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Analytica — An experiment in combining theorem proving and symbolic computation

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Artificial Intelligence and Symbolic Mathematical Computation (AISMC 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1138))

Abstract

Analytica is an automatic theorem prover for theorems in elementary analysis. The prover is written in Mathematica language and runs in the Mathematica environment. The goal of the project is to use a powerful symbolic computation system to prove theorems that are beyond the scope of previous automatic theorem provers. The theorem prover is also able to guarantee the correctness of certain steps that are made by the symbolic computation system and therefore prevent common errors like division by a symbolic expression that could be zero.

We describe the structure of Analytica and explain the main techniques that it uses to construct proofs. Analytica has been able to prove several non-trivial theorems. In this paper, we show how it can prove a series of lemmas that lead to Bernstein approximation theorem.

This research was sponsored in part by the National Science Foundation under grant no. CCR-8722633, by the Semiconductor Research Corporation under contract 92-DJ-294, and by the Wright Laboratory, Aeronautical Systems Center, Air Force Materiel Command, USAF, and the Advanced Research Projects Agency (ARPA) under grant F33615-93-1-1330.

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Author information

Authors and Affiliations

  1. School of Computer Science, Carnegie Mellon University, 5000 Forbes Avenue, 15213, Pittsburgh, PA, USA

    Andrej Bauer, Edmund Clarke & Xudong Zhao

Authors
  1. Andrej Bauer
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  2. Edmund Clarke
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  3. Xudong Zhao
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Editor information

Jacques Calmet John A. Campbell Jochen Pfalzgraf

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© 1996 Springer-Verlag Berlin Heidelberg

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Bauer, A., Clarke, E., Zhao, X. (1996). Analytica — An experiment in combining theorem proving and symbolic computation. In: Calmet, J., Campbell, J.A., Pfalzgraf, J. (eds) Artificial Intelligence and Symbolic Mathematical Computation. AISMC 1996. Lecture Notes in Computer Science, vol 1138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61732-9_48

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  • DOI: https://doi.org/10.1007/3-540-61732-9_48

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61732-7

  • Online ISBN: 978-3-540-70740-0

  • eBook Packages: Springer Book Archive

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