Type inference for light affine logic via constraints on words

Light Affine Logic (LAL) is a system due to Girard and Asperti capturing the complexity class P in a proof-theoretical approach based on Linear Logic. LAL provides a typing for lambda-calculus which guarantees that a well-typed program is executable in polynomial time on any input. We prove that the LAL type inference problem for lambda-calculus is decidable (for propositional LAL). To establish this result we reformulate the type-assignment system into an equivalent one which makes use of subtyping and is more flexible. We then use a reduction to a satisfiability problem for a system of inequations on words over a binary alphabet, for which we provide a decision procedure. © 2004 Elsevier B.V. All rights reserved.