The (In)Efficiency of interaction

Evaluating higher-order functional programs through abstract machines inspired by the geometry of interaction is known to induce space efficiencies, price being time performances often poorer than those obtainable with traditional, environment-based, machines. Although families lambda-terms for which former exponentially less efficient latter do exist, it currently unknown how general this phenomenon is, and far inefficiencies can go, in worst case. We answer these questions formulating four different well-known inside a common definitional framework, way able give sharp results about relative efficiencies. also prove that non-idempotent intersection type theories are precisely reflect interactive machine, showing its time-inefficiency ultimately descends from presence types.