## Computer algebra meets automated theorem proving: Integrating Maple and pvs (2001)

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Venue: | Theorem Proving in Higher Order Logics (TPHOLs 2001), volume 2152 of LNCS |

Citations: | 19 - 3 self |

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@INPROCEEDINGS{Dunstan01computeralgebra,

author = {Martin Dunstan and Hanne Gottliebsen and Tom Kelsey and Ursula Martin},

title = {Computer algebra meets automated theorem proving: Integrating Maple and pvs},

booktitle = {Theorem Proving in Higher Order Logics (TPHOLs 2001), volume 2152 of LNCS},

year = {2001},

pages = {27--42},

publisher = {Springer-Verlag}

}

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### Citations

103 | Redlog: Computer algebra meets computer logic
- Dolzmann, Sturm
- 1997
(Show Context)
Citation Context ...neric CAS and ATP systems [5, 15]. Another solution is the sub-package approach, in which communication issues are side-stepped by building an ATP within a CAS. Examples include Analytica [4], REDLOG =-=[12]-=-, the Theorema project [6, 7], and a logical extension to the type system of the AXIOM CAS [19, 26]. The third common approach involves the choice of preferred CAS and ATP environments, and the constr... |

86 |
Maple V Language Reference Manual
- Char, Geddes, et al.
- 1991
(Show Context)
Citation Context ...ormat: a core proof engine which is integrated with a non-formal system via a script interface. Our target, however, is the engineering/scientific/mathematical community of CAS users. 1.3 Maple Maple =-=[9]-=- is a commercial CAS, consisting of a kernel library of numeric, symbolic and graphics routines, together with packages aimed at specific areas such as linear algebra and differential equations. The k... |

50 | Theorems and algorithms: An interface between Isabelle and Maple
- Ballarin, Homann, et al.
- 1995
(Show Context)
Citation Context ...common approach involves the choice of preferred CAS and ATP environments, and the construction of a specific interface for communication between them. Examples include Maple-HOL [16], Maple-Isabelle =-=[3]-=-, and Weyl-NuPrl [17]. The common-knowledge approach depends on wholesale acceptance of the protocols by both the CAS and ATP communities. Since this has not yet happened, we concentrate on the remain... |

47 | An Overview of the Theorema Project
- Buchberger, Jebelean, et al.
- 1997
(Show Context)
Citation Context ...5, 15]. Another solution is the sub-package approach, in which communication issues are side-stepped by building an ATP within a CAS. Examples include Analytica [4], REDLOG [12], the Theorema project =-=[6, 7]-=-, and a logical extension to the type system of the AXIOM CAS [19, 26]. The third common approach involves the choice of preferred CAS and ATP environments, and the construction of a specific interfac... |

39 | The PROSPER Toolkit
- Dennis, Norrish, et al.
- 2000
(Show Context)
Citation Context ...to PVS [14, 2] which allow reasoning in the theory of real analysis, so that properties of symbolic expressions can be described and checked. The project is in approach similar to the PROSPER toolkit =-=[10]-=-, which allows systems designers using CAD and CASE tools access to mechanised verification. The PROSPER paradigm involves the CAD/CASE system as the master, with a slave proof engine running in the b... |

27 | Specification and integration of theorem provers and computer algebra systems
- Bertoli, Calmet, et al.
- 1999
(Show Context)
Citation Context ... any mathematical computation system. Examples of this common knowledge approach include the OpenMath project [1,11], and protocols for the exchange of information between generic CAS and ATP systems =-=[5,15]-=-. Another solution is the sub-package approach, in which communication issues are side-stepped by building an ATP within a CAS. Examples include Analytica [4], REDLOG [12], the Theorema project [6,7],... |

26 |
Analytica — an Experiment in Combining Theorem Proving and Symbolic Computation
- Bauer, Clarke, et al.
- 1998
(Show Context)
Citation Context ...on between generic CAS and ATP systems [5,15]. Another solution is the sub-package approach, in which communication issues are side-stepped by building an ATP within a CAS. Examples include Analytica =-=[4]-=-, REDLOG [12], the Theorema project [6,7], and a logical extension to the type system of the AXIOM CAS [18,25]. The third common approach involves the choice of preferred CAS and ATP environments, and... |

26 | Symbolic Computation: Computer Algebra and Logic
- Buchberger
- 1996
(Show Context)
Citation Context ...5, 15]. Another solution is the sub-package approach, in which communication issues are side-stepped by building an ATP within a CAS. Examples include Analytica [4], REDLOG [12], the Theorema project =-=[6, 7]-=-, and a logical extension to the type system of the AXIOM CAS [19, 26]. The third common approach involves the choice of preferred CAS and ATP environments, and the construction of a specific interfac... |

23 | MP: A Protocol for the Efficient Exchange of Mathematical Data
- Gray
- 1998
(Show Context)
Citation Context ...any mathematical computation system. Examples of this common knowledge approach include the OpenMath project [1, 11], and protocols for the exchange of information between generic CAS and ATP systems =-=[5, 15]-=-. Another solution is the sub-package approach, in which communication issues are side-stepped by building an ATP within a CAS. Examples include Analytica [4], REDLOG [12], the Theorema project [6, 7]... |

19 | Elements of mathematical analysis in PVS
- Dutertre
- 1996
(Show Context)
Citation Context ... PVS library of transcendental functions was provided in [14]. The library can be used to check continuity of functions such as � Ü �sÜ� � (4) The library is based on Dutertre’s real analysis library =-=[13]-=- and contains a development of power series, which is used to describe and reason about functions such as �ÜÔ, Ó×, ×�Ò and Ø�Ò and their inverses. The library also contains a large set of lemmas about... |

12 | Transcendental functions and continuity checking in PVS
- Gottliebsen
- 2000
(Show Context)
Citation Context ...ich links the major commercial CAS Maple [20] to the widely used ATP PVS [22] in a way which minimises the inherent problems of linking two unrelated systems. We also utilise recent extensions to PVS =-=[14, 2]-=- which allow reasoning in the theory of real analysis, so that properties of symbolic expressions can be described and checked. The project is in approach similar to the PROSPER toolkit [10], which al... |

10 | Automated theorem proving in support of computer algebra: Symbolic definite integration as a case study
- Adams, Gottliebsen, et al.
- 1999
(Show Context)
Citation Context ...ich links the major commercial CAS Maple [19] to the widely used ATP PVS [21] in a way which minimises the inherent problems of linking two unrelated systems. We also utilise recent extensions to PVS =-=[14,2]-=- which allow reasoning in the theory of real analysis, so that properties of symbolic expressions can be described and checked. The project is in approach similar to the PROSPER toolkit [10], which al... |

10 | Classification of communication and cooperation mechanisms for logical and symbolic computation systems
- Calmet, Homann
- 1996
(Show Context)
Citation Context ... (3) These proofs allow the user to correct, modify or disregard the incorrect results from Maple. 1.2 Background Previous approaches to the combination of CAS and ATP are discussed and classified in =-=[8]-=-. We mention selected examples which are direct or indirect predecessors to this work. All approaches share the common problem of communicating mathematical information between the CAS and ATP systems... |

10 | Reasoning About the Reals: The Marriage of HOL and Maple
- Harrison, Thery
- 1993
(Show Context)
Citation Context ... [19, 26]. The third common approach involves the choice of preferred CAS and ATP environments, and the construction of a specific interface for communication between them. Examples include Maple-HOL =-=[17]-=-, Maple-Isabelle [3], and Weyl-NuPrl [18]. The common-knowledge approach depends on wholesale acceptance of the protocols by both the CAS and ATP communities. Since this has not yet happened, we conce... |

4 |
Objectives of OpenMath. Available from http://www.can.nl/~abbott/OpenMath
- Abbott, Leeuwen, et al.
- 1995
(Show Context)
Citation Context ...to define a standard for mathematical information that can, in principle, be understood by any mathematical computation system. Examples of this common knowledge approach include the OpenMath project =-=[1, 11]-=-, and protocols for the exchange of information between generic CAS and ATP systems [5, 15]. Another solution is the sub-package approach, in which communication issues are side-stepped by building an... |

4 |
Special Issue on OPENMATH
- Dewar
- 2000
(Show Context)
Citation Context ...to define a standard for mathematical information that can, in principle, be understood by any mathematical computation system. Examples of this common knowledge approach include the OpenMath project =-=[1, 11]-=-, and protocols for the exchange of information between generic CAS and ATP systems [5, 15]. Another solution is the sub-package approach, in which communication issues are side-stepped by building an... |

3 |
editors. Theorem Proving in Higher Order Logics
- Harrison, Aagaard
- 2000
(Show Context)
Citation Context ...t easy to prove by hand. 4.3 A Generic Application to IVPs We now describe a methodology for validating and improving Maple procedures for solving IVPs of the form Ý Ü �Ö ÜsÕ Ü Ý Ü � Ý � ��� Ü ��� �℄ =-=(16)-=- We can use the interface to check the following requirements on inputs (bearing in mind that each input can be a complicated symbolic expression involving parameters): 1. Ö Ü and Õ Ü are continuous o... |

1 |
Objectives of OpenMath. Available from
- Abbott, Leeuwen, et al.
- 1995
(Show Context)
Citation Context ...to define a standard for mathematical information that can, in principle, be understood by any mathematical computation system. Examples of this common knowledge approach include the OpenMath project =-=[1,11]-=-, and protocols for the exchange of information between generic CAS and ATP systems [5,15]. Another solution is the sub-package approach, in which communication issues are side-stepped by building an ... |