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Our research interests in this project are in exploring how automated reasoning systems can learn theorem proving strategies. In particular, we are looking into how a proof planning system (Bundy, 1988) can automatically learn

Abstract. In this paper we present a framework for automatedlearning within mathematical reasoning systems. In particular, this framework enables proof planning systems to automatically learnnew proof methods from well chosen examples of proofs which use a similar reasoning pattern to prove related theorems. Our frameworkconsists of a representation formalism for methods and a machine learning technique which can learn methods using this representationformalism. We present the implementation of this framework within the \Omega MEGA proof planning system, and some experiments we ran onthis implementation to evaluate the validity of our approach.

In recent years several computational systems and techniques for theorem proving by analogy have been developed. The obvious practical question, however, as to whether and when to use analogy has been neglected badly in these developments. This paper addresses this question, identifies situations where analogy is useful, and discusses the merits of theorem proving by analogy in these situations. The results can be generalized to other domains.

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Abstract: This article analyzes the current state of case-based plan adaptation research. Rather than perform an exhaustive literature review, we identify six dimensions to classify the various contributions in the field and to analyze current issues and trends. These dimensions are: the type of adaptation, the role of the case, the case content, the use of case merging, the representation formalism, and the computational complexity of the algorithm. Our analysis clarifies some common misconceptions about plan adaptation and proposes a set of future research directions. 1.

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...

Abstract. We discuss several problems of analogy-driven proof plan construction which prevent a solution for more di�cult target problems or make a solution very expensive. Some of these problems are due to the previously assumed �xed order of matching, reformulation, and replay in case-based reasoning and from a too restricted combination of planning from �rst principles with the analogy process. In order to overcome these problems we suggest to interleave matching and replay aswell as casebased planning with planning from �rst principles. Secondly, the restricted mixture of case-based planning and planning from �rst principles in previous systems is generalised to intelligently employing di�erent planning strategies with the objective to solve more problems at all and to solve problems more e�ciently. 1

In type-theory based proof systems that provide inductive structures, computation tools are automatically associated to inductive de nitions. Choosing a particular representation for a given concept has a strong inuence on proof structure. We propose a method to make the change from one representation to another easier, by systematically translating proofs from one context to another. We show how this method works by using it on natural numbers, for which a unary representation (based on Peano axioms) and a binary representation are available. This method leads to an automatic translation tool that we have implemented in Coq and successfully applied to several arithmetical theorems.

The REBOUND adaptation framework organizes a collection of adaptation tactics in a way that they can be selected based on the components available for adaptation. Adaptation tactics are specified formally in terms of the relationship between the component to be adapted and the resulting adapted component. The tactic specifications are used as matching conditions for specification-based component retrieval, creating a ``retrieval for adaptation' ' scenario. The results of specification matching are used to guide component adaptation. Several examples illustrate how the framework guides component and tactic selection and how basic tactics are composed to form more powerful tactics.