## Logical Aspects of Digital Mathematics Libraries (2001)

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@MISC{Allen01logicalaspects,

author = {Stuart Allen and James Caldwell and Robert Constable},

title = {Logical Aspects of Digital Mathematics Libraries},

year = {2001}

}

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### Abstract

this article are based on the formalization of particular fragments of computational mathematics, but the results are general. In this paper we focus on capabilities of digital mathematics libraries that are enabled by formalism. Specifically we report results on these topics

### Citations

74 |
Implementing Mathematics with the Nuprl Development System
- Constable
- 1986
(Show Context)
Citation Context ...ave been designing, implementing and applying constructive systems to the formalization of algorithmic mathematics and to modeling and verifying complex computer systems. Our production system, Nuprl =-=[7]-=- has been used in several major applications [15, 5, 14, 1] and has been used to solve difficult problems in mathematics [17, 16, 13]. The mathematics formalized in the system have been used to teach ... |

73 | Building reliable, high-performance communication systems from components
- Liu, Kreitz, et al.
- 1999
(Show Context)
Citation Context ...nstructive systems to the formalization of algorithmic mathematics and to modeling and verifying complex computer systems. Our production system, Nuprl [7] has been used in several major applications =-=[15, 5, 14, 1]-=- and has been used to solve difficult problems in mathematics [17, 16, 13]. The mathematics formalized in the system have been used to teach computer science and logic courses [8]. Many of the questio... |

44 | The Nuprl open logical environment
- Allen, Constable, et al.
(Show Context)
Citation Context ...d from using them. The paper will refer to the on-line library and to features of it that readers of this paper can examine. Our latest implementation is an open Logical Programming Environment (LPE) =-=[3]-=-. One of the key components of our LPE is a database of thousands of formally proved mathematical statements of general mathematical interest, many related to data types and algorithms. Our logic expr... |

34 |
The Horus and Ensemble projects: Accomplishments and limitations
- Birman, Constable, et al.
- 2000
(Show Context)
Citation Context ...nstructive systems to the formalization of algorithmic mathematics and to modeling and verifying complex computer systems. Our production system, Nuprl [7] has been used in several major applications =-=[15, 5, 14, 1]-=- and has been used to solve difficult problems in mathematics [17, 16, 13]. The mathematics formalized in the system have been used to teach computer science and logic courses [8]. Many of the questio... |

25 |
a formula language, modeled upon that for arithmetic for pure thought
- Begriffsschrift
- 1967
(Show Context)
Citation Context ...ore one must rely on such arguments in order to have any confidence in the correctness of ones work. The possibility of such an argument is one of the great values of formalization in the first place =-=[11]-=-, and we must not give it up simply because we require flexibility and naturalness of expression. In the full paper we will present examples that forced us toward the implementation of abstract object... |

23 |
A computational analysis of girard’s translation and lc
- Murthy
- 1992
(Show Context)
Citation Context ...deling and verifying complex computer systems. Our production system, Nuprl [7] has been used in several major applications [15, 5, 14, 1] and has been used to solve difficult problems in mathematics =-=[17, 16, 13]-=-. The mathematics formalized in the system have been used to teach computer science and logic courses [8]. Many of the questions that arise in an effort to build a global digital library of mathematic... |

21 |
The nuprl proof development system (version 4.2) reference manual and user’s guide. Unpublished manuscript
- Jackson
- 1996
(Show Context)
Citation Context ...nstructive systems to the formalization of algorithmic mathematics and to modeling and verifying complex computer systems. Our production system, Nuprl [7] has been used in several major applications =-=[15, 5, 14, 1]-=- and has been used to solve difficult problems in mathematics [17, 16, 13]. The mathematics formalized in the system have been used to teach computer science and logic courses [8]. Many of the questio... |

18 | Verbalization of high-level formal proofs
- Holland-Minkley, Barzilay, et al.
- 1999
(Show Context)
Citation Context ...roofs to obtain new ones, translate between them, transform theories to create new ones, and we are increasing our capability for generating natural language versions of proofs from the formal proofs =-=[12]-=-. In order to create complete formal proofs, we need theorem provers that exploit a mix of interactive and fully automatic methods. The automatic ones comprise decision procedures, model checkers, and... |

