
Be the first to like this
Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.
Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.
Published on
The linearalgebraic lambdacalculus (arXiv:quantph/0612199) extends the lambdacalculus with the possibility of making arbitrary linear combinations of lambdacalculus terms a.t+b.u. In this paper we provide a System F like type system for the linearalgebraic lambdacalculus, which keeps track of \'the amount of a type\' that is present in a term. We show that this scalar type system enjoys both the subjectreduction property and the strongnormalisation property, which constitute our main technical results. The latter yields a significant simplification of the linearalgebraic lambdacalculus itself, by removing the need for some restrictions in its reduction rules  and thus leaving it more intuitive. More importantly we show that our type system can readily be modified into a probabilistic type system, which guarantees that terms define correct probabilistic functions. Thus we are able to specialize the linearalgebraic lambdacalculus into a higherorder, probabilistic lambdacalculus. Finally we discuss the more longterm aims of this reseach in terms of establishing connections with linear logic, and building up towards a quantum physical logic through the CurryHoward isomorphism. Thus we begin to investigate the logic induced by the scalar type system, and prove a nocloning theorem expressed solely in terms of the possible proof methods in this logic.
Be the first to like this
Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.
Be the first to comment