A new formula for the execution of categorical combinators
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Journal of Symbolic Computation
Confluence results for the pure strong categorical logic CCL. &lgr;-calculi as subsystems of CCL
Theoretical Computer Science
A rewriting system for categorical combinators with multiple arguments
SIAM Journal on Computing
An abstract frame work for environment machines
Theoretical Computer Science
Handbook of theoretical computer science (vol. B)
Handbook of logic in computer science (vol. 2)
Combinatory reduction systems: introduction and survey
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
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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)
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Explicit substitution on the edge of strong normalization
Theoretical Computer Science
Tree-Manipulating Systems and Church-Rosser Theorems
Journal of the ACM (JACM)
Confluence of extensional and non-extensional &lgr;-calculi with explicit substitutions
Theoretical Computer Science
Term Rewriting Systems
Typed lambda-calculi with explicit substitutions may not terminate
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Characterising Explicit Substitutions which Preserve Termination
TLCA '99 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications
On Explicit Substitution and Names (Extended Abstract)
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
A de Bruijn Notation for Higher-Order Rewriting
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
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
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
Proof nets and explicit substitutions
Mathematical Structures in Computer Science
A λ-calculus with explicit weakening and explicit substitution
Mathematical Structures in Computer Science
Resource operators for λ-calculus
Information and Computation
Information and Computation
Nominal Techniques in Isabelle/HOL
Journal of Automated Reasoning
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
The theory of calculi with explicit substitutions revisited
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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This paper recounts the origins of the 驴x family of calculi of explicit substitution with proper variable names, including the original result of preservation of strong β-normalization based on the use of synthetic reductions for garbage collection. We then discuss the properties of a variant of the calculus which is also confluent for "open" terms (with meta-variables), and verify that a version with garbage collection preserves strong β-normalization (as is the state of the art), and we summarize the relationship with other efforts on using names and garbage collection rules in explicit substitution.