Quantitative Models and Implicit Complexity
Abstract
We give new proofs of soundness (all representable functions on base types lies in certain complexity classes) for Elementary Affine Logic, LFPL (a language for polytime computation close to realistic functional programming introduced by one of us), Light Affine Logic and Soft Affine Logic. The proofs are based on a common semantical framework which is merely instantiated in four different ways. The framework consists of an innovative modification of realizability which allows us to use resourcebounded computations as realisers as opposed to including all Turing computable functions as is usually the case in realizability constructions. For example, all realisers in the model for LFPL are polynomially bounded computations whence soundness holds by construction of the model. The work then lies in being able to interpret all the required constructs in the model. While being the first entirely semantical proof of polytime soundness for light logi cs, our proof also provides a notable simplification of the original already semantical proof of polytime soundness for LFPL. A new result made possible by the semantic framework is the addition of polymorphism and a modality to LFPL thus allowing for an internal definition of inductive datatypes.
 Publication:

arXiv eprints
 Pub Date:
 June 2005
 arXiv:
 arXiv:cs/0506079
 Bibcode:
 2005cs........6079D
 Keywords:

 Computer Science  Logic in Computer Science;
 Computer Science  Computational Complexity;
 F.4.1
 EPrint:
 29 pages