Affiliation:
1. Università di Bologna, Bologna, Italy
Abstract
We show that context semantics can be fruitfully applied to the quantitative analysis of proof normalization in linear logic. In particular, context semantics lets us define the
weight
of a proof-net as a measure of its inherent complexity: it is both an upper bound to normalization time (modulo a polynomial overhead, independently on the reduction strategy) and a lower bound to the amount of resources needed to compute the normal form. Weights are then exploited in proving strong soundness theorems for various subsystems of linear logic, namely elementary linear logic, soft linear logic, and light linear logic.
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science
Reference21 articles.
1. Asperti A. and Guerrini S. 1998. The Optimal Implementation of Functional Programming Languages. Cambridge University Press. Asperti A. and Guerrini S. 1998. The Optimal Implementation of Functional Programming Languages. Cambridge University Press.
2. Intuitionistic Light Affine Logic
3. Light Logics and Optimal Reduction: Completeness and Complexity
4. Elementary complexity and geometry of interaction;Baillot P.;Fundamenta Informaticae,2001
5. The Geometry of Linear Higher-Order Recursion
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