Analytica – An Experiment in Combining Theorem Proving and Symbolic Computation

  • Authors:

  • Andrej Bauer;Edmund Clarke;Xudong Zhao

  • Affiliations:

  • School of Computer Science, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, U.S.A. e-mail: andrej@cs.cmu.edu/ emc@cs.cmu.edu;School of Computer Science, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, U.S.A. e-mail: andrej@cs.cmu.edu/ emc@cs.cmu.edu;Mail Stop: JFT-102, Intel Corporation, 2111 N.E. 25th Ave., Hillsboro, OR 97124, U.S.A. e-mail: xzhao@cs.cmu.edu

  • Venue:
  • Journal of Automated Reasoning
  • Year:
  • 1998

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Abstract

Analytica is an automatic theorem prover for theorems in elementaryanalysis. The prover is written in the Mathematica language and runs in theMathematica environment. The goal of the project is to use a powerfulsymbolic computation system to prove theorems that are beyond the scope ofprevious automatic theorem provers. The theorem prover is also able todeduce the correctness of certain simplification steps that would otherwisenot be performed. We describe the structure of Analytica and explain themain techniques that it uses to construct proofs. Analytica has been able toprove several nontrivial theorems. In this paper, we show how it can prove aseries of lemmas that lead to the Bernstein approximation theorem.