Realizability proof for normalization of full differential linear logic

Authors:
Stéphane Gimenez
Affiliations:
Laboratoire PPS, Université Paris-Diderot - Paris 7
Venue:
TLCA'11 Proceedings of the 10th international conference on Typed lambda calculi and applications
Year:
2011

Citing 9
Cited 0

Linear logic

Theoretical Computer Science
Interaction nets

POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
From proof-nets to interaction nets

Proceedings of the workshop on Advances in linear logic
The differential Lambda-calculus

Theoretical Computer Science
Differential interaction nets

Theoretical Computer Science - Logic, language, information and computation
Uniformity and the Taylor expansion of ordinary lambda-terms

Theoretical Computer Science
The Cut-Elimination Theorem for Differential Nets with Promotion

TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
Strong normalization property for second order linear logic

Theoretical Computer Science
Intuitionistic differential nets and lambda-calculus

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

Realizability methods allowed to prove normalization results on many typed calculi. Girard adapted these methods to systems of nets and managed to prove normalization of second order Linear Logic [4]. Our contribution is to provide an extension of this proof that embrace Full Differential Linear Logic (a logic that can describe both single-use resources and inexhaustible resources). Anchored within the realizability framework our proof is modular enough so that further extensions (to second order, to additive constructs or to any other independent feature that can be dealt with using realizability) come for free.