@inproceedings{Roversi+Vercelli:2010-DICE10,
  volume = {23},
  author = {Roversi, Luca and Vercelli, Luca},
  series = {{Electronic Proceedings in Theoretical Computer Science}},
  booktitle = {{Proceedings of the Workshop on Developments in Implicit
               Computational complexity (DICE 2010)}},
  url = {http://www.di.unito.it/~rover/RESEARCH/PUBLICATIONS/2010-DICE/RoversiVercelli2010DICE.pdf},
  title = {{Safe Recursion on Notation into a Light Logic by Levels}},
  abstract = {We embed Safe Recursion on Notation (SRN) into Light Affine Logic
              by Levels (LALL), derived from the logic ML4. LALL is an
              intuitionistic deductive system, with a polynomial time cut
              elimination strategy. The embedding allows to represent every term
              t of SRN as a family of nets in LALL. Every net in the family
              simulates t on arguments whose bit length is bounded by the index
              of the net. The embedding is based on two crucial features. One is
              the recursive type in LALL that encodes Scott binary numerals,
              i.e. Scott words, as nets. Scott words represent the arguments of
              t in place of the more standard Church binary numerals. Also, the
              embedding exploits the "fuzzy" borders of paragraph boxes that
              LALL inherits from ML4 to "freely" duplicate the arguments,
              especially the safe ones, of t. Finally, the type of the net
              depends on the number of composition and recursion schemes used to
              define t, namely the structural complexity of t. Moreover, the
              size of the net is a polynomial in the index of the net in the
              family, whose degree depends on the structural complexity of t.
              So, this work makes closer both the predicative recursive
              theoretic principles SRN relies on, and the proof theoretic one,
              called stratification, at the base of Light Linear Logic. },
  pages = {63 -- 77},
  year = {2010},
}

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