Light types for polynomial time computation in lambda-calculus
<|reference_start|>Light types for polynomial time computation in lambda-calculus: We propose a new type system for lambda-calculus ensuring that well-typed programs can be executed in polynomial time: Dual light affine logic (DLAL).   DLAL has a simple type language with a linear and an intuitionistic type arrow, and one modality. It corresponds to a fragment of Light affine logic (LAL). We show that contrarily to LAL, DLAL ensures good properties on lambda-terms: subject reduction is satisfied and a well-typed term admits a polynomial bound on the reduction by any strategy. We establish that as LAL, DLAL allows to represent all polytime functions. Finally we give a type inference procedure for propositional DLAL.<|reference_end|>
@article{baillot2004light,
    title={Light types for polynomial time computation in lambda-calculus},
    author={Patrick Baillot, Kazushige Terui},
    journal={arXiv preprint arXiv:cs/0402059},
    year={2004},
    archivePrefix={arXiv},
    eprint={cs/0402059},
    primaryClass={cs.LO}
}