The generic proof assistant Isabelle provides a landscape of specification contexts that is considerably richer than that of most other provers. Theories are the level of specification where object-logics are axiomatised. Isabelle’s proof language Isar enables local exploration in contexts generated in the course of natural deduction proofs. Finally, locales, which may be seen as detached proof contexts, offer an intermediate level of specification geared towards reuse. All three kinds of contexts are structured, to different extents. We analyse the “topology ” of Isabelle’s landscape of specification contexts, by means of development graphs, in order to establish what kinds of reuse are possible.

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In this paper we sketch the outline and the underlying theoretical framework for a general repository to maintain mathematical or logic-based documents while keeping track of the various semantical dependencies between different parts of various types of documents (documentations, specifications, proofs, etc). The sketched approach is a generalization of the notion of development graphs (as implemented in the MAYA-system) used to maintain formal software developments. We isolate maintenance mechanisms that solely depend on the structuring of objects and their relations. These mechanisms define the core of the general repository while mechanisms that are specific to individual semantics are sourced out to individual plug-ins attached to the general system. 1

Locales are the theory development modules of the Isabelle proof assistant. Interpretation is a powerful technique of theorem reuse which facilitates their automatic transport to other contexts. This paper is concerned with the interpretation of locales in the context of other locales. Our main concern is to make interpretation an effective tool in an interactive proof environment. Interpretation dependencies between locales are maintained explicitly, by means of a development graph, so that theorems proved in one locale can be propagated to other locales that interpret it. Proof tools in Isabelle are controlled by sets of default theorems they use. These sets are required to be finite, but can become infinite in the presence of arbitrary interpretations. We show that finiteness can be maintained.

For automatic theorem provers it is as important to disprove false conjectures as it is to prove true ones, especially if it is not known ahead of time if a formula is derivable inside a particular inference system.

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Although in recent years considerable progress has been made in the theory of automated theorem proving, the use of theorem provers in practice is still more or less restricted to a limited number of academic groups. A lot of effort has been spent in techniques to optimize the underlying logic engine by, for instance, developing efficient datastructures or controlling redundancy in large search spaces (see [29]). However, the development of techniques and methodologies to integrate such a logic engine into an overall proof assistant has gained less attention. In this paper we discuss the related research problems and will explore possible ways to tackle these problems. 1