Intersection Types for Light Affine Lambda Calculus

Light Affine Lambda Calculus is a term calculus for polynomial time computation ([K. Terui. Light affine lambda calculus and polytime strong normalization. In Proceedings of LICS'01, pages 209-220, 2001]). Some of the terms of Light Affine Lambda Calculus must however be regarded as errors. Intuitionistic Light Affine Logic (ILAL) types only terms without errors, but not all of them. We introduce two type assignment systems with intersection types : in the first one, typable pseudo-terms are exactly the terms without errors ; in the second one, they are exactly those that reduce to normal terms without errors.