Theoretical Computer Science
An algorithm for optimal lambda calculus reduction
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A simple proof of a theorem of Statman
Theoretical Computer Science
The geometry of optimal lambda reduction
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Optimality and inefficiency: what isn't a cost model of the lambda calculus?
Proceedings of the first ACM SIGPLAN international conference on Functional programming
On the complexity of beta-reduction
POPL '96 Proceedings of the 23rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
On global dynamics of optimal graph reduction
ICFP '97 Proceedings of the second ACM SIGPLAN international conference on Functional programming
Parallel beta reduction is not elementary recursive
POPL '98 Proceedings of the 25th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Information and Computation
The optimal implementation of functional programming languages
The optimal implementation of functional programming languages
Intuitionistic Light Affine Logic
ACM Transactions on Computational Logic (TOCL)
On the Dynamics of Sharing Graphs
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Typing lambda terms in elementary logic with linear constraints
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
Principal typing in elementary affine logic
TLCA'03 Proceedings of the 6th international conference on Typed lambda calculi and applications
Linear Logic, Comonads And Optimal Reductions
Fundamenta Informaticae
Derivational complexity is an invariant cost model
FOPARA'09 Proceedings of the First international conference on Foundational and practical aspects of resource analysis
Light logics and optimal reduction: Completeness and complexity
Information and Computation
Sharing in the weak lambda-calculus
Processes, Terms and Cycles
Elementary linear logic revisited for polynomial time and an exponential time hierarchy
APLAS'11 Proceedings of the 9th Asian conference on Programming Languages and Systems
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In 1998, Asperti and Mairson proved that the cost of reducing a λ-term using an optimal λ-reducer (a la Lévy) cannot be bound by any elementary function in the number of shared-beta steps. We prove in this paper that an analogous result holds for Lamping's abstract algorithm. That is, there is no elementary function in the number of shared beta steps bounding the number of duplication steps of the optimal reducer. This theorem vindicates the oracle of Lamping's algorithm as the culprit for the negative result of Asperti and Mairson. The result is obtained using as a technical tool Elementary Affine Logic.