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A Generic Modular Data Structure for Proof Attempts Alternating on Ideas and Granularity [chapter]

Serge Autexier, Christoph Benzmüller, Dominik Dietrich, Andreas Meier, Claus-Peter Wirth
2006 Lecture Notes in Computer Science  
The proof data structure enables, in particular, the flexible handling of lemmas, the maintenance of different proof alternatives, and the representation of different granularities of proof attempts.  ...  We describe a parameterized proof data structure for the management of proofs, which includes our experience with the development of two proof assistants.  ...  In the fragment on the left-hand side, the node n 1 has two alternative proof attempts and each at alternative granularities.  ... 
doi:10.1007/11618027_9 fatcat:6aoctu22wfd35dqwiz766bgtmm

A Proof-Theoretic Approach to Hierarchical Math Library Organization [chapter]

Kamal Aboul-Hosn, Terese Damhøj Andersen
2006 Lecture Notes in Computer Science  
Textbook-Style Matrices Atan Sexton, Volker Sorge 111 A Generic Modular Data Structure for Proof Attempts Alternating on Ideas and Granularity Serge A utexier, Christoph Benzmüller, Dominik Dietrieh  ...  A Tough Nut for Mathematical Knowledge Management Manfred Kerber, Martin Pollet 81 Textbook Proofs Meet Formal Logic -The Problem of Underspecification and Granularity Serge Autexier, 96 Processing  ... 
doi:10.1007/11618027_1 fatcat:pyxfr6f4fvcavfw74kbxfqpcli

Computer supported mathematics with Ωmega

Jörg Siekmann, Christoph Benzmüller, Serge Autexier
2006 Journal of Applied Logic  
It is a modular system with a central proof data structure and several supplementary subsystems including automated deduction and computer algebra systems.  ...  In particular, MEGA supports proof development at a human-oriented abstract level of proof granularity.  ...  Proof objects The central data structure for the overall search is the proof plan data structure PDS in Fig. 1 and the subsystems cooperate to construct a proof whose status is stored again in the PDS  ... 
doi:10.1016/j.jal.2005.10.008 fatcat:bfpsfvprmnfnddfvwwx5cqbjiq

Organization, Transformation, and Propagation of Mathematical Knowledge in Ωmega

Serge Autexier, Christoph Benzmüller, Dominik Dietrich, Marc Wagner
2008 Mathematics in Computer Science  
Our approach has resulted in a lean and maintainable system code and makes the system open for extensions.  ...  Mathematical assistance systems and proof assistance systems in general have traditionally been developed as large, monolithic systems which are often hard to maintain and extend.  ...  Moreover, we thank the members of the Ωmega team for their contributions and their feedback.  ... 
doi:10.1007/s11786-008-0054-6 fatcat:qoxkghx6c5epfjjaw5oykgfjjy

MetaPRL – A Modular Logical Environment [chapter]

Jason Hickey, Aleksey Nogin, Robert L. Constable, Brian E. Aydemir, Eli Barzilay, Yegor Bryukhov, Richard Eaton, Adam Granicz, Alexei Kopylov, Christoph Kreitz, Vladimir N. Krupski, Lori Lorigo (+3 others)
2003 Lecture Notes in Computer Science  
The MetaPRL system combines the properties of an interactive LCF-style tactic-based proof assistant, a logical framework, a logical programming environment, and a formal methods programming toolkit.  ...  This paper provides an overview of the system focusing on the features that did not exist in the previous generations of PRL systems.  ...  For example, suppose we wish to formalize a data structure for labeled binary trees.  ... 
doi:10.1007/10930755_19 fatcat:nker4ros75gvzpadxblbenbsky

Proof-Pattern Recognition and Lemma Discovery in ACL2 [article]

Jónathan Heras, Ekaterina Komendantskaya, Moa Johansson, Ewen Maclean
2013 arXiv   pre-print
We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery.  ...  The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition to pre-processes data from libraries, and then suggests auxiliary lemmas in new proofs by analogy with already  ...  proofs; symbolic tools can use this data for more efficient lemma discovery.  ... 
arXiv:1308.1780v2 fatcat:e2vvq2y3a5e6jglfkqxdgtrji4

Proof-Pattern Recognition and Lemma Discovery in ACL2 [chapter]

Jónathan Heras, Ekaterina Komendantskaya, Moa Johansson, Ewen Maclean
2013 Lecture Notes in Computer Science  
We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery.  ...  The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition to pre-processes data from libraries, and then suggests auxiliary lemmas in new proofs by analogy with already  ...  proofs; symbolic tools can use this data for more efficient lemma discovery.  ... 
doi:10.1007/978-3-642-45221-5_27 fatcat:fzqriuvmi5afterecszjwzjcdi

Interactive Theorem Proving: An Empirical Study of User Activity

J.S. Aitken, P. Gray, T. Melham, M. Thomas
1998 Journal of symbolic computation  
Second, we describe and present the results of an empirical study of intermediate and expert HOL users. The results are analysed for evidence in support of the proposed view of proof activity in HOL.  ...  We believe that this approach provides a principled basis for the assessment and design of interfaces to theorem provers.  ...  This is strong evidence for the idea that users organise the proof attempt at a signi cantly larger granularity than the tactic level.  ... 
doi:10.1006/jsco.1997.0175 fatcat:rupygmga65gz3ja27kpjhgd36q

