Confluence results for the pure strong categorical logic CCL. &lgr;-calculi as subsystems of CCL
Theoretical Computer Science
Handbook of logic in computer science (vol. 2)
Confluence properties of weak and strong calculi of explicit substitutions
Journal of the ACM (JACM)
Categorical Combinators, Sequential Algorithms and Funtional Programming
Categorical Combinators, Sequential Algorithms and Funtional Programming
Typed lambda-calculi with explicit substitutions may not terminate
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
A Lambda-Calculus `a la de Bruijn with Explicit Substitutions
PLILPS '95 Proceedings of the 7th International Symposium on Programming Languages: Implementations, Logics and Programs
Confluence and Preservation of Strong Normalisation in an Explicit Substitutions Calculus
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Characterising Explicit Substitutions which Preserve Termination
TLCA '99 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications
TLCA '99 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications
Characterising Strong Normalisation for Explicit Substitutions
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
TYPES '98 Selected papers from the International Workshop on Types for Proofs and Programs
Tradeoffs in the Intensional Representation of Lambda Terms
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
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
Explicit substitutions in the reduction of lambda terms
Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming
Reductions, intersection types, and explicit substitutions
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
Sequent combinators: a Hilbert system for the lambda calculus
Mathematical Structures in Computer Science
The λse-calculus does not preserve strong normalisation
Journal of Functional Programming
Intersection types for explicit substitutions
Information and Computation
Choices in Representation and Reduction Strategies for Lambda Terms in Intensional Contexts
Journal of Automated Reasoning
A treatment of higher-order features in logic programming
Theory and Practice of Logic Programming
Fundamenta Informaticae - Typed Lambda Calculi and Applications (TLCA'99)
Principal Typings for Explicit Substitutions Calculi
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Abstract Conditions for the Confluence of Explicit Substitution Calculi
Electronic Notes in Theoretical Computer Science (ENTCS)
Intersection type systems and explicit substitutions calculi
WoLLIC'10 Proceedings of the 17th international conference on Logic, language, information and computation
Fundamenta Informaticae - Typed Lambda Calculi and Applications (TLCA'99)
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The last 15 years have seen an explosion in work on explicit substitution, most of which is done in the style of the λσ-calculus. In Kamareddine and Ríos (1995a), we extended the λ-calculus with explicit substitutions by turning de Bruijn's meta-operators into object-operators offering a style of explicit substitution that differs from that of λσ. The resulting calculus, λs, remains as close as possible to the λ-calculus from an intuitive point of view and, while preserving strong normalisation (Kamareddine and Ríos, 1995a), is extended in this paper to a confluent calculus on open terms: the λse-caculus. Since the establishment of these results, another calculus, λζ, came into being in Muñoz Hurtado (1996) which preserves strong normalisation and is itself confluent on open terms. However, we believe that λse still deserves attention because, while offering a new style to work with explicit substitutions, it is able to simulate one step of classical β-reduction, whereas λζ is not. To prove confluence we introduce a generalisation of the interpretation method (cf. Hardin, 1989; Curien et al., 1992) to a technique which uses weak normal forms (instead of strong ones). We consider that this extended method is a useful tool to obtain confluence when strong normalisation of the subcalculus of substitutions is not available. In our case, strong normalisation of the corresponding subcalculus of substitutions se, is still a challenging open problem to the rewrite community, but its weak normalisation is established here via an effective strategy.