scholarly journals DefunT: A Tool for Automating Termination Proofs by Using the Community Books (Extended Abstract)

2018 ◽  
Vol 280 ◽  
pp. 161-163 ◽  
Author(s):  
Matt Kaufmann
Keyword(s):  
Termination Proofs

Modular and Incremental Automated Termination Proofs

2004 ◽  
Vol 32 (4) ◽  
pp. 315-355 ◽  
Author(s):  
Xavier Urbain
Keyword(s):  
Termination Proofs

scholarly journals Verifying a Solver for Linear Mixed Integer Arithmetic in Isabelle/HOL

2020 ◽  
pp. 233-250
Author(s):  
Ralph Bottesch ◽  
Max W. Haslbeck ◽  
Alban Reynaud ◽  
René Thiemann
Keyword(s):  
Linear Programming ◽  
Branch And Bound ◽  
Decision Procedure ◽  
Simplex Algorithm ◽  
Upper Bounds ◽  
Mixed Integer ◽  
Small Solution ◽  
Code Generator ◽  
Integer Arithmetic ◽  
Termination Proofs

AbstractWe implement a decision procedure for linear mixed integer arithmetic and formally verify its soundness in Isabelle/HOL. We further integrate this procedure into one application, namely into , a formally verified certifier to check untrusted termination proofs. This checking involves assertions of unsatisfiability of linear integer inequalities; previously, only a sufficient criterion for such checks was supported. To verify the soundness of the decision procedure, we first formalize the proof that every satisfiable set of linear integer inequalities also has a small solution, and give explicit upper bounds. To this end we mechanize several important theorems on linear programming, including statements on integrality and bounds. The procedure itself is then implemented as a branch-and-bound algorithm, and is available in several languages via Isabelle’s code generator. It internally relies upon an adapted version of an existing verified incremental simplex algorithm.

scholarly journals Certification of Automated Termination Proofs

2007 ◽  
pp. 148-162 ◽  
Author(s):  
Evelyne Contejean ◽  
Pierre Courtieu ◽  
Julien Forest ◽  
Olivier Pons ◽  
Xavier Urbain
Keyword(s):  
Termination Proofs
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