Helen Lowe

An Editor for Helping Novices to Learn Standard ML

This paper describes a novel editor intended as an aid in the learning of the functional programming language Standard ML. A common technique used by novices is programming by analogy whereby students refer to similar programs that they have written before or have seen in the course literature and use these programs as a basis to write a new program. We present a novel editor for ML which supports programming by analogy by providing a collection of editing commands that transform old programs into new ones. Each command makes changes to an isolated part of the program. These changes are propagated to the rest of the program using analogical techniques. We observed a group of novice ML students to determine the most common programming errors in learning ML and restrict our editor such that it is impossible to commit these errors. In this way, students encounter fewer bugs and so their rate of learning increases. Our editor, CYNTHIA, has been implemented and is due to be tested on students of ML from September, 1997.

XBarnacle: Making Theorem Provers More Accessible

XBarnacle provides: 1. An extension to the capabilities of CLAM, as not all theorems may be proved automatically, even with the provision of lemmas. 2. A more useable version of CLAM, with potential to extend its user base. 3. A tool for experimenting with different methods and heuristics.

Proof planning for maintainable configuration systems

Configuration is a complex task generally involving varying measures of constraint satisfaction, optimization, and the management of soft constraints. Although many successful systems have been developed, these are often difficult to maintain and to generalize in rapidly changing domains. In this paper, we consider building intelligent knowledge-based systems with maintainability well to the fore in our requirements for such systems. We introduce two case studies: the initial proof of concept, which was in the domain of computer configuration, and a further field-tested study, the configuration of compressors. Central to our approach is the use of the proof planning technique, and the clean separation of different kinds of knowledge: factual, heuristic, and strategic.

An ML editor based on proofs-as-programs

C/sup Y/NTHIA is a novel editor for the functional programming language ML in which each function definition is represented as the proof of a simple specification. Users of C/sup Y/NTHIA edit programs by applying sequences of high-level editing commands to existing programs. These commands make changes to the proof representation from which a new program is then extracted. The use of proofs is a sound framework for analysing ML programs and giving useful feedback about errors. Amongst the properties analysed within C/sup Y/NTHIA at present is termination. C/sup Y/NTHIA has been successfully used in the teaching of ML in two courses at Napier University, Scotland. C/sup Y/NTHIA is a convincing, real-world application of the proofs-as-programs idea.

The Use of Proof Planning for Co-operative Theorem Proving

We describebarnacle: a co-operative interface to theclaminductive theorem proving system. For the foreseeable future, there will be theorems which cannot be proved completely automatically, so the ability to allow human intervention is desirable; for this intervention to be productive the problem of orienting the user in the proof attempt must be overcome. There are many semi-automatic theorem provers: we call our style of theorem provingco-operative, in that the skills of both human and automaton are used each to their best advantage, and used together may find a proof where other methods fail. The co-operative nature of thebarnacleinterface is made possible by the proof planning technique underpinningclam. Our claim is that proof planning makes new kinds of user interaction possible.Proof planning is a technique for guiding the search for a proof in automatic theorem proving. Common patterns of reasoning in proofs are identified and represented computationally as proof plans, which can then be used to guide the search for proofs of new conjectures. We have harnessed the explanatory power of proof planning to enable the user to understand where the automatic prover got to and why it is stuck. A user can analyse the failed proof in terms ofclams specification language, and hence override the prover to force or prevent the application of a tactic, or discover a proof patch. This patch might be to apply further rules or tactics to bridge the gap between the effects of previous tactics and the preconditions needed by a currently inapplicable tactic.

Proof planning: A methodology for developing AI systems incorporating design issues

In cases where a domain theory can be successfully expressed in a logical formalism and can be used to formulate a task in that domain in mathematical terms, the task of building sound knowledge-based systems is greatly facilitated. However, it is not immediately obvious how the design aspects of such tasks, where these are an important feature of problem solving, can be incorporated in this approach. Design issues differ from search problems in that there may be several choices, each valid in some sense, but not (necessarily) equally good or equally appropriate in the current context. A case study is described in which a methodology is used based on the development of proof plans. The ability to conduct research according to the Popperian framework of hypothesis, validation, testing, and modification in response to empirical evidence —the hypothetico-deductive approach — seems essential to any rigorous scientific endeavor. It is believed that proof planning is a method which readily exploits this inherently incrementalist approach and could prove to be a powerful tool in designing AI systems.

System Description: Interactive Proof Critics in XBarnacle

Proof critics [2] extend the power of a theorem prover by, for example, allowing lemmas to be postulated and proved in the course of a proof. However, extending the automated theorem prover CLAM by adding critics also increases the search space. XBarnacle [5] was developed to make the process of interacting with a semi-automatic theorem prover more tractable for the non-expert user. We have now substantially amplified and extended XBarnacle so that it makes the work of expert users more efficient as they interact with proof critics. Of course, we have also made cosmetic improvements to aid navigability and to bridge the gulf of evaluation [1] which proves such an obstacle in making theorem provers more accessible, and even their expert users more efficient.

System Description: CyNTHIA

Current programming environments for novice functional programming (FP) are inadequate. This paper describes ways of using proofs as a foundation to improve the situation, in the context of the language ML [4]. The most common way to write ML programs is via a text editor and compiler (such as the Standard ML of New Jersey compiler). But program errors, in particular type errors, are generally difficult to track down. For novices, the lack of debugging support forms a barrier to learning FP concepts [5].