The Use of Proof Planning for Cooperative Theorem Proving

AbstractWe 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 ofclam's 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

XQuery for Archivists: Understanding EAD Finding Aids as Data

[Excerpt] XQuery is a simple, yet powerful, scripting language designed to enable users without formal programming training to extract, transform, and manipulate XML data. Moreover, the language is an accepted standard and a W3C recommendation much like its sister standards, XML and XSLT. In other words, XQuery’s raison d’etre coincides perfectly with the needs of today’s archivists. What follows is a brief, pragmatic, overview of XQuery for archivists that will enable archivists with a keen understanding of XML, XPath, and EAD to begin experimenting with manipulating EAD data using XQuery

A techniques-based framework for domain-specific synthesis of simulation models

The formal specification community has produced many languages but few structured design methods. Those which exist tend to be abstract, providing little guidance in tackling problems in particular domains. One way of devising domain -specific design methods is by reconstructing an example in the domain using the target method; then generalising the design structures to cover a class of designs in the domain and finally building an environment in which these structures may more easily be re- applied to new problems. We demonstrate this approach using animal population dynamics models as the domain and Prolog techniques as the target method.We have identified domain -specific techniques which use a parameterisation method from techniques editing but which contain information specific to the population dynamics domain; we define a problem description language which uses concepts from population dynamics; an interface which allows these concepts to be supplied; and provide an automated system which bridges between population dynamics problem description and the domain -specific techniques needed for model generation.TeMS - Techniques -based Model Synthesiser, is the system constructed as the main instrument of our research. Because it is an embodiment of our views on the issues addressed, we submitted TeMS to user evaluation by ecological modelling experts, which produced material for a broad discussion of the system itself, its approach to modelling and its potential uses on the ecological modelling scenario

APT: A principled design for an animated view of program execution for novice programmers

This thesis is concerned with the principled design of a computational environment which depicts an animated view of program execution for novice programmers. We assert that a principled animated view of program execution should benefit novice programmers by: (i) helping students conceptualize what is happening when programs are executed; (ii) simplifying debugging through the presentation of bugs in a manner which the novice will understand; (iii) reducing program development time. The design is based on principles which have been extracted from three areas: (i) the problems that novices encounter when learning a programming language; (ii) the general design principles for computer systems; and (iii) systems which present a view of program execution. The design principles have been embodied in three 'canned stepper displays for Prolog, Lisp and 6502 Assembler. These prototypes, called APT-0 (Animated Program Tracer), demonstrate that the design principles can be broadly applied to procedural and declarative; low and high level languages. Protocol data was collected from subjects using the prototypes in order to check the direction of the research and to suggest improvements in the design. These improvements have been incorporated in a real implementation of APT for Prolog. This principled approach embodied by APT provides two important facilities which have previously not been available, firstly a means of demonstrating dynamic programming concepts such as variable binding, recursion, and backtracking, and secondly a debugging tool which allows novices to step through their own code watching the virtual machine in action. This moves towards simplifying the novice's debugging environment by supplying program execution information in a form that the novice can easily assimilate. An experiment into the misconceptions novices hold concerning the execution of Prolog programs shows that the order of database search, and the concepts of variable binding, unification and backtracking are poorly understood. A further experiment was conducted which looked at the effect that APT had on the ability of novice Prolog programmers to understand the execution of Prolog programs. This demonstrated that the performance of subjects significantly increased after being shown demonstrations of the execution of Prolog programs on APT, while the control group who saw no demonstration showed no improvement. The experimental evidence demonstrates the potential of APT, and the principled approach which it embodies, to communicate run-time information to novice programmers, increasing their understanding of the dynamic aspects of the Prolog interpreter. APT, uses an object centred representation, is built on top of a Prolog interpreter and environment, and is implemented in Common Lisp and Zeta Lisp and runs on the Symbolics 3600 range of machines

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, C Y NTHIA, has been implemented and is due to be tested on st..

Use of proofs-as-programs to build an anology-based functional program editor

This thesis presents a novel application of the technique known as proofs-as-programs. Proofs-as-programs defines a correspondence between proofs in a constructive logic and functional programs. By using this correspondence, a functional program may be represented directly as the proof of a specification and so the program may be analysed within this proof framework. CʸNTHIA is a program editor for the functional language ML which uses proofs-as-programs to analyse users' programs as they are written. So that the user requires no knowledge of proof theory, the underlying proof representation is completely hidden. The proof framework allows programs written in CʸNTHIA to be checked to be syntactically correct, well-typed, well-defined and terminating. CʸNTHIA also embodies the idea of programming by analogy — rather than starting from scratch, users always begin with an existing function definition. They then apply a sequence of high-level editing commands which transform this starting definition into the one required. These commands preserve correctness and also increase programming efficiency by automating commonly occurring steps. The design and implementation of CʸNTHIA is described and its role as a novice programming environment is investigated. Use by experts is possible but only a sub-set of ML is currently supported. Two major trials of CʸNTHIA have shown that CʸNTHIA is well-suited as a teaching tool. Users of CʸNTHIA make fewer programming errors and the feedback facilities of CʸNTHIA mean that it is easier to track down the source of errors when they do occur