In a previous work Baillot and Terui introduced Dual light affine logic (DLAL) as a variant of Light linear logic suitable for guaranteeing complexity properties on lambda calculus terms: all typable terms can be evaluated in polynomial time by beta reduction and all Ptime functions can be represented. In the present work we address the problem of typing lambda-terms in second-order DLAL. For that we give a procedure which, starting with a term typed in system F, determines whether it is typable in DLAL and outputs a concrete typing if there exists any. We show that our procedure can be run in time polynomial in the size of the original Church typed system F term.

• 03B70 - Logic in computer science
• 60G07 - General theory of stochastic processes
• 68Q60 - Specification and verification (program logics, model checking, etc.)