Theory of linear and integer programming
Theory of linear and integer programming
The Omega test: a fast and practical integer programming algorithm for dependence analysis
Proceedings of the 1991 ACM/IEEE conference on Supercomputing
SIAM Review
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Deciding Linear Inequalities by Computing Loop Residues
Journal of the ACM (JACM)
A compiled implementation of strong reduction
Proceedings of the seventh ACM SIGPLAN international conference on Functional programming
A Skeptic’s Approach to Combining HOL and Maple
Journal of Automated Reasoning
A new polynomial-time algorithm for linear programming
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
DATE '03 Proceedings of the conference on Design, Automation and Test in Europe - Volume 1
Extracting a data flow analyser in constructive logic
Theoretical Computer Science - Applied semantics: Selected topics
Proof-carrying code from certified abstract interpretation and fixpoint compression
Theoretical Computer Science - Applied semantics
A computational approach to pocklington certificates in type theory
FLOPS'06 Proceedings of the 8th international conference on Functional and Logic Programming
Verifying and reflecting quantifier elimination for presburger arithmetic
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Proving equalities in a commutative ring done right in coq
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Proving bounds for real linear programs in Isabelle/HOL
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Certified result checking for polyhedral analysis of bytecode programs
TGC'10 Proceedings of the 5th international conference on Trustworthly global computing
On the generation of positivstellensatz witnesses in degenerate cases
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
Formal study of plane delaunay triangulation
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
A modular integration of SAT/SMT solvers to coq through proof witnesses
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Modular SMT proofs for fast reflexive checking inside coq
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Tactics for reasoning modulo AC in coq
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Certification of bounds of non-linear functions: the templates method
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
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When goals fall in decidable logic fragments, users of proof-assistants expect automation. However, despite the availability of decision procedures, automation does not come for free. The reason is that decision procedures do not generate proof terms. In this paper, we show how to design efficient and lightweight reflexive tactics for a hierarchy of quantifier-free fragments of integer arithmetics. The tactics can cope with a wide class of linear and non-linear goals. For each logic fragment, off-the-shelf algorithms generate certificates of infeasibility that are then validated by straightforward reflexive checkers proved correct inside the proof-assistant. This approach has been prototyped using the Coq proofassistant. Preliminary experiments are promising as the tactics run fast and produce small proof terms.