Generalisation of Induction Formulae based on Proving by Symbolic Execution

17 pages•Published: June 22, 2012

Abstract

Induction is a powerful method that can be used to prove the total correctness of program loops. Unfortunately the induction proving process in an interactive theorem prover is often very cumbersome. In particular it can be difficult to find the right induction formula. We describe a method for generalising induction formulae by analysing a symbolic proof attempt in a semi-interactive first-order theorem prover. Based on the proof attempt we introduce universally quantified variables, meta-variables and sets of constraints on these. The constraints describe the conditions for a successful proof. By the help of examples, we outline some classes of problems and their associated constraint solutions, and possible ways to automate the constraint solving.

In: Andrei Voronkov, Laura Kovacs and Nikolaj Bjorner (editors). WING 2010. Workshop on Invariant Generation 2010, vol 1, pages 187-203.

Links:	https://easychair.org/publications/paper/Bpc
	https://doi.org/10.29007/72nn

BibTeX entry

@inproceedings{WING2010:Generalisation_Induction_Formulae_based,
  author    = {Angela Wallenburg},
  title     = {Generalisation of Induction Formulae based on Proving by Symbolic Execution},
  booktitle = {WING 2010. Workshop on Invariant Generation 2010},
  editor    = {Andrei Voronkov and Laura Kovacs and Nikolaj Bjorner},
  series    = {EPiC Series in Computing},
  volume    = {1},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/Bpc},
  doi       = {10.29007/72nn},
  pages     = {187-203},
  year      = {2012}}

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