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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