A Survey of Linear Logic Programming

Abstract. 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. §1. Introduction. It is now common place to recognize the important role of logic in the foundations of computer science in general and programming languages more specifically. For this reason, when a major new advance is made in our understanding of logic, we can expect to see that advance ripple into other areas of computer science. Such rippling has been observed during the year