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Section: Scientific Foundations

Keywords : proof search, logic programming, linear logic.

Proof search

Participants : David Baelde, Dale Miller, Alexis Saurin, Lutz Stra├čburger.

The term ``proof search'' refers to a modern updating of the logic programming paradigm. In particular, that update implies several things that have not been generally embraced by the logic programming community.

The proof theory of proof search has been used to design various logic programming languages. In the late 1980's, sequent calculus for intuitionistic logic was used to motivate the various extensions now incorporated into $ \lambda$ Prolog. Later, linear logic programming languages have been introduced: in particular, LO of Andreoli and Pareschi [17] , Lolli of Hodas and Miller [30] , and Forum of Miller [39] .

A key application area for proof search and the above logic programs is the specification of operational semantics. Particularly successful specifications along these lines are those of evaluation and typing for the untyped $ \lambda$ -calculus [36] and reachability within progress calculi, such as the $ \pi$ -calculus [11] , [45] , [48] , [15] .


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