Proving Equalities in a Commutative Ring Done Right in Coq

• Published in: Lecture notes in computer science pp. 98 - 113
• Main Authors: Grégoire, Benjamin, Mahboubi, Assia
• Format: Book Chapter Conference Proceeding
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 01.01.2005; Springer
• Series: Lecture Notes in Computer Science
• Subjects: Applied sciences; Computer Algebra System; Computer science; control theory; systems; Decision Procedure; Exact sciences and technology; Logical, boolean and switching functions; Normal Form; Polynomial Expression; Proof Assistant; Theoretical computing; Theorem proving; Algorithm complexity; High order logic; Commutative ring; Proof theory; Program verification; Ring structure
• ISBN: 3540283722; 9783540283720
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/11541868_7

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.