Director strings as combinators
ACM Transactions on Programming Languages and Systems (TOPLAS)
A call-by-need lambda calculus
POPL '95 Proceedings of the 22nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Confluence properties of weak and strong calculi of explicit substitutions
Journal of the ACM (JACM)
YALE: yet another lambda evaluator based on interaction nets
ICFP '98 Proceedings of the third 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
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
Functional runtime systems within the lambda-sigma calculus
Journal of Functional Programming
An interaction net implementation of closed reduction
IFL'08 Proceedings of the 20th international conference on Implementation and application of functional languages
Extending the explicit substitution paradigm
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Sharing in the weak lambda-calculus
Processes, Terms and Cycles
Encoding strategies in the lambda calculus with interaction nets
IFL'05 Proceedings of the 17th international conference on Implementation and Application of Functional Languages
On Explicit Substitution with Names
Journal of Automated Reasoning
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Closed reductions in the λ-calculus is a strategy for a calculus of explicit substitutions which overcomes many of the usual syntactical problems of substitution. This is achieved by only moving closed substitutions through certain constructs, which gives a weak form of reduction, but is rich enough to capture the usual strategies in the λ-calculus (call-by-value, call-by-need, etc.) and is adequate for the evaluation of programs. An interesting point is that the calculus permits substitutions to move through abstractions, and reductions are allowed under abstractions, if certain conditions hold. The calculus naturally provides an efficient notion of reduction (with a high degree of sharing), which can easily be implemented.