14 |
Types in logic, mathematics and programming
- Constable
- 1998
(Show Context)
Citation Context ...er based proof technology that will] enable a diverse community of mathematicians, computer scientists and educators to build a new artifact — a globally distributed library of formalized mathematics.=-=[9]-=- The solution will include (at least) the best of data-base techniques, distributed systems and web technology, and of course will build on the significant developments in theorem proving and symbolic... |

14 |
The computational behaviour of Girard’s paradox
- Howe
(Show Context)
Citation Context ...deling and verifying complex computer systems. Our production system, Nuprl [7] has been used in several major applications [15, 5, 14, 1] and has been used to solve difficult problems in mathematics =-=[17, 16, 13]-=-. The mathematics formalized in the system have been used to teach computer science and logic courses [8]. Many of the questions that arise in an effort to build a global digital library of mathematic... |

11 |
Verifying a logic synthesis tool in Nuprl
- Aagaard, Leeser
- 1993
(Show Context)
Citation Context |

10 |
Constructively formalizing automata
- Constable, Jackson, et al.
- 1997
(Show Context)
Citation Context ...s and formal proofs. We have already explored some of the benefits of connecting formal content to text. Our web libraries [19] provide a number of examples of how we have done this, and our articles =-=[20, 10, 4]-=- describe the process and potential applications. Our experiments in education give examples of the use. Mixing formal and informal presentations encourages people to take steps toward precision and f... |

6 | Creating and evaluating interactive formal courseware for mathematics and computing
- Constable
- 1996
(Show Context)
Citation Context ...lications [15, 5, 14, 1] and has been used to solve difficult problems in mathematics [17, 16, 13]. The mathematics formalized in the system have been used to teach computer science and logic courses =-=[8]-=-. Many of the questions that arise in an effort to build a global digital library of mathematics arise also in the formal setting. We see interesting possibilities for sharing ideas and methods with t... |

3 | A Formula Language, Modeled upon that of Arithmetic, for Pure Thought - Begrisschrift - 1967 |

3 |
Alexey Nogin. JProver: Integrating connection-based theorem proving into interactive proof assistants
- Schmitt, Lorigo, et al.
- 2001
(Show Context)
Citation Context ...loit a mix of interactive and fully automatic methods. The automatic ones comprise decision procedures, model checkers, and heuristic provers. Our systems combine these; recently we added the JProver =-=[21]-=-, a fast prover for Intuitionistic first-order logic. Nuprl is connected to the JProver through MetaPRL. The interactive components call upon these automatic methods and also execute high level descri... |

2 | The prospects for mathematical logic in the twenty-frst century - Buss, Kechris, et al. - 2001 |

2 |
Finding the answers in classical proofs: A unifying framework
- Murthy
- 1992
(Show Context)
Citation Context ...deling and verifying complex computer systems. Our production system, Nuprl [7] has been used in several major applications [15, 5, 14, 1] and has been used to solve difficult problems in mathematics =-=[17, 16, 13]-=-. The mathematics formalized in the system have been used to teach computer science and logic courses [8]. Many of the questions that arise in an effort to build a global digital library of mathematic... |

1 |
Discrete math lessons. http://www.cs.cornell.edu/Info/People/sfa/Nuprl/eduprl/Xcounting intro.html
- Allen
- 2001
(Show Context)
Citation Context ... formal concepts. It allows formal tools to support logical connections between sections of mixed material. In the final paper we will use material from Stuart Allen’s library of discrete mathematics =-=[2]-=- to illustrate the importance of having readable formal proofs. We will show how detail can be progressively exposed, how readings can be linked to the proof and how the proof can we interlinked to in... |

1 | Predicate transformers for in state automata - Bickford, Hickey - 1999 |

1 |
Predicate transformers for infinite state automata
- Bickford, Hickey
- 1999
(Show Context)
Citation Context ...s and formal proofs. We have already explored some of the benefits of connecting formal content to text. Our web libraries [19] provide a number of examples of how we have done this, and our articles =-=[20, 10, 4]-=- describe the process and potential applications. Our experiments in education give examples of the use. Mixing formal and informal presentations encourages people to take steps toward precision and f... |