Learning from experts to aid the automation of proof search (original) (raw)
2009
Many formal methods are “posit and prove” where a designer posits a specification, and then seeks to justify it. This justification is in the form of proof obligations (POs), putative lemmas that need proof. A large proportion of these can be discharged by automatic theorem provers, but there are still some that require user interaction (typically of the order of 5-20%). Discharging these POs can become a bottleneck in the use of formal methods in practical applications, and there are two approaches to dealing with them:
Automatic Learning of Proof Methods in Proof Planning
Logic Journal of IGPL, 2003
In this paper we present an approach to automated learning within mathematical reasoning systems. In particular, the approach enables proof planning systems to automatically learn new proof methods from well-chosen examples of proofs which use a similar reasoning pattern to prove related theorems. Our approach consists of an abstract representation for methods and a machine learning technique which can learn methods using this representation formalism. We present an implementation of the approach within the Ωmega proof planning system, which we call LearnΩmatic. We also present the results of the experiments that we ran on this implementation in order to evaluate if and how it improves the power of proof planning systems.
A Model for Capturing and Replaying Proof Strategies
Lecture Notes in Computer Science, 2014
Modern theorem provers can discharge a significant proportion of Proof Obligations (POs) that arise in the use of Formal Methods (FMs). Unfortunately, the residual POs require tedious manual guidance. 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 maximising 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 construct new strategies based on expert guidance. This paper describes this meta-information and how it is used to lessen the burden of FM proofs.
3.9 Capturing and Inferring the Proof Process (Part 1: Case Studies)
2013
We report current work on inferring the proof process of an expert by wire-tapping various theorem proving environments (eg Isabelle/HOL, Z/EVES, etc). The idea is to have enough (meta-) proof information (ie user intent, lemmas used, points of failure and ways of recovery, various proof attempts [sub-] trees, etc.), in order to be able to do meta-level reasoning about proofs, in particular for proof reuse, but also for proof maintenance and transferability to non-expert users.
A Survey on Theorem Provers in Formal Methods
ArXiv, 2019
Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians to prove theorems by computer programs. However, these tools evolved with time and now play vital role in the modeling and reasoning about complex and large-scale systems, especially safety-critical systems. Technically, mathematical formalisms and automated reasoning based-approaches are employed to perform inferences and to generate proofs in theorem provers. In literature, there is a shortage of comprehensive documents that can provide proper guidance about the preferences of theorem provers with respect to their designs, performances, logical frameworks, strengths, differences and their application areas. In this work, more than 40 theorem provers are studied in detail and compared to present a comprehensive analysis and evaluation of these to...
Towards a framework to integrate proof search paradigms
2003
Research on automated and interactive theorem proving aims at the mechanization of logical reasoning. Aside from the development of logic calculi it became rapidly apparent that the organization of proof search on top of the calculi is an essential task in the design of powerful theorem proving systems. Different paradigms of how to organize proof search have emerged in that area of research, the most prominent representatives are generally described by the buzzwords: automated theorem proving, tactical theorem proving and ...
Proof Patterns for Formal Methods
Lecture Notes in Computer Science, 2014
Design patterns are a highly successful technique in software engineering, giving a reusable 'best practice' solution to commonly occurring problems in software design. Taking inspiration, this paper introduces proof patterns, which aim to provide a common vocabulary for solving formal methods proof obligations by capturing and describing solutions to common patterns of proof, hence increasing effectiveness.
Ecole Polytechnique Project PSI: “Proof Search control in Interaction with domain-specific methods”
2013
In this paper, we introduce two focussed sequent calculi, LK p (T) and LK + (T), that are based on Miller-Liang’s LKF system [LM09] for polarised classical logic. The novelty is that those sequent calculi integrate the possibility to call a decision procedure for some background theory T, and the possibility to polarise literals "on the fly " during proof-search. These features are used in other works [FLM12, FGLM13] to simulate the DPLL(T) procedure [NOT06] as proof-search in the extension of LK p (T) with a cut-rule. In this report we therefore prove cut-elimination in LK p (T). Contrary to what happens in the empty theory, the polarity of literals affects the provability of formulae in presence of a theory T. On the other hand, changing the polarities of connectives does not change the provability of formulae, only the shape of proofs. In order to prove this, we introduce a second sequent calculus, LK + (T) that extends LK p (T) with a relaxed focussing discipline, but ...
An Interactive Driver for Goal-directed Proof Strategies
Electronic Notes in Theoretical Computer Science, 2009
Interactive Theorem Provers (ITPs) are tools meant to assist the user during the formal development of mathematics. Automatic proof searching procedures are a desirable aid, and most ITPs supply the user with an extensive set of facilities to improve automation. However, the black-box nature of most automatic procedure conflicts with the interactive nature of these tools: a newcomer running an automatic procedure learns nothing by its execution (especially in case of failure), and a trained user has no opportunities to interactively guide the procedure towards the solution, e.g. pruning wrong or not promising branches of the search tree. In this paper we discuss the implementation of the resolution based automatic procedure of the Matita ITP, explicitly conceived to be interactively driven by the user through a suitable, simple graphical interface.