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Theorems and algorithms: an interface between Isabelle and Maple

1995

As

doi:10.5445/ir/303595
fatcat:3vy6i7c6hre5nesnpheg25ekpy
*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 . ...##
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Combining theorem proving and symbolic mathematical computing
[chapter]

1995
*
Lecture Notes in Computer Science
*

This paper disscusses di erent possible levels of interaction

doi:10.1007/3-540-60156-2_3
fatcat:gptoyfozcnb73kgiy6mwgus46m
*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. ...##
###
Computer Algebra Meets Automated Theorem Proving: Integrating Maple and PVS
[chapter]

2001
*
Lecture Notes in Computer Science
*

We describe

doi:10.1007/3-540-44755-5_4
fatcat:cfup3xln4vduzd5y5zs2ziouye
*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. ...##
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Robust Computer Algebra, Theorem Proving, and Oracle AI

2017
*
Social Science Research Network
*

We review approaches to

doi:10.2139/ssrn.3038545
fatcat:w3bzqxgopbdwtbqvsckcsfdjoq
*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. ...##
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Robust Computer Algebra, Theorem Proving, and Oracle AI
[article]

2017
*
arXiv
*
pre-print

We review approaches to

arXiv:1708.02553v2
fatcat:hesasayvljb3vmjqsw7sniutdm
*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. ...##
###
Functional design and implementation of graphical user interfaces for theorem provers

1999
*
Journal of functional programming
*

We present a prototypical implementation of a generic

doi:10.1017/s0956796899003421
fatcat:wbpy7xslpncujfecd2igfwjes4
*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. ...##
###
Toward Computer-Assisted Discovery and Automated Proofs of Cutting Plane Theorems
[chapter]

2016
*
Lecture Notes in Computer Science
*

Using a metaprogramming technique

doi:10.1007/978-3-319-45587-7_29
fatcat:i7ev3qd6kjc4recd6fi5uufaya
*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. ...##
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Towards the Mathematics Software Bus

1997
*
Theoretical Computer Science
*

The needs

doi:10.1016/s0304-3975(97)00066-2
fatcat:xl6sovpvdbgpzohaegycja4edy
*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*. ...##
###
Proof Certificates for Algebra and Their Application to Automatic Geometry Theorem Proving
[chapter]

2011
*
Lecture Notes in Computer Science
*

In this paper, we describe how, starting from Hilbert's Nullstellensatz

doi:10.1007/978-3-642-21046-4_3
fatcat:ssvv2zgqena3joe3tdtr7sus6y
*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. ...##
###
Classification of Communication and Cooperation Mechanisms for Logical and Symbolic Computation Systems
[chapter]

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 ...

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

2012
*
Electronical Notes in Theoretical Computer Science
*

A concrete implementation combining the

doi:10.1016/j.entcs.2012.06.010
fatcat:dtl2dsfsqfcgxfpzbsc5v3j6qi
*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. ...##
###
Structures for symbolic mathematical reasoning and computation
[chapter]

1996
*
Lecture Notes in Computer Science
*

The composition of reasoning

doi:10.1007/3-540-61697-7_23
fatcat:njrhn52k2ve5ndbkdbigzq3u2e
*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]. ...##
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Applications of real number theorem proving in PVS

2012
*
Formal Aspects of Computing
*

Here is

doi:10.1007/s00165-012-0232-9
fatcat:cttlm47ehreezkk2ikywgwuixu
*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. ...##
###
Dealing with algebraic expressions over a field in Coq using Maple

2005
*
Journal of symbolic computation
*

We describe

doi:10.1016/j.jsc.2004.12.004
fatcat:z3bl7pqh5vhm7p3y76zy6pq5yi
*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*. ...##
###
Hidden verification for computational mathematics

2005
*
Journal of symbolic computation
*

These are called directly from

doi:10.1016/j.jsc.2004.12.005
fatcat:lqoooacsufcvnbx5jgsdkk35ke
*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. ...
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