Theoretical Computer Science
Control delimiters and their hierarchies
Lisp and Symbolic Computation
LFP '90 Proceedings of the 1990 ACM conference on LISP and functional programming
Representing control in the presence of first-class continuations
PLDI '90 Proceedings of the ACM SIGPLAN 1990 conference on Programming language design and implementation
An algorithm for optimal lambda calculus reduction
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A formulae-as-type notion of control
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Linear graph reduction: confronting the cost of naming
Linear graph reduction: confronting the cost of naming
The geometry of optimal lambda reduction
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Programs with continuations and linear logic
TACS'91 Selected papers of the conference on Theoretical aspects of computer software
POPL '94 Proceedings of the 21st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A generic account of continuation-passing styles
POPL '94 Proceedings of the 21st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
ESOP'92 Selected papers of the symposium on Fourth European symposium on programming
Reasoning about programs in continuation-passing style
Lisp and Symbolic Computation - Special issue on continuations—part I
Representing control in the presence of one-shot continuations
PLDI '96 Proceedings of the ACM SIGPLAN 1996 conference on Programming language design and implementation
YALE: yet another lambda evaluator based on interaction nets
ICFP '98 Proceedings of the third ACM SIGPLAN international conference on Functional programming
Lambda-My-Calculus: An Algorithmic Interpretation of Classical Natural Deduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
Paths, Computations and Labels in the Lambda-Calculus
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
deltao!Epsilon = 1 - Optimizing Optimal lambda-Calculus Implementations
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
Extracting constructive content from classical proofs
Extracting constructive content from classical proofs
Proofnets and Context Semantics for the Additives
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Hi-index | 0.00 |
We introduce graph reduction technology that implements functional languages with control, such as Scheme with call/cc, where continuations can be manipulated explicitly as values, and can be optimally reduced in the sense of LÉvy. The technology is founded on proofnets for multiplicative-exponential linear logic, extending the techniques originally proposed by Lamping, where we adapt the continuation-passing style transformation to yield a new understanding of sharable values. Confluence is maintained by returning multiple answers to a (shared) continuation. Proofnets provide a concurrent version of linear logic proofs, eliminating structurally irrelevant sequentialization, and ignoring asymmetric distinctions between inputs and outputs--dually, expressions and continuations. While Lamping's graphs and their variants encode an embedding of intuitionistic logic into linear logic, our construction implicitly contains an embedding of classical logic into linear logic. We propose a family of translations, produced uniformly by beginning with a continuation-passing style semantics for the languages, employing standard codings into proofnets using call-by-value, call-by-name--or hybrids of the two--to locate proofnet boxes, and converting the proofnets to direct style. The resulting graphs can be reduced simply (cut elimination for linear logic), have a consistent semantics that is preserved by reduction (geometry of interaction, via the so-called context semantics), and allow shared, incremental evaluation of continuations (optimal reduction).