An Overview of Linear Logic Programming

Logic programming can be given a foundation in sequent calculus, viewing computation as the process of building a cut-free sequent proof from the bottom-up. Earliest accounts of logic programming were based in classical logic and then later in intuitionistic logic. The use of linear logic to design new logic programming languages was inevitable given that it allows for more dynamics in the way sequents change during the search for a proof and since it can account for logic programming in these other logics. We overview how linear logic has been used to design new logic programming languages and describe some applications and implementation issues for such languages. §