Abstract Interpretation of Linear Logic Programming

Linear Logic is gaining momentum in computer science because it ooers a uniied framework and a common vocabulary for studying and analyzing diierent aspects of programming and computation. We focus here on models where computation is identiied with proof search in the sequent system of Linear Logic. A proof normalization procedure, called \focusing", has been proposed to make the problem of proof search tractable. Correspondingly, there is a normalization procedure mapping formulae of Linear Logic into a syntactic fragment of that logic, called LinLog, and in which the focusing normalization for proofs can be most conveniently expressed. In this paper, we propose to push this compilation/normalization process further, by applying abstract interpretation and partial evaluation techniques to (focused) proofs in LinLog. These techniques provide information concerning the evolution of the computational resources (formulae) during the execution (proof construction). The practical outcome that we expect from this theoretical eeort is the deenition of a general tool for statically analyzing and reasoning about the runtime behavior of programs in frameworks where computations can be accounted for in terms of proof search in Linear Logic.