Lightweight Formal Verification in Classroom Instruction of Reasoning about Functional Code

In college courses dealing with material that requires mathematical rigor, the adoption of a machine-readable representation for formal arguments can be advantageous. Students can focus on a specific collection of constructs that are represented consistently. Examples and counterexamples can be evaluated. Assignments can be assembled and checked with the help of an automated formal reasoning system. However, usability and accessibility do not have a high priority and are not addressed sufficiently well in the design of many existing machine-readable representations and corresponding formal reasoning systems. In earlier work [Lap09], we attempt to address this broad problem by proposing several specific design criteria organized around the notion of a natural context: the sphere of awareness a working human user maintains of the relevant constructs, arguments, experiences, and background materials necessary to accomplish the task at hand. We report on our attempt to evaluate our proposed design criteria by deploying within the classroom a lightweight formal verification system designed according to these criteria. The lightweight formal verification system was used within the instruction of a common application of formal reasoning: proving by induction formal propositions about functional code. We present all of the formal reasoning examples and assignments considered during this deployment, most of which are drawn directly from an introductory text on functional programming. We demonstrate how the design of the system improves the effectiveness and understandability of the examples, and how it aids in the instruction of basic formal reasoning techniques. We make brief remarks about the practical and administrative implications of the system’s design from the perspectives of the student, the instructor, and the grader.

Reasoning about trust, entrepreneurial services, and the virtual team

This Portfolio of Exploration (PoE) tracks a transformative learning developmental journey that is directed at changing meaning making structures and mental models within an innovation practice. The explicit purpose of the Portfolio is to develop new and different perspectives that enable the handling of new and more complex phenomena through self transformation and increased emotional intelligence development. The Portfolio provides a response to the question: ‘What are the key determinants that enable a Virtual Team (VT) to flourish where flourishing means developing and delivering on the firm’s innovative imperatives?’ Furthermore, the PoE is structured as an investigation into how higher order meaning making promotes ‘entrepreneurial services’ within an intra-firm virtual team, with a secondary aim to identify how reasoning about trust influence KGPs to exchange knowledge. I have developed a framework which specifically focuses on the effectiveness of any firms’ Virtual Team (VT) through transforming the meaning making of the VT participants. I hypothesized it is the way KGPs make meaning (reasoning about trust) which differentiates the firm as a growing firm in the sense of Penrosean resources: ‘inducement to expand and a limit of expansion’ (1959). Reasoning about trust is used as a higher order meaning-making concept in line with Kegan’s (1994) conception of complex meaning making, which is the combining of ideas and data in ways that transform meaning and implicates participants to find new ways of knowledge generation. Simply, it is the VT participants who develop higher order meaning making that hold the capabilities to transform the firm from within, providing a unique competitive advantage that enables the firm to grow.

Searching and planning: Young children's reasoning about past and future event sequences

Six experiments examined children's ability to make inferences using temporal order information. Children completed versions of a task involving a toy zoo; one version required reasoning about past events (search task) and the other required reasoning about future events (planning task). Children younger than 5 years failed both the search and the planning tasks, whereas 5-year-olds passed both (Experiments 1 and 2). However, when the number of events in the sequence was reduced (Experiment 3), 4-year-olds were successful on the search task but not the planning task. Planning difficulties persisted even when relevant cues were provided (Experiments 4 and 5). Experiment 6 showed that improved performance on the search task found in Experiment 3 was not due to the removal of response ambiguity.

Young children's reasoning about the order of past events

Four studies are reported that employed an object location task to assess temporal-causal reasoning. In Experiments 1-3, successfully locating the object required a retrospective consideration of the order in which two events had occurred. In Experiment 1, 5- but not 4-year-olds were successful; 4-year-olds also failed to perform at above-chance levels in modified versions of the task in Experiments 2 and 3. However, in Experiment 4, 3-year-olds were successful when they were able to see the object being placed first in one location and then in the other, rather than having to consider retrospectively the sequence in which two events had happened. The results suggest that reasoning about the causal significance of the temporal order of events may not be fully developed before 5 years. (C) 2007 Elsevier Inc. All rights reserved.

Reasoning about orchestrations of web services using partial correctness

A service is a remote computational facility which is made available for general use by means of a wide-area network. Several types of service arise in practice: stateless services, shared state services and services with states which are customised for individual users. A service-based orchestration is a multi-threaded computation which invokes remote services in order to deliver results back to a user (publication). In this paper a means of specifying services and reasoning about the correctness of orchestrations over stateless services is presented. As web services are potentially unreliable the termination of even finite orchestrations cannot be guaranteed. For this reason a partial-correctness powerdomain approach is proposed to capture the semantics of recursive orchestrations.

Children’s Reasoning About the Temporal Order of Past and Future Events

Four- and five-year-olds completed two sets of tasks that involved reasoning about the temporal order in which events had occurred in the past or were to occur in the future. Four-year-olds succeeded on the tasks that involved reasoning about the order of past events but not those that involved reasoning about the order of future events, whereas 5-year-olds passed both types of tasks. Individual children who failed the past-event tasks were not particularly likely to fail the more difficult future-event tasks. However, children's performance on the reasoning tasks was predictive of their performance on a task assessing their comprehension of the terms “before” and “after.” Our results suggest that there may be a developmental change over this age range in the ability to flexibly represent and reason about the before-and-after relationships between events.

A Framework for Prototyping and Reasoning about Distributed Systems

A framework supporting fast prototyping as well as tuning of distributed applications is presented. The approach is based on the adoption of a formal model that is used to describe the orchestration of distributed applications. The formal model (Orc by Misra and Cook) can be used to support semi-formal reasoning about the applications at hand. The paper describes how the framework can be used to derive and evaluate alternative orchestrations of a well know parallel/distributed computation pattern; and shows how the same formal model can be used to support generation of prototypes of distributed applications skeletons directly from the application description.

Adding metadata to Orc to support reasoning about grid programs

Following earlier work demonstrating the utility of Orc as a means of specifying and reasoning about grid applications we propose the enhancement of such specifications with metadata that provide a means to extend an Orc specification with implementation oriented information. We argue that such specifications provide a useful refinement step in allowing reasoning about implementation related issues ahead of actual implementation or even prototyping. As examples, we demonstrate how such extended specifications can be used for investigating security related issues and for evaluating the cost of handling grid resource faults. The approach emphasises a semi-formal style of reasoning that makes maximum use of programmer domain knowledge and experience.

Children’s essentialist reasoning about language and race

Across four studies, we directly compared children’s essentialist reasoning about the stability of race and language throughout an individual’s lifespan. Monolingual English-speaking children were presented with a series of images of children who were either White or Black; each face was paired with a voice clip in either English or French. Participants were asked which of two adults each target child would grow up to be – one who was a ‘match’ to the target child in race but not language, and the other a ‘match’ in language but not race. Nine- to 10-year-old European American children chose the race-match, rather than the language-match. In contrast, 5–6-year-old European American children in both urban, racially diverse, and rural, racially homogeneous environments chose the language-match, even though this necessarily meant that the target child would transform racial categories. Although surprising in light of adult reasoning, these young children demonstrated an intuition about the relative stability of an individual’s language compared to her racial group membership. Yet, 5–6-year-old African American children, similar to the older European American children, chose the race-match, suggesting that membership in a racial minority group may highlight children’s reasoning about race as a stable category. Theoretical implications for our understanding of children’s categorization of human kinds are discussed.