@MISC{Smith91acomputational, author = {Scott Smith}, title = {A Computational Induction Principle}, year = {1991} }

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Abstract

It is critical to have an induction method for reasoning about recursive programs expressed as fixed points, for otherwise our reasoning ability is severely impaired. The fixed point induction rule developed by deBakker and Scott is one such well known principle. Here we propose a new induction method, computational induction, which is an induction on the computation process. Computational induction is founded on different principles than the fixed point induction principle---it can only be defined in deterministic settings, and it cannot be modeled denotationally. Fixed point induction and computational induction prove many of the same facts; the relation between the two is examined in detail. 1 Introduction In a theory for reasoning about programs, in particular recursive functions defined via fixed points, there must exist induction principles if interesting results are to be proven. A number of different induction principles have been developed; for a review, see [Man74]. Author'...