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A Generic Modular Data Structure for Proof Attempts Alternating on Ideas and Granularity
[chapter]
2006
Lecture Notes in Computer Science
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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]
2006
Lecture Notes in Computer Science
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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
2006
Journal of Applied Logic
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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
2008
Mathematics in Computer Science
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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]
2003
Lecture Notes in Computer Science
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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]
2013
arXiv
pre-print
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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]
2013
Lecture Notes in Computer Science
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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
1998
Journal of symbolic computation
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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
2012
Electronic Proceedings in Theoretical Computer Science
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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
2007
2007 40th Annual Hawaii International Conference on System Sciences (HICSS'07)
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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
2009
ACM SIGMultimedia Records
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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
1994
The Journal of Logic Programming
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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
2006
Formal Aspects of Computing
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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]
2005
Lecture Notes in Computer Science
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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
2015
Proceedings of the 2015 Conference on Certified Programs and Proofs - CPP '15
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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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