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Asperti+Roversi:2002-ToCL (Article)
Author(s) Andrea Asperti and Luca Roversi
Title« Intuitionistic Light Affine Logic »
JournalACM Transactions on Computational Logic
Volume3
Number1
Page(s)1 -- 39
Year2002
URLhttp://www.di.unito.it/~rover/RESEARCH/PUBLICATIONS/2002-ToCL/AspertiRoversi2002ToCL.ps.gz
Abstract
This paper 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 to have a good catch on the meaning of the paragraph modality, which is a peculiarity of light logics. The expressive power of ILAL is demonstrated in full details. Such a proof gives a flavor of the non trivial task of programming with resource limitations, using ILAL derivations as programs.

BibTeX code

@article{Asperti+Roversi:2002-ToCL,
  number = {1},
  volume = {3},
  month = {January},
  author = {Asperti, Andrea and Roversi, Luca},
  url = {http://www.di.unito.it/~rover/RESEARCH/PUBLICATIONS/2002-ToCL/AspertiRoversi2002ToCL.ps.gz},
  abstract = {This paper 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
              to have a good catch on the meaning of the paragraph modality,
              which is a peculiarity of light logics. The expressive power of
              ILAL is demonstrated in full details. Such a proof gives a flavor
              of the non trivial task of programming with resource limitations,
              using ILAL derivations as programs.},
  title = {Intuitionistic Light Affine Logic},
  year = {2002},
  pages = {1 -- 39},
  journal = {ACM Transactions on Computational Logic},
}


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