The Syntax Zooming Aleksandar Perović, Nedeljko Stefanović, Aleksandar Jovanović GIS (Group for Intelligent Systems), Faculty of Mathematics, Belgrade E-mail: peramail314@yahoo.com Abstract: We shall present various procedures for the syntax analysis in certain formal systems defined by the user, which are integrated in the proof checker. The flexibility and the applicability of the method lies in the fact that the program treats formal theories as parameters (both axioms and derivation rules are parts of the input), so developed algorithms work for any formalism which can be expressed within the language of the predicate logic. 1 Introduction By syntax zooming we assume variety of algorithms for processing of syntax forms, i.e. algorithms that can allow us to resolve problems such as syntax correctness, pattern matching, proof correctness, and in general, analysis and better understanding of information bearing structures. We shall present a solution for the mentioned problems in the form of the proof checker. The flexibility and the applicability of the method lie in the fact that the program treats formal theories as parameters (both axioms and derivation rules are parts of the input), so developed algorithms work for any formalism which can be expressed within the language of the first order predicate calculus (recall that the language of the predicate calculus contains just variables, constant, functional and relational symbols, logical connectives, quantifiers, brackets, the comma symbol and the symbol for equality). Let us proceed with some basic definitions. A predicate theory T is, in our case, a finite nonempty set of predicate axioms, axiom schemata and derivation rules. The notion of a term we define recursively as follows: • Constant symbols and variables are terms. • If F is an arbitrary functional symbol of arity n and if n t t ,..., 1 are arbitrary terms, then the string ) ,..., ( 1 n t t F is also a term. • Terms can be obtained only by finite use of the above clauses.