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A Skeptic's Approach to Combining HOL and Maple
- J. Harrison, Laurent Théry
- Computer Science, MathematicsJournal of Automated Reasoning
- 1 December 1998
A systematic separation of search for a solution and checking the solution, using a physical connection between systems, is described in some detail, relating it to proof planning and to the complexity class NP, and different ways of exploiting a physical link between systems.
A Modular Integration of SAT/SMT Solvers to Coq through Proof Witnesses
- Michaël Armand, G. Faure, B. Grégoire, Chantal Keller, Laurent Théry, Benjamin Werner
- Computer ScienceCPP
- 7 December 2011
A way to enjoy the power of SAT and SMT provers in Coq without compromising soundness is presented, conceived in a modular way, in order to tame the proofs' complexity and to be extendable.
A Machine-Checked Proof of the Odd Order Theorem
This paper reports on a six-year collaborative effort that culminated in a complete formalization of a proof of the Feit-Thompson Odd Order Theorem in the Coq proof assistant, using a comprehensive set of reusable libraries of formalized mathematics.
Extending Coq with Imperative Features and Its Application to SAT Verification
This paper presents two extensions of the evaluation mechanism that preserve its correctness and make it possible to deal with cpu-intensive tasks such as proof checking of SAT traces.
Proof by Pointing
This principle provides a natural and effective use of the mouse in the user-interface of computer proof assistants and annotates the inference rules to specify an algorithm that associates the construction of a proof tree to a location within a goal sequent.
A Modular Formalisation of Finite Group Theory
- Georges Gonthier, A. Mahboubi, L. Rideau, E. Tassi, Laurent Théry
- Mathematics, Computer ScienceTPHOLs
- 10 September 2007
This work is the first milestone of a long-term effort to formalise the Feit-Thompson theorem and took special care to articulate it in the most compositional way.
A Generic Library for Floating-Point Numbers and Its Application to Exact Computing
A general library to reason about floating-point numbers within the Coq system with a special emphasis on proving properties for exact computing, i.e. computing without rounding errors.
Extracting Text from Proofs
A transducer is described from proof objects to pseudo natural language that has been implemented for the Coq system to present formal proofs in an intelligible form.
A Machine-Checked Implementation of Buchberger's Algorithm
- Laurent Théry
- Computer ScienceJournal of Automated Reasoning
- 1 February 2001
This work presents an implementation of Buchberger's algorithm that has been proved correct within the proof assistant Coq and contains the basic algorithm plus two standard optimizations.
Theorem Proving in Higher Order Logics
This paper introduces disjoint sums over type classes containing possibly a countably infinite number of monomorphic types and presents a monomorphic sum type together with an overloaded function which represents the family of injections.