Light types for polynomial time computation in lambda calculus

Patrick Baillot, Kazushige Terui
2009 Information and Computation  
We present a polymorphic 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 (and not only on proof-nets): subject reduction is satisfied and a well-typed term admits a polynomial
more » ... on the length of any of its beta reduction sequences. We also give a translation of LAL into DLAL and deduce from it that all polynomial time functions can be represented in DLAL.
doi:10.1016/j.ic.2008.08.005 fatcat:vtr4yo6kz5dsfp6qzoqe3szxte