Applications of Linear Logic to Computation: An Overview

This paper is an overview of existing applications of Linear Logic (LL) to issues of computation. After a substantial introduction to LL, it discusses the implications of LL to functional programming, logic programming, concurrent and object-oriented programming and some other applications of LL, like semantics of negation in LP, non-monotonic issues in AI planning, etc. Although the overview covers pretty much the state-of-the-art in this area, by necessity many of the works are only mentioned and referenced, but not discussed in any considerable detail. The paper does not presuppose any previous exposition to LL, and is addressed more to computer scientists (probably with a theoretical inclination) than to logicians. The paper contains over 140 references, of which some 80 are about applications of LL. 1 Linear Logic Linear Logic (LL) was introduced in 1987 by Girard 62]. From the very beginning it was recognized as relevant to issues of computation (especially concurrency and state change), an evidence of which is that the paper appeared not in a journal of logic, but in Theoretical Computer Science. Also, it was recognized as a novel and important contribution: it was allotted a whole issue of the journal (about 100 pages) and was published with the following caveat \We warn the reader that because of the length and novelty of this paper, it was not passed through the normal review process". The paper is organized as follows: this section provides an introduction to LL (no previous exposure to LL is needed). For other short introductions to LL, including intuitive motivations and full presentation of the sequent system, see e.g. 109, 148, 154]. A very complete yet brief reference of LL theory is 136]. Unfortunately it is in Japanese, but one can still read the formulas. No references are included. Subsequent sections discuss in turn applications of LL in various areas of computing: functional programming , logic programming, concurrent and object-oriented programming, deductive planning. A comprehensive (although somewhat out of date) coverage of both proof theory and semantics of LL is provided in the book by Anne Troelstra 151] (well-written and easy to read; above all the only book on LL to date), and a good book on proof-theoretical issues and their computational interpretation is Proofs and Types 73]. A WWW page about LL is maintained by Lincoln,