Completion of a set of rules modulo a set of equations
SIAM Journal on Computing
Information and Computation - Semantics of Data Types
Unification in a combination of arbitrary disjoint equational theories
Journal of Symbolic Computation
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Conditional rewriting logic as a unified model of concurrency
Selected papers of the Second Workshop on Concurrency and compositionality
Confluence properties of weak and strong calculi of explicit substitutions
Journal of the ACM (JACM)
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
Autarkic Computations in Formal Proofs
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
Inductive Definitions in the system Coq - Rules and Properties
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
An Interface between Clam and HOL
Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics
Faster Proof Checking in the Edinburgh Logical Framework
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Ordered Rewriting and Confluence
Proceedings of the 10th International Conference on Automated Deduction
Automated Proof Construction in Type Theory Using Resolution
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Proof-assistants using dependent type systems
Handbook of automated reasoning
Efficient Representation and Validation of Proofs
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Definitions by Rewriting in the Calculus of Constructions
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Journal of Automated Reasoning
A ρ-calculus of explicit constraint application
Higher-Order and Symbolic Computation
Certification of Automated Termination Proofs
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
A3PAT, an approach for certified automated termination proofs
Proceedings of the 2010 ACM SIGPLAN workshop on Partial evaluation and program manipulation
Validation of the JavaCard platform with implicit induction techniques
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Rule-based programming and proving: the ELAN experience outcomes
ASIAN'04 Proceedings of the 9th Asian Computing Science conference on Advances in Computer Science: dedicated to Jean-Louis Lassez on the Occasion of His 5th Cycle Birthday
Term rewriting meets aspect-oriented programming
Processes, Terms and Cycles
Tactics for reasoning modulo AC in coq
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Rewriting Computation and Proof
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This paper presents the design, the implementation, and experiments of the integration of syntactic, conditional possibly associative-commutative term rewriting into proof assistants based on constructive type theory. Our approach is called external because it consists in performing term rewriting in a specific and efficient environment and checking the computations later in a proof assistant. Two typical systems are considered in this work: ELAN, based on the rewriting calculus, as the term rewriting-based environment, and Coq, based on the calculus of inductive constructions as the proof assistant. We first formalize the proof terms for deduction by rewriting and strategies in ELAN using the rewriting calculus with explicit substitutions. We then show how these proof terms can soundly be translated into Coq syntax where they can be directly type checked. For the method to be applicable for rewriting modulo associativity and commutativity, we provide an effective method to prove equalities modulo these axioms in Coq using ELAN. These results have been integrated into an ELAN-based rewriting tactic in Coq.