Abstract

We present an Isabelle/HOL formalization and total correctness proof for the incremental version of the Simplex algorithm which is used in most state-of-the-art SMT solvers. It supports extraction of satisfying assignments, extraction of unsatisfiable cores, incremental assertion of constraints and backtracking. Formalization relies on stepwise program refinement, starting from a simple specification, going through a number of refinement steps, and ending up in a fully executable functional implementation. Symmetries present in the algorithm are handled with special care.

BibTeX

@article{Simplex-AFP,
  author  = {Filip Mari\'c and Mirko Spasi\'c and Ren\'e Thiemann},
  title   = {An Incremental Simplex Algorithm with Unsatisfiable Core Generation},
  journal = {Archive of Formal Proofs},
  month   = aug,
  year    = 2018,
  note    = {\url{http://isa-afp.org/entries/Simplex.html},
            Formal proof development},
  ISSN    = {2150-914x},
}