Rippling: Meta-Level Guidance for Mathematical Reasoning

Rippling: Meta-Level Guidance for Mathematical Reasoning

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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.The conditional version of the rewrite rule of inference is Cond -agt; Lhs =3- Rhs Cond E[Rhs(fagt;] E[Suh] Its parts are defined as follows. a€c The usual, forwards reading of this notation for rules of inference is aquot;i1 the formulas above the horizontal lineanbsp;...

Title:Rippling: Meta-Level Guidance for Mathematical Reasoning
Author:Alan Bundy
Publisher:Cambridge University Press - 2005-06-30


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