Is the optimal implementation inefficient? Elementarily not.

Stefano Guerrini, Marco Solieri

Research output: Contribution to conferencePaperpeer-review

1 Citation (Scopus)

Abstract

Sharing graphs are a local and asynchronous implementation of lambda-calculus beta-reduction (or linear logic proof-net cut-elimination) that avoids useless duplications. Empirical benchmarks suggest that they are one of the most efficient machineries, when one wants to fully exploit the higher-order features of lambda-calculus. However, we still lack confirming grounds with theoretical solidity to dispel uncertainties about the adoption of sharing graphs.

Aiming at analysing in detail the worst-case overhead cost of sharing operators, we restrict to the case of elementary and light linear logic, two subsystems with bounded computational complexity of multiplicative exponential linear logic. In these two cases, the bookkeeping component is unnecessary, and sharing graphs are simplified to the so-called "abstract algorithm". By a modular cost comparison over a syntactical simulation, we prove that the overhead of shared reductions is quadratically bounded to cost of the naive implementation, i.e. proof-net reduction. This result generalises and strengthens a previous complexity result, and implies that the price of sharing is negligible, if compared to the obtainable benefits on reductions requiring a large amount of duplication.
Original languageEnglish
Pages17:1-17:15
Number of pages15
Publication statusPublished - 3 Sep 2017
Event2nd International Conference on Formal Structures for Computation and Deduction - Oxford, UK United Kingdom
Duration: 3 Sep 20179 Sep 2017
Conference number: 2
https://www.cs.ox.ac.uk/conferences/fscd2017/

Conference

Conference2nd International Conference on Formal Structures for Computation and Deduction
Abbreviated titleFSCD 2017
CountryUK United Kingdom
CityOxford
Period3/09/179/09/17
Internet address

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