Computer proofs of limit theorems

  • Authors:

  • W. W. Bledsoe;Robert S. Boyer;William H. Henneman

  • Affiliations:

  • Massachusetts Institute of Technology, University of Texas;Massachusetts Institute of Technology, University of Texas;Massachusetts Institute of Technology, University of Texas

  • Venue:
  • IJCAI'71 Proceedings of the 2nd international joint conference on Artificial intelligence
  • Year:
  • 1971

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Abstract

Some relatively simple concepts have been developed which, when incorporated into existing automatic theorem proving programs (including those using resolution), enable them to prove efficiently a number of the limit theorems of elementary calculus, including the theorem that differentiate functions are continuous. These concepts include: (1) A limited theory of types, to designate whether a given variable belongs to a certain interval on the real line, (2) An algebraic simplification routine, (3) A routine for solving linear inequalities, applicable to all areas of analysis, and (4) A "limit heuristic", designed especially for the limit theorems of calculus.