the language. We conclude with lessons learned from this work, a brief history of Oz, and many entry points into the Oz literature.Comment: 48 pages, to appear in the journal "Theory and Practice of Logic Programming

A tutorial on cue combination and Signal Detection Theory: Using changes in sensitivity to evaluate how observers integrate sensory information

Many sensory inputs contain multiple sources of information (‘cues’), such as two sounds of different frequencies, or a voice heard in unison with moving lips. Often, each cue provides a separate estimate of the same physical attribute, such as the size or location of an object. An ideal observer can exploit such redundant sensory information to improve the accuracy of their perceptual judgments. For example, if each cue is modeled as an independent, Gaussian, random variable, then combining Ncues should provide up to a √N improvement in detection/discrimination sensitivity. Alternatively, a less efficient observer may base their decision on only a subset of the available information, and so gain little or no benefit from having access to multiple sources of information. Here we use Signal Detection Theory to formulate and compare various models of cue-combination, many of which are commonly used to explain empirical data. We alert the reader to the key assumptions inherent in each model, and provide formulas for deriving quantitative predictions. Code is also provided for simulating each model, allowing expected levels of measurement error to be quantified. Based on these results, it is shown that predicted sensitivity often differs surprisingly little between qualitatively distinct models of combination. This means that sensitivity alone is not sufficient for understanding decision efficiency, and the implications of this are discussed

Contemporary developments in teaching and learning introductory programming: Towards a research proposal

The teaching and learning of introductory programming in tertiary institutions is problematic. Failure rates are high and the inability of students to complete small programming tasks at the completion of introductory units is not unusual. The literature on teaching programming contains many examples of changes in teaching strategies and curricula that have been implemented in an effort to reduce failure rates. This paper analyses contemporary research into the area, and summarises developments in the teaching of introductory programming. It also focuses on areas for future research which will potentially lead to improvements in both the teaching and learning of introductory programming. A graphical representation of the issues from the literature that are covered in the document is provided in the introduction