Parsing categorial grammars in natural deduction

We present an algorithm for parsing in the product-free fragment of Categorial Grammars (CG) using a Natural Deduction (ND) Calculus à la Prawitz. Since this is not the usual formalism of choice, we must first introduce the rules of the calculus and some of the geometric properties of deductions in which lies the parsing process. The resulting algorithm generates only natural deductions in normal form so that it is devoid of spurious ambiguity. The parsing is quite efficient with some top-down (goal directed) steps followed by bottom-up ones