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this paper we provide a Gentzen-type formulation of Schroeder-Heister'ssystem of [1]. This system is important from both philosophical and practicalpoints of view: Its philisophical importance is due to the characterizationwhich it provides for the intuitionistic connectives, while the practical one isdue to the fact that its notion of higher-order rules and its method of treatingthe elimination rules were incorporated into the Edinburgh LF (A generallogical framework for implementing...

Gentzenizing Schroeder-Heister's natural extension of natural deduction.