Completion of a set of rules modulo a set of equations
SIAM Journal on Computing
A rewriting system for categorical combinators with multiple arguments
SIAM Journal on Computing
A gentle introduction to Haskell
ACM SIGPLAN Notices - Haskell special issue
From λσ to λν: a journey through calculi of explicit substitutions
POPL '94 Proceedings of the 21st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Confluence properties of weak and strong calculi of explicit substitutions
Journal of the ACM (JACM)
Higher order unification via explicit substitutions
Information and Computation
Software—Practice & Experience
POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
External Rewriting for Skeptical Proof Assistants
Journal of Automated Reasoning
Exceptions in the Rewriting Calculus
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
X.R.S: Explicit Reduction Systems - A First-Order Calculus for Higher-Order Calculi
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
Combinatory Reduction Systems with Explicit Substitution that Preserve Strong Nomalisation
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Church-Rosser Theorems for Abstract Reduction Modulo an Equivalence Relation
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
A λ-calculus with explicit weakening and explicit substitution
Mathematical Structures in Computer Science
iRho: an imperative rewriting calculus
PPDP '04 Proceedings of the 6th ACM SIGPLAN international conference on Principles and practice of declarative programming
Choices in Representation and Reduction Strategies for Lambda Terms in Intensional Contexts
Journal of Automated Reasoning
Formal validation of pattern matching code
PPDP '05 Proceedings of the 7th ACM SIGPLAN international conference on Principles and practice of declarative programming
Journal of Logic and Computation
A pattern matching compiler for multiple target languages
CC'03 Proceedings of the 12th international conference on Compiler construction
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
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Theoretical presentations of the rewriting or ρ-calculusoften treat the matching constraint computations as an atomicoperation although matching constraints are explicitly expressed.Actual implementations have to take a more realistic view:computations needed in order to find the solutions of a matchingequation can have an important impact on the (efficiency of the)calculus for some matching theories and the substitutionapplication usually involves a term traversal.Following the works on explicit substitutions in theρ-calculus, we present two versions of the ρ-calculus, onewith explicit matching and one with explicitsubstitutions, together with a version that combines the twoand considers efficiency issues and more precisely thecomposition of substitutions. The approach is general,allowing for potential extensions to various matching theories. Weestablish the confluence of the calculus and the termination of theexplicit constraint handling and application sub-calculus.