Patrick Baillot and Marco Pedicini. Elementary complexity and geometry of interaction. Fund. Inform., 45(1-2):1-31, 2001. Typed lambda calculi and applications (L'Aquila, 1999).

We introduce a geometry of interaction model given by an algebra of clauses equipped with resolution (following citeGirard95d) into which proofs of Elementary Linear Logic can be interpreted. In order to extend geometry of interaction computation (the so called execution formula) to a wider class of programs in the algebra than just those coming from proofs, we define a variant of execution (called weak execution). Its application to any program of clauses is shown to terminate with a bound on the number of steps which is elementary in the size of the program. We establish that weak execution coincides with standard execution on programs coming from proofs.

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