Computational interpretations of linear logic
Theoretical Computer Science - Special volume of selected papers of the Sixth Workshop on the Mathematical Foundations of Programming Semantics, Kingston, Ont., Canada, May 1990
Handbook of logic in computer science (vol. 2)
A call-by-need lambda calculus
POPL '95 Proceedings of the 22nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Combinatory weak reduction in lambda calculus
Theoretical Computer Science
Tree-Manipulating Systems and Church-Rosser Theorems
Journal of the ACM (JACM)
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
HOL-λσ: an intentional first-order expression of higher-order logic
Mathematical Structures in Computer Science
A λ-calculus with explicit weakening and explicit substitution
Mathematical Structures in Computer Science
Functional runtime systems within the lambda-sigma calculus
Journal of Functional Programming
Efficient reductions with director strings
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Choices in Representation and Reduction Strategies for Lambda Terms in Intensional Contexts
Journal of Automated Reasoning
Nominal rewriting with name generation: abstraction vs. locality
PPDP '05 Proceedings of the 7th ACM SIGPLAN international conference on Principles and practice of declarative programming
Information and Computation
A Fully Labelled Lambda Calculus: Towards Closed Reduction in the Geometry of Interaction Machine
Electronic Notes in Theoretical Computer Science (ENTCS)
The Power of Closed Reduction Strategies
Electronic Notes in Theoretical Computer Science (ENTCS)
Complete Laziness: a Natural Semantics
Electronic Notes in Theoretical Computer Science (ENTCS)
Minimality in a Linear Calculus with Iteration
Electronic Notes in Theoretical Computer Science (ENTCS)
Token-passing Nets for Functional Languages
Electronic Notes in Theoretical Computer Science (ENTCS)
Encoding the Pure Lambda Calculus into Hierarchical Graph Rewriting
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
New Developments in Environment Machines
Electronic Notes in Theoretical Computer Science (ENTCS)
Electronic Notes in Theoretical Computer Science (ENTCS)
Theoretical Computer Science
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Linearity and recursion in a typed Lambda-calculus
Proceedings of the 13th international ACM SIGPLAN symposium on Principles and practices of declarative programming
Linearity and iterator types for Gödel's System
Higher-Order and Symbolic Computation
An interaction net implementation of closed reduction
IFL'08 Proceedings of the 20th international conference on Implementation and application of functional languages
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Call-by-name and call-by-value as token-passing interaction nets
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
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Starting from the $\lambda$-calculus with names, we develop a family of calculi with explicit substitutions that overcome the usual syntactical problems of substitution. The key idea is that only closed substitutions can be moved through certain constructs. This gives a weak form of reduction, called closed reduction, which is rich enough to capture both the call-by-value and call-by-name evaluation strategies in the $\lambda$-calculus. Moreover, since substitutions can move through abstractions and reductions are allowed under abstractions (if certain conditions hold), closed reduction naturally provides an efficient notion of reduction with a high degree of sharing and low overheads. We present a family of abstract machines for closed reduction. Our benchmarks show that closed reduction performs better than all standard weak strategies, and its low overheads make it more efficient than optimal reduction in many cases.