Rippling: Meta-Level Guidance for Mathematical Reasoning

Front Cover
Cambridge University Press, Jun 30, 2005 - Computers - 202 pages
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.
 

Contents

2
2
2
16
Varieties of rippling
24
4
36
6
44
9
50
4
61
A formal account of rippling 3832
82
The scope and limitations of rippling
118
From rippling to a general methodology
144
Conclusions
175
Unification algorithm
183
Definitions of functions used in this book
190
Index
200
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