From light logics to type assignments: a case study

@article{Gaboardi2009FromLL,
  title={From light logics to type assignments: a case study},
  author={Marco Gaboardi and Simona Ronchi Della Rocca},
  journal={Log. J. IGPL},
  year={2009},
  volume={17},
  pages={499-530}
}
Using Soft Linear Logic (SLL) as case study, we analyze a method for transforming a light logic into a type assignment system for the λ-calculus, inheriting the complexity properties of the logics. Namely the typing assures the strong normalization in a number of steps polynomial in the size of the term, and moreover all polynomial functions can be computed by λ-terms that can be typed in the system. The proposed method is general enough to be used also for other light logics. 

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