Rippling is a type of rewriting developed in inductive theorem proving for removing differences between terms; the induction conclusion is annotated to mark its differences from the induction hypothesis and rippling attempts to move these differences. Until now rippling has been primarily employed in proofs where there is a single induction hypothesis. This paper describes an extension to rippl...

Cells in the early stages of starvation-induced fruiting body development migrate in a highly organized periodic pattern of equispaced accumulations that move as traveling waves. Two sets of waves are observed moving in opposite directions with the same wavelength and speed. To learn how the behavior of individual cells contributes to the wave pattern, fluorescent cells were tracked within a ri...

Rippling muscle disease (RMD) is a benign myopathy with symptoms and signs of muscular hyperirritability. We report a 17-year-old patient who presented with muscular hypertrophy, local mounding on percussion, and a rippling phenomenon. Needle electromyography showed electrical silence during the rippling phenomenon. Muscle protein immunohistochemical analysis showed a partial deficiency of cave...

Rippling is a heuristic used to guide rewriting and is typically used for inductive theorem proving. We introduce a method to support case-analysis within rippling. Like earlier work, this allows goals containing if-statements to be proved automatically. The new contribution is that our method also supports case-analysis on datatypes. By locating the case-analysis as a step within rippling we a...

We present a succinct account of dynamic rippling, a technique used to guide the automation of inductive proofs. This simplifies termination proofs for rippling and hence facilitates extending the technique in ways that preserve termination. We illustrate this by extending rippling with a terminating version of middle-out reasoning for lemma speculation. This supports automatic speculation of s...

This paper studies the evolution mechanism of surface rippling in polymer nanofibers under axial stretching. This rippling phenomenon has been detected in as-electrospun polyacrylonitrile in recent single-fiber tension tests, and in electrospun polyimide nanofibers after imidization. We herein propose a one-dimensional nonlinear elastic model that takes into account the combined effect of surfa...

Diierence matching is a generalization of rst-order matching where terms are made identical both by variable instantiation and by structure hiding. After matching, the hidden structure may be removed by a type of controlled rewriting, called rippling, that leaves the rest of the term unaltered. Rippling has proved highly successful in inductive theorem proving. Diierence matching allows us to u...

The Rippling heuristic developed by the Mathematical Reasoning Group in the Dept of Artiicial Intelligence, Edinburgh is a proven method of reducing the search space for a proof by induction through the use of annotated rewrite rules in the induction step case. Rippling is one of the 'methods' of the Clam proof planning system, which is used by both students and researchers. The diiculty of und...

R.Dyckhoff, ed., International Conference TABLEAUX-2000, LNAI 1847, pp. 294–309, c ©Springer Verlag, 2000. Abstract. We present an approach to inductive theorem proving that integrates rippling-based rewriting into matrix-based logical proof search. The selection of appropriate connections in a matrix proof is guided by the symmetries between induction hypothesis and induction conclusion while ...