The rôle of linear logic in coalgebraical approach of computing

Linear logic provides a logical perspective on computational issues such as control of resources and order of evaluation. The most important feature of linear logic is that formulae are considered as actions. While classical logic treats the sentences that are always true or false, in linear logic it depends on an internal state of a dynamic system. Curry-Howard correspondence is a correspondence between logic and computing in informatics. In this contribution we present two ways of computations which correctness we prove by Curry-Howard correspondence. We show a standard way and a new way of computing based on hylomorphism by using coalgebras which is an alternative method. Our method of recursive and corecursive computations we apply in simple authentication system.