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In this short position paper we briefly review the development history of automated inductive theorem proving and computer-assisted mathematical induction. ... Our main motivation is to explain--on an abstract but hopefully sufficiently descriptive level--why we believe that future progress in the field is to result from human-orientedness and descente infinie ... Moreover, it is a pleasure to thank Tobias for the wonderful years we shared working on QUODLIBET and descente infinie. ...doi:10.1093/jigpal/jzr048 fatcat:qps74fzzmngmzaluxlcaqogt4y
We review the history of the automation of mathematical induction ... Why descente infinie and human-orientedness should remain on the agenda for induction in mathematics assistance systems is explained in the manifesto [ Wirth, 2012c ] . ... areas of automated theorem proving with bigger search spaces and, in particular, in descente infinie. ...arXiv:1309.6226v5 fatcat:i7nzngq47zfd7its4kfynlfpti
Using a human-oriented formal example proof of the (lim+) theorem, i.e. that the sum of limits is the limit of the sum, which is of value for reference on its own, we exhibit a non-permutability of beta-steps ... and delta+-steps (according to Smullyan's classification), which is not visible with non-liberalized delta-rules and not serious with further liberalized delta-rules, such as the delta++-rule. ... I would also like to thank the lecturers and students of the course (Autexier et al., 2004/05) ...doi:10.1016/j.jsc.2011.12.035 fatcat:g2uh2ml62zgi7bnoffo74dczgi
Shallow confluence implies [level] confluence, has applications in functional logic programming, and guarantees the object-level consistency of the underlying data types in the inductive theorem prover ... To this end, we restrict the introduction of extra variables of right-hand sides to binding equations and require the critical pairs to have somehow complementary literals in their conditions. ... Notes Note 1 to Section 1.2 (Literature on Explicit Induction) For the inductive theorem proving software system Nqthm cf. Moore (1979, 1988). For Inka cf. e.g. Autexier et al. (1999) . ...doi:10.1016/j.jsc.2008.05.005 fatcat:zjp4ce43onbfxbt3sv5g5wndoq