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Theorems and algorithms: an interface between Isabelle and Maple

Clemens Ballarin, Karsten Homann, Jacques Calmet
1995
As an example for such a mechanized mathematics environment w e describe a prototype implementation of an interface between Isabelle and Maple.  ...  Additionaly, w e specify syntax translations for the concrete syntax of Maple which enables the communication between both systems illustrated by some examples that can be solved by theorems and algorithms  ...  The integration presented in this paper describes a prototype implementation of an interface with Maple Char et al. 92 as a slave to the tactical theorem prover Isabelle Paulson 94 .  ... 
doi:10.5445/ir/303595 fatcat:3vy6i7c6hre5nesnpheg25ekpy

Combining theorem proving and symbolic mathematical computing [chapter]

Karsten Homann, Jacques Calmet
1995 Lecture Notes in Computer Science  
This paper disscusses di erent possible levels of interaction between a symbolic calculator based on algebraic algorithms and a theorem prover.  ...  We describe a model for such a knowledge base mainly consisting of type and algorithm schemata, algebraic algorithms and theorems.  ...  On the other hand, they o er an extensive collection of e cient mathematical algorithms which can improve the e ciency of the theorem prover.  ... 
doi:10.1007/3-540-60156-2_3 fatcat:gptoyfozcnb73kgiy6mwgus46m

Computer Algebra Meets Automated Theorem Proving: Integrating Maple and PVS [chapter]

Andrew Adams, Martin Dunstan, Hanne Gottliebsen, Tom Kelsey, Ursula Martin, Sam Owre
2001 Lecture Notes in Computer Science  
We describe an interface between version 6 of the Maple computer algebra system with the PVS automated theorem prover.  ...  The interface is designed to allow Maple users access to the robust and checkable proof environment of PVS.  ...  Introduction In this paper we describe an interface between version 6 of the Maple computer algebra system, henceforth CAS, and the PVS automated theorem prover, ATP.  ... 
doi:10.1007/3-540-44755-5_4 fatcat:cfup3xln4vduzd5y5zs2ziouye

Robust Computer Algebra, Theorem Proving, and Oracle AI

Gopal P. Sarma, Nick J. Hay
2017 Social Science Research Network  
We review approaches to interfacing CASs with theorem provers, describe well-defined architectural deficiencies that have been identified with CASs, and suggest possible lines of research and practical  ...  On the other hand, we identify computer algebra systems (CASs) as being primitive examples of domain-specific oracles for mathematics and argue that efforts to integrate computer algebra systems with theorem  ...  and feedback on the manuscript.  ... 
doi:10.2139/ssrn.3038545 fatcat:w3bzqxgopbdwtbqvsckcsfdjoq

Robust Computer Algebra, Theorem Proving, and Oracle AI [article]

Gopal P. Sarma, Nick J. Hay
2017 arXiv   pre-print
We review approaches to interfacing CASs with theorem provers, describe well-defined architectural deficiencies that have been identified with CASs, and suggest possible lines of research and practical  ...  On the other hand, we identify computer algebra systems (CASs) as being primitive examples of domain-specific oracles for mathematics and argue that efforts to integrate computer algebra systems with theorem  ...  and feedback on the manuscript.  ... 
arXiv:1708.02553v2 fatcat:hesasayvljb3vmjqsw7sniutdm

Functional design and implementation of graphical user interfaces for theorem provers

C. LÜTH, B. WOLFF
1999 Journal of functional programming  
We present a prototypical implementation of a generic and open interface system architecture, and show how it can be instantiated to an interface for Isabelle, called IsaWin, as well as to a tailored tool  ...  This paper attempts to develop a metaphor suited to visualize the LCF-style prover design, and a methodology for the implementation of graphical user interfaces for these provers and encapsulations of  ...  Tuijnman and W. Schulte at the University of Ulm. Finally, we would like to thank Stefan Westmeier, Kolyang and Thomas Meier for improvements of sml tk and and fruitful discussions.  ... 
doi:10.1017/s0956796899003421 fatcat:wbpy7xslpncujfecd2igfwjes4

Toward Computer-Assisted Discovery and Automated Proofs of Cutting Plane Theorems [chapter]

Matthias Köppe, Yuan Zhou
2016 Lecture Notes in Computer Science  
Using a metaprogramming technique and semialgebraic computations, we provide computer-based proofs for old and new cutting-plane theorems in Gomory--Johnson's model of cut generating functions.  ...  Many sophisticated automated theorem provers, by names such are HOL light, Coq, Isabelle, Mizar, etc. are available nowadays; see [28] and the references within for an interesting overview.  ...  use an automated theorem proving system.  ... 
doi:10.1007/978-3-319-45587-7_29 fatcat:i7ev3qd6kjc4recd6fi5uufaya

Towards the Mathematics Software Bus

Jacques Calmet, Karsten Homann
1997 Theoretical Computer Science  
The needs and requirements for the Mathematics Software Bus and its architecture are demonstrated through some implementations of powerful interfaces between mathematical services.  ...  Such an environment will provide combinations of graphics, editing and computation tools through interfaces to already existing powerful software by flexible and powerful semantically integration.  ...  Example We implemented several interfaces between mathematical services, e.g. ISABELLE and MAPLE, DTP and MAGMA, IMPS and MAPLE.  ... 
doi:10.1016/s0304-3975(97)00066-2 fatcat:xl6sovpvdbgpzohaegycja4edy

Proof Certificates for Algebra and Their Application to Automatic Geometry Theorem Proving [chapter]

Benjamin Grégoire, Loïc Pottier, Laurent Théry
2011 Lecture Notes in Computer Science  
In this paper, we describe how, starting from Hilbert's Nullstellensatz theorem, we combine a modified version of Buchberger's algorithm and some reflexive techniques to get an effective procedure that  ...  automatically produces formal proofs of theorems in geometry.  ...  It gives an explicit interface between the computation that is done externally of the proof assistant and the proof checking that is done inside the proof assistant.  ... 
doi:10.1007/978-3-642-21046-4_3 fatcat:ssvv2zgqena3joe3tdtr7sus6y

Classification of Communication and Cooperation Mechanisms for Logical and Symbolic Computation Systems [chapter]

Jacques Calmet, Karsten Homann
1996 Applied Logic Series  
and their characteristics, capabilities, requirements, and di erences.  ...  Communication and cooperation mechanisms of systems performing any kind of mathematical service enable to study and solve new classes of problems and to perform e cient computation by distributed specialized  ...  The interfaces between HOL and Maple 13] and Isabelle and Maple 4] introduce the powerful arithmetics of a computer algebra system into a tactical theorem prover to reason about numbers or polynomials  ... 
doi:10.1007/978-94-009-0349-4_11 fatcat:eyqxsebedvdvfjr4rbrrllbrri

Integrating Systems around the User: Combining Isabelle, Maple, and QEPCAD in the Prover's Palette

Laura I. Meikle, Jacques D. Fleuriot
2012 Electronical Notes in Theoretical Computer Science  
A concrete implementation combining the theorem prover Isabelle with the computer algebra systems Maple and QEPCAD-B is then presented.  ...  This illustrates that the design principles of the Prover's Palette simplify tool integrations while enhancing the power and usability of theorem provers.  ...  Introducing the Prover's Palette Interactive theorem proving today permits the verification of sophisticated theorems and complex algorithms, although the process remains cumbersome and timeconsuming.  ... 
doi:10.1016/j.entcs.2012.06.010 fatcat:dtl2dsfsqfcgxfpzbsc5v3j6qi

Structures for symbolic mathematical reasoning and computation [chapter]

Karsten Homann, Jacques Calmet
1996 Lecture Notes in Computer Science  
The composition of reasoning and computation theories and structures provide a formal framework for the speci cation of symbolic mathematical problem solving by cooperation of algorithms and theorems.  ...  Recent research towards integrating symbolic mathematical reasoning and computation has led to prototypes of interfaces and environments.  ...  Analytica 6] , interfaces between Hol and Maple 10], Isabelle and Maple 2] , and Nuprl and Weyl 12]. We classify communication and cooperation methods for such environments in 5].  ... 
doi:10.1007/3-540-61697-7_23 fatcat:njrhn52k2ve5ndbkdbigzq3u2e

Applications of real number theorem proving in PVS

Hanne Gottliebsen, Ruth Hardy, Olga Lightfoot, Ursula Martin
2012 Formal Aspects of Computing  
Here is an example of the kind of problem we are interested in taken from an air traffic control application: Let a, b, c be the lengths of the edges of a triangle and let φ be the angle between the edges  ...  that builds on the capabilities of Maple and PVS to provide a verified and automatic analysis of Nichols plots.  ...  Nicholls plots as an application.  ... 
doi:10.1007/s00165-012-0232-9 fatcat:cttlm47ehreezkk2ikywgwuixu

Dealing with algebraic expressions over a field in Coq using Maple

David Delahaye, Micaela Mayero
2005 Journal of symbolic computation  
We describe an interface between the Coq proof assistant and the Maple symbolic computation system, which mainly consists in importing, in Coq, Maple computations regarding algebraic expressions over fields  ...  The implementation of this interface is quite light and can be very easily extended to get other Maple functions (in addition to the four functions we have imported and used in the examples given here)  ...  ., to import computation in DSs, and we want to share our experience of an interface between Coq and Maple.  ... 
doi:10.1016/j.jsc.2004.12.004 fatcat:z3bl7pqh5vhm7p3y76zy6pq5yi

Hidden verification for computational mathematics

Hanne Gottliebsen, Tom Kelsey, Ursula Martin
2005 Journal of symbolic computation  
These are called directly from Maple by a simple pipe-lined interface.  ...  Hence we are able to support the analysis of differential equations in Maple by direct calls to PVS for: result refinement and verification, discharge of verification conditions, harnesses to ensure more  ...  Acknowledgements The authors acknowledge support from UK EPSRC GR/L48265 and NAG ltd., with additional sabbatical support from SRI International and the UK Royal Academy of Engineering.  ... 
doi:10.1016/j.jsc.2004.12.005 fatcat:lqoooacsufcvnbx5jgsdkk35ke
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