Lessons Learned From Microkernel Verification — Specification is the New Bottleneck

Christoph Baumann, Bernhard Beckert, Holger Blasum, Thorsten Bormer
2012 Electronic Proceedings in Theoretical Computer Science  
In this paper we report on lessons learned for verification of large software systems based on the experience gained in microkernel verification in the Verisoft XT project.  ...  Software verification tools have become a lot more powerful in recent years. Even verification of large, complex systems is feasible, as demonstrated in the L4.verified and Verisoft XT projects.  ...  the existence of a correctness proof (e.g., loop invariants or data-structure invariants and abstractions).  ... 
doi:10.4204/eptcs.102.4 fatcat:rkhqobyravgezemborw6ay2zea

Modular Integration Through Aspects: Making Cents of Legacy Systems

Celina Gibbs, Daniel Lohmann, Chunjian Liu, Yvonne Coady
2007 2007 40th Annual Hawaii International Conference on System Sciences (HICSS'07)  
Recently, Continua Health Alliance has brought together a powerhouse team, including Cisco, IBM, Motorola and others, for personal telehealth products and services.  ...  Aspect-Oriented Software Development (AOSD) is focused on novel notions of modularity that crosscut traditional abstraction boundaries.  ...  The basic idea is to retrieve some cached data from remote systems and build a local copy in order to save the time spent on network communication.  ... 
doi:10.1109/hicss.2007.390 dblp:conf/hicss/GibbsLLC07 fatcat:f323etfxkvgmdnuvd2q4h2syqa

Modularization and multi-granularity reuse of learning resources

Marek Meyer, Ralf Steinmetz, Abdulmotaleb El Saddik
2009 ACM SIGMultimedia Records  
Queries should work on abstract structures and properties instead of format-specific data bindings.  ...  According to Baldwin and Clark, "Two subsidiary ideas are subsumed in the general concept [of modularity]. The first is the idea of interdependence within and independence across modules.(...)  ...  Evaluation The prototype described in this chapter implements the concepts for the base modular operations from the previous chapters of this thesis -modularization, aggregation and adaptation of learning  ... 
doi:10.1145/1662529.1662533 fatcat:cykmsfw3p5dvrfmnw4dzgvca3y

Modularity in Logic Programming

Michele Bugliesi, Evelina Lamma, Paola Mello
1994 The Journal of Logic Programming  
Other proposals have instead concentrated on the problem of programming-in-the-small in an attempt to enrich logic programming with abstraction and scoping mechanisms available in other programming paradigms  ...  The research on modular logic programming has evolved along two different directions during the past decade. Various papers have focused primarily on the problems of programming-in-the-large.  ...  Special thanks to Antonio Brogi, Laura Giordano, Dale Miller, Albert0 Martelli, Andrea Omicini, Franc0 Turini, and the anonymous referees for their useful comments on the first version of this paper.  ... 
doi:10.1016/0743-1066(94)90032-9 fatcat:xkz7isn57zgcphapihejhwy4gm

On assertion-based encapsulation for object invariants and simulations

David A. Naumann
2006 Formal Aspects of Computing  
In object-oriented programming, reentrant method invocations and shared references make it difficult to achieve adequate encapsulation for sound modular reasoning.  ...  Encapsulation is assessed in terms of modular reasoning about invariants and simulations.  ...  This paper is based on one that appeared in the proceedings of FMCO 2005 [Nau05a] . A number of changes have been made; the major difference is the addition of Section 8.  ... 
doi:10.1007/s00165-006-0020-5 fatcat:t7c4ix3qvvhj7ph4qwi6x7rwp4

Assertion-Based Encapsulation, Object Invariants and Simulations [chapter]

David A. Naumann
2005 Lecture Notes in Computer Science  
In object-oriented programming, reentrant method invocations and shared references make it difficult to achieve adequate encapsulation for sound modular reasoning.  ...  Encapsulation is assessed in terms of modular reasoning about invariants and simulations.  ...  This paper is based on one that appeared in the proceedings of FMCO 2005 [Nau05a] . A number of changes have been made; the major difference is the addition of Section 8.  ... 
doi:10.1007/11561163_11 fatcat:wxcykt6alndg5g372ytc7e6cuy

Clean-Slate Development of Certified OS Kernels

Zhong Shao
2015 Proceedings of the 2015 Conference on Certified Programs and Proofs - CPP '15  
We advocate a modular certification framework for kernel components, which mirrors and enhances the modularity of the kernel itself.  ...  Formal methods for automated analysis and proofs.  ...  Our proposed kernel design in a sense takes the OS Kit one step further, building a modular kernel structure whose component interfaces are formally defined and suitable for modular certification.  ... 
doi:10.1145/2676724.2693180 dblp:conf/cpp/Shao15 fatcat:ffiwrhqsdnbcflselj27eevbre
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