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
Using Reflection to Build Efficient and Certified Decision Procedures
TACS '97 Proceedings of the Third International Symposium on Theoretical Aspects of Computer Software
A Simple Model for Quotient Types
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Journal of Functional Programming
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
A tactic language for the system Coq
LPAR'00 Proceedings of the 7th international conference on Logic for programming and automated reasoning
Implementing the cylindrical algebraic decomposition within the Coq system
Mathematical Structures in Computer Science
Context Aware Calculation and Deduction
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Certified Size-Change Termination
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
MetiTarski: An Automatic Theorem Prover for Real-Valued Special Functions
Journal of Automated Reasoning
Extending a resolution prover for inequalities on elementary functions
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Fast reflexive arithmetic tactics the linear case and beyond
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Improving Coq propositional reasoning using a lazy CNF conversion scheme
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Untyping typed algebraic structures and colouring proof nets of cyclic linear logic
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Certifying compilers using higher-order theorem provers as certificate checkers
Formal Methods in System Design
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
A formalization of polytime functions
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
How to make ad hoc proof automation less ad hoc
Proceedings of the 16th ACM SIGPLAN international conference on Functional programming
Defining and reasoning about recursive functions: a practical tool for the coq proof assistant
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
PADL'10 Proceedings of the 12th international conference on Practical Aspects of Declarative Languages
Formal global optimisation with taylor models
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
An efficient coq tactic for deciding kleene algebras
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Formalization of wu's simple method in coq
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
Full reduction at full throttle
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Towards a formal foundation of behavioral types for UML state-machines
ACM SIGSOFT Software Engineering Notes
Kleene algebra with tests and coq tools for while programs
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
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We present a new implementation of a reflexive tactic which solves equalities in a ring structure inside the Coq system. The efficiency is improved to a point that we can now prove equalities that were previously beyond reach. A special care has been taken to implement efficient algorithms while keeping the complexity of the correctness proofs low. This leads to a single tool, with a single implementation, which can be addressed for a ring or for a semi-ring, abstract or not, using the Leibniz equality or a setoid equality. This example shows that such reflective methods can be effectively used in symbolic computation.