From Proof-Nets to Linear Logic Type Systems for Polynomial Time Computing

In this presentation we give an overview of Dual Light Affine Logic (DLAL), a polymorphic type system for lambda calculus ensuring that typable lambda terms are executable in polynomial time. We stress the importance of proof-nets from Light linear logic for the design of this type system and for a result establishing that typable lambda-terms can be evaluated efficiently with optimal reduction. We also discuss the issue of DLAL type inference, which can be performed in polynomial time for system F terms. These results have been obtained in collaborations with Terui [1], Atassi and Terui [2], and Coppola and Dal Lago [3].

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