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)
Functional back-ends within the lambda-sigma calculus
Proceedings of the first ACM SIGPLAN international conference on Functional programming
Typed lambda-calculi with explicit substitutions may not terminate
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Explicit Substitutions with de Bruijn's Levels
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
Higher-order Unification via Explicit Substitutions
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Proof-term synthesis on dependent-type systems via explicit substitutions
Theoretical Computer Science
Characterising Explicit Substitutions which Preserve Termination
TLCA '99 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications
TYPES '98 Selected papers from the International Workshop on Types for Proofs and Programs
Using Fields and Explicit Substitutions to Implement Objects and Functions in a de Bruijn Setting
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
Closed Reductions in the lambda-Calculus
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
Perpetuality in a named lambda calculus with explicit substitutions
Mathematical Structures in Computer Science
Dependent types and explicit substitutions: a meta-theoretical development
Mathematical Structures in Computer Science
Cut rules and explicit substitutions
Mathematical Structures in Computer Science
A λ-calculus with explicit weakening and explicit substitution
Mathematical Structures in Computer Science
Journal of Functional Programming
Choices in Representation and Reduction Strategies for Lambda Terms in Intensional Contexts
Journal of Automated Reasoning
Closed reduction: explicit substitutions without $\alpha$-conversion
Mathematical Structures in Computer Science
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Explicit substitutions calculi are formal systems that implement beta-reduction by means of an internal substitution operator. In that calculi it is possible to delay the application of a substitution to a term or to consider terms with partially applied substitutions. The lambda-sigma-calculus of explicit substitutions, proposed by Abadi, Cardelli, Curien and Levy, is a first-order rewriting system that implements substitution and renaming mechanism of lambda-calculus. However, lambda-sigma does not preserve strong normalisation of lambda-calculus and it is not a confluent system. Typed variants of lambda-sigma without composition are strongly normalising but not confluent, while variants with composition are confluent but do not preserve strong normalisation. Neither of them enjoys both properties. In this paper we propose the lambda-zeta-calculus. This is, as far as we know, the first confluent calculus of explicit substitutions that preserves strong normalisation.