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  3. Rippling: Meta-Level Guidance for Mathematical Reasoning
  • Cited by 66
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    • Publisher:
      Cambridge University Press
      Publication date:
      August 2009
      June 2005
      ISBN:
      9780511543326
      9780521834490
      DOI:
      https://doi.org/10.1017/CBO9780511543326
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.475kg, 216 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Logic, Categories and Sets, Computer Science
      Series:
      Cambridge Tracts in Theoretical Computer Science (56)
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    Subjects:
    Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Logic, Categories and Sets, Computer Science
    Series:
    Cambridge Tracts in Theoretical Computer Science (56)
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    Book description

    Rippling is a radically new technique for the automation of mathematical reasoning. It is widely applicable whenever a goal is to be proved from one or more syntactically similar givens. It was originally developed for inductive proofs, where the goal was the induction conclusion and the givens were the induction hypotheses. It has proved to be applicable to a much wider class of tasks, from summing series via analysis to general equational reasoning. The application to induction has especially important practical implications in the building of dependable IT systems, and provides solutions to issues such as the problem of combinatorial explosion. Rippling is the first of many new search control techniques based on formula annotation; some additional annotated reasoning techniques are also described here. This systematic and comprehensive introduction to rippling, and to the wider subject of automated inductive theorem proving, will be welcomed by researchers and graduate students alike.

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