A. Bauer, E. Clarke, and X. Zhao. Analytica: an Experiment in Combining Theorem Proving and Symbolic Computation. J. of Autom. Reasoning, 21(3):295--325, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of computer algebra and automated theorem proving are discussed and classified in [12] One solution is the sub package approach in which communication issues are side stepped by building a AS inside a theorem prover (for examp]e IS] or vice versa. xamp]es of the latter include Analytica [6], REDLOG [19] the Theorema project [10, 11] and a logical extension to the type system of the AXIOM CAS [30, 38] While this may give the user added reassurance there remains the underlying problem of soundness: for example simplification errors or undetected division by zero could propagate ....

A. Bauer, E. Clarke, and X. Zhao. Analytica - an experiment in combining theorem proving and symbolic computation. Journal of Automated Reason- ing, 21:295 325, 1998.

....computer algebra system with theorem proving capabilities. The system consists of a collection of special purpose provers. These include a prover for induction over the natural numbers, another for induction over lists, as well as an interface to external theorem provers. The Analytica prover [BCZ96] also adds theorem proving capabilities to the Mathematica computer algebra 11 system. The system is able to prove some complex theorems in analysis about sums and limits, as well as some simple inductive theorems. 8 Future Work and Conclusions We have described a new application for proof ....

A. Bauer, E. Clarke, and X. Zhao. Analytica: an experiment in combining theorem proving and symbolic computation. In Proceedings of the International Conference on Articial Intelligence and Symbolic Computation, AISMC-3, 1996.

....other situations such as Martin s analysis example mentioned earlier reasoning can allow computations to proceed where in general this would not be possible. The literature contains a number of di erent strategies proposed for combining computer algebra and theorem proving; see, for instance, [4, 6, 3]. This paper describes another approach: we use the type system of the Axiom computer algebra system [13] to represent a logic, and thus to use the constructions of Axiom to handle the logic and represent proofs and propositions, in the same way as is done in theorem provers based on type theory ....

....mentioned above, or we can indeed adopt an intermediate position of proving properties seen as crucial while asserting the validity of others. 6 Conclusion We have described a new way to combine or rather, to integrate computer algebra and theorem proving. Our approach is similar to [3] and [4] in that theorem proving capabilities are incorporated in a computer algebra system. In the classi cation of possible combinations of computer algebra and theorem proving of [6] all these are instance of the subpackage approach. But the way in which we do this is completely di erent: ....

Andrej Bauer, Edmund Clarke, and Xudong Zhao. Analytica - an experiment in combining theorem proving and symbolic computation. In AISMC-3, volume 1138 of LNCS. Springer, 1996.

....project [BJK 97] is extending the Mathematica computer algebra system with theorem proving capabilities. The system consists of a collection of special purpose provers. These include a prover for induction over the natural numbers, and another for induction over lists. The Analytica prover [BCZ96] also adds theorem proving capabilities to the Mathematica computer algebra system. The system is able to prove some complex theorems in analysis about sums and limits, as well as some simple inductive theorems. In both the Theorema and Analytica projects, the prover s heuristics are hard wired ....

A. Bauer, E. Clarke, and X. Zhao. Analytica: an experiment in combining theorem proving and symbolic computation. In Proceedings of the International Conference on Artificial Intelligence and Symbolic Computation, AISMC-3, 1996.

....mega system. 1 Introduction In recent years there have been many attempts at combining computer algebra systems (CAS) and deduction systems (DS) Either for the purpose of enhancing the computational power of the DS [17, 18, 3] or in order to strengthen the reasoning capabilities of a CAS [1, 4]. For the former integration there exist basically three approaches: 1) to fully trust the CAS, 2) to use the CAS as an oracle and to try to reconstruct the proof in the DS with purely logical inferences, and (3) to generate protocol output during a CAS calculation and to use this protocol to ....

....maintenance of processes and passing of messages is managed by the MathWeb [11] environment Omega mega is embedded into. The role of sapper in the integration has two distinct aspects: Firstly, arbitrary CAS can be easily used as black box systems for term rewriting (similar to approaches of [4, 3]) and sapper works as a simple bridge between the planner and the CAS. Secondly, sapper also offers means to use a CAS as a proof planner. That is, if the CAS can provide additional information on its computations, this information is recorded by sapper and translated into a sequence of tactics ....

A. Bauer, E. Clarke, and X. Zhao. Analytica: an Experiment in Combining Theorem Proving and Symbolic Computation. J. of Autom. Reasoning, 21(3):295--325, 1998.

....could be used to express the assumptions upon which an answer rests, and in critical cases be used to establish the truth of those assumptions. The literature contains a number of different strategies proposed for combining computer algebra and theorem proving; see, for instance, Buc96, CH96, BCZ96] This paper examines another proposal: that of using the type system of the Axiom [JS92] computer algebra system to represent a logic, and thus to use the constructions of Axiom to handle the logic and represent proofs and propositions, in the same way as is done in theorem provers based on type ....

....mentioned above, or we can indeed adopt an intermediate position of proving properties seen as crucial while asserting the validity of others. 6 Conclusion We have proposed a new way to combine or rather, to integrate computer algebra and theorem proving. Our proposal is similar to [BCZ96] and [Buc96] in that theorem proving capabilities are incorporated in a computer algebra system. In the classification of possible combinations of computer algebra and theorem proving of [CH96] all these are instance of the subpackage approach. But the way in which we propose to do this is ....

Andrej Bauer, Edmund Clarke, and Xudong Zhao. Analytica - an experiment in combining theorem proving and symbolic computation. In Artificial Intelligence and Symbolic Mathematical Computation (AISMC3) , volume 1138 of Lecture Notes in Computer Science, pages 21--37. Springer, 1996.

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A. Bauer, E. Clarke, and X. Zhao. Analytica: an Experiment in Combining Theorem Proving and Symbolic Computation. J. of Autom. Reasoning, 21(3):295--325, 1998.

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A. Bauer, E. Clarke, and X. Zhao. Analytica--an Experiment in Combining Theorem Proving and Symbolic Computation. Journal of Automated Reasoning, 21(3):295--325, 1998.

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Bauer, A., Clarke, E., and Zhao, X. Analytica - an experiment in combining theorem proving and symbolic computation. Journal of Automated Reasoning 21 (1998), 295-325.

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Bauer, A., Clarke, E., Zhao, X., 1998. Analytica --- an experiment in combining theorem proving and symbolic computation. Journal of Automated Reasoning 21, 295--325.

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Bauer, A., Clarke, E. M., and Zhao, X. Analytica: - An Experiment in Combining Theorem Proving and Symbolic Computation. In International Conference on Arti cial Intelligence and Symbolic Mathematical Computation, AISMC-3, Steyr, Austria (1996), pp. 21-37.

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