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  3. Rippling: Meta-Level Guidance for Mathematical Reasoning
  • Cited by 66
Publisher:
Cambridge University Press
Online publication date:
August 2009
Print publication year:
2005
Online ISBN:
9780511543326
DOI:
https://doi.org/10.1017/CBO9780511543326
Subjects:
Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Logic, Categories and Sets, Computer Science
Series:
Cambridge Tracts in Theoretical Computer Science (56)
Information

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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