Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Constructing recursion operators in intuitionistic type theory
Journal of Symbolic Computation
Mathematica: a system for doing mathematics by computer
Mathematica: a system for doing mathematics by computer
Algorithms for computer algebra
Algorithms for computer algebra
Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Synthesis of ML programs in the system Coq
Journal of Symbolic Computation - Special issue on automatic programming
A survey of the Theorema project
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
A Skeptic’s Approach to Combining HOL and Maple
Journal of Automated Reasoning
Analytica – An Experiment in Combining Theorem Proving and Symbolic Computation
Journal of Automated Reasoning
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
PVS: Combining Specification, Proof Checking, and Model Checking
FMCAD '96 Proceedings of the First International Conference on Formal Methods in Computer-Aided Design
Expressing Computational Complexity in Constructive Type Theory
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
A Certified Version of Buchberger's Algorithm
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
Enhancing the Nuprl Proof Development System and Applying it to Computational Abstract Algebra
Enhancing the Nuprl Proof Development System and Applying it to Computational Abstract Algebra
Theorem Proving with the Real Numbers
Theorem Proving with the Real Numbers
A Certified Polynomial-Based Decision Procedure for Propositional Logic
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Implementing the cylindrical algebraic decomposition within the Coq system
Mathematical Structures in Computer Science
Providing a formal linkage between MDG and HOL
Formal Methods in System Design
Dependent Types, Theorem Proving, and Applications for a Verifying Compiler
Verified Software: Theories, Tools, Experiments
Certifying properties of an efficient functional program for computing Gröbner bases
Journal of Symbolic Computation
A verified Common Lisp implementation of Buchberger's algorithm in ACL2
Journal of Symbolic Computation
Proof certificates for algebra and their application to automatic geometry theorem proving
ADG'08 Proceedings of the 7th international conference on Automated deduction in geometry
Gröbner bases: theory refinement in the mizar system
MKM'05 Proceedings of the 4th international conference on Mathematical Knowledge Management
Proving formally the implementation of an efficient gcd algorithm for polynomials
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Towards a certified and efficient computing of gröbner bases
EUROCAST'05 Proceedings of the 10th international conference on Computer Aided Systems Theory
Constructive formalization of hybrid logic with eventualities
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
| Hi-index | 0.00 |
We present an implementation of Buchberger's algorithm that has been proved correct within the proof assistant Coq. The implementation contains the basic algorithm plus two standard optimizations.