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Lambda Calculus Characterizations of Poly-Time
- Publisher
- Association for Computing Machinery
- Copyright
- Copyright © 2002 by ACM Inc.
- ISSN
- 1529-3785
- DOI
- 10.1145/504077.504081
- Publisher site
- See Article on Publisher Site
Abstract
This article is a structured introduction to Intuitionistic Light Affine Logic ( ILAL ). ILAL has a polynomially costing normalization, and it is expressive enough to encode, and simulate, all PolyTime Turing machines. The bound on the normalization cost is proved by introducing the proof-nets for ILAL . The bound follows from a suitable normalization strategy that exploits structural properties of the proof-nets. This allows us to have a good understanding of the meaning of the § modality, which is a peculiarity of light logics. The expressive power of ILAL is demonstrated in full detail. Such a proof gives a hint of the nontrivial task of programming with resource limitations, using ILAL derivations as programs.
Journal
ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery
Published: Jan 1, 2002