A left part theorem for grammatical trees

We consider a global property of the derivation (or parse) trees of context-free grammars. This property of the derivation trees of context-free grammars can be considered as a restricted version of the left part property for the trees of strict deterministic grammars [3,4,5,6]. In this paper it is shown that this left part property is satisfied by the set of grammatical trees of a left pati grummur, a type of context-free grammar which we introduce here. The class of left part grammars is B_ small extension of the class of simgb chuin grammars [ 101. If a context-free grammar is unambiguous then each terminal string generated by this grammar has a unique derivation tree. Informally, our left part property requires that every prefix of such a terminal string ha0 a unique “partial” tree. This notion of “partial” tree will be specified. The aim of this paper is to present this left part property and the class of grammars for which the set of grammatical trees satisfies this property. Except for some informal remarks, in this short paper we will not be concerned with a parsing method for left part grammars, However, the reader who is familiar with simple chain grammars will have no difficulty in finding a very simple parsing method for the left part grammars. To present the left part property and to describe grammatical trees we use the notations and definitions from [SJ. For convenience we repeat, as far as necessary, some of these notions here. For more details the reader is referred to [5,7]. Among others, an intuitive assumption on “translations” of prefixes of sentences which is discussed in [9] motivated us to introduce this left Fart property.