Synopses & Reviews
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.
Synopsis
The automation of mathematical reasoning has been an important topic of research almost since computers were invented. The new technique of rippling, described here for the first time in book form, is designed to be an approach to mathematical reasoning that takes into account ideas of heuristics and searching. Rippling addresses the problem of combinatorial explosion which has proved a huge obstacle in the past, and the book offers a systematic and comprehensive introduction to this and to the wider subject of automated inductive theorem proving.
Synopsis
The new technique of rippling and its use in automated reasoning are described here. The method uses heuristics and search to help address the problem of combinatorial explosion. The book provides a unique, systematic and comprehensive introduction to this and to the wider subject of automated inductive theorem proving.
Table of Contents
Preface; 1. An introduction to rippling; 2. Varieties of rippling; 3. Productive use of failure; 4. A formal account of rippling; 5. The scope and limitations of rippling; 6. From rippling to a general methodology; 7. Conclusions; Appendix 1. An annotated calculus and a unification algorithm; Appendix 2. Definitions of functions used in this book; Bibliography; Index.