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Computer-assisted human-oriented inductive theorem proving by descente infinie--a manifesto

C.-P. Wirth
2012 Logic Journal of the IGPL  
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

Automation of Mathematical Induction as part of the History of Logic [article]

J Strother Moore, Claus-Peter Wirth
2014 arXiv   pre-print
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

, , and Non-Permutability of -Steps

Claus-Peter Wirth
2012 Journal of symbolic computation  
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 of conditional term rewriting systems

Claus-Peter Wirth
2009 Journal of symbolic computation  
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