A Model for Capturing and Replaying Proof Strategies Leo Freitas, Cliff B. Jones, Andrius Velykis and Iain Whiteside School of Computing Science, Newcastle University, NE1 7RU, UK first.last@newcastle.ac.uk Abstract. Modern theorem provers can discharge a significant propor- tion of Proof Obligations (POs) that arise in the use of Formal Meth- ods (FMs). Unfortunately, the residual POs require tedious manual guid- ance. On the positive side, these “difficult” POs tend to fall into families each of which requires only a few key ideas to unlock. This paper outlines a system that will identify and characterise ways of discharging POs of a family by tracking an interactive proof of one member of the family. This opens the possibility of capturing ideas from an expert and/or max- imising reuse of ideas after changes to definitions. The proposed system has to store a wealth of meta-information about conjectures, which can be matched against previously learned strategies, or can be used to con- struct new strategies based on expert guidance. This paper describes this meta-information and how it is used to lessen the burden of FM proofs. 1 Introduction Formal methods based on one or another chosen specification language are now used to document different levels of abstraction for many systems. In those methods that adopt a “posit and prove” style of development, engineering deci- sions are recorded in concrete models and Proof Obligations (POs) are generated whose discharge establishes that the reified model has a behaviour compatible with a more abstract model. (There are also POs that establish internal consis- tency of one level of model — e.g. respecting invariants.) Both clever engineering and AI techniques have led to Automated Theorem Provers (ATPs) that can discharge an impressively large proportion of POs but the manual discharge of the remaining POs is an impediment to wider use of formal methods. The research hypothesis of the AI 4 FM project is that a system can be built that learns, from interactive proof, ideas that will facilitate auto- matic discharge of other recalcitrant POs in the same family. The emphasised qualification in the previous sentence indicates that the system is not intended to discover general heuristics; the aim is to extract intuition about functions and data structures used in the specific family of POs. The design of the AI 4 FM system is itself being conducted formally. Moreover, exploration of the design space is being undertaken by recording and modifying formal models of the proposed system. A similar process was used to considerable effect in the creation of the mural theorem proving assistant [JJLM